Dr Chi Wu

Box-sectioned beam structures offer significant potential in various engineering fields, and can be tailored to specific design criteria by adjusting the size parameters. In engineering practice, box-sectioned beam structures are often available in standard or discrete thicknesses, considering manufacturing constraints and cost efficiency. This article proposes an improved method to optimize the discrete size of box-sectioned beam structures using size-weighted coefficients. The method integrates the rational Timoshenko beam element with an improved bi-value coding parameterization scheme to optimize the weighted coefficients associated with each discrete size. During optimization, design domains are narrowed down before filtering to obtain the discrete thickness of box-sectioned beam structures. Numerical examples demonstrate the effectiveness of the method in achieving high solving efficiency and overcoming convergence difficulties. In the optimization of the bus frame, the mass is reduced by 25.44%, and torsional stiffness, which serves as a constraint, is only 0.08% higher than the set lower limit.

Phase field models have gained increasing popularity in analysing fracture behaviour of materials. However, few studies have been explored to simulate dynamic ductile fracture to date. This study aims to develop a phase field framework that considers strain rate, stress state, and orientation dependent ductile fracture under dynamic loading. Firstly, the governing equations of displacement and phase fields are formulated within an explicit finite element framework. Secondly, constitutive relations are established using a hypoelastic-plasticity framework, encompassing the influence of material orientation and strain rate on both plasticity and fracture initiation. Stress state dependent fracture initiation is also considered. Thirdly, the finite element implementation and corotational formulation of constitutive equations are derived. Finally, to validate the proposed model, additively manufactured samples, including material-level and crack propagation specimens, are tested under dynamic loading conditions. Overall, the proposed phase field model can properly reproduce the experimental force-displacement curves and crack paths. Uniaxial tension tests reveal that a higher strain rate can lead to a higher hardening curve and reduced ductility. Other material specimens further demonstrate the model's capability to predict stress state and orientation dependent dynamic fracture. To simulate dynamic crack paths accurately, it is necessary to consider anisotropic fracture initiation. Lastly, the phase field model was applied for the first time to predict the dynamic response of triply periodic minimal surface (TPMS) structures. Dynamic crack patterns were effectively captured, and the fracture mechanisms were thoroughly analysed. This study provides an explicit phase field framework for dynamic ductile fracture, with applications to additively manufactured materials and structures.

Finite periodic layout for multicomponent systems signifies a compelling design strategy for constructing complex larger structures through assembling repeating representative unit-cells with various orientations. In addition to better transportability, handleability and replaceability, design with structural segmentation has been considered particularly valuable for additive manufacturing of large workpiece due to limited printing dimension of machine. However, existing design optimization of periodic structures has been largely restricted to simple translational placements of unit-cells, sophisticated tessellation with differently oriented topological unit-cells remains underexplored. This paper presents an efficient and adaptable topology optimization framework for concurrently optimizing periodic structures comprised of repeating topological unit-cells and their tailored orientations. By introducing a weighting factor associated with different orientation states of unit-cells, a dominant orientation for each unit-cell can gradually emerge in the course of optimization process. The proposed procedure combines the solid isotropic material with penalization (SIMP) model for topology optimization of unit-cell and the discrete material optimization (DMO) technique for the optimization of its orientation. The optimization objective is to minimize structural compliance subject to volume fraction constraint. Through sensitivity analysis, optimality criteria can be applied to simultaneously optimize a representative unit-cell (RUC) topology and the orientation weighting factors in the periodic macrostructure. Several 2D and 3D examples are investigated to demonstrate significant enhancement in compliance reduction of up to 34% compared to conventional periodic design without orientation optimization. This represents a notable improvement in finite periodic structural optimization, particularly leveraging the topology optimization to tailor unit-cell orientation rather than relying on brute-force search approaches. Our methodology paves a new avenue for designing more efficient and readily manufacturable lightweight structures with enhanced performance metrics.

Titanium reconstruction plates are often used to bridge mandibulectomy defects in load bearing scenarios when bone grafts are not well integrated to the host bone. The residual stress within a standard reconstruction plate is generated when being bent and installed to adapt to a patient-specific anatomical contour and it may have a detrimental effect on the structural stability and reliability of the reconstruction system. This study aimed to evaluate the impact of residual stress on the mechanical strength of the reconstructed mandibular system by utilizing both conventional finite element method (FEM) and eXtended Finite Element Method (XFEM). The mechanical stresses introduced by plate pre-bending and screw tightening were first modeled computationally and the residual stress data induced by the surgical procedure was incorporated to the deformed reconstruction plate for the subsequent biomechanical evaluation. Static and cyclic loading conditions were then imposed on the mandibular plate models to further investigate two common failure types, namely overloading fracture and fatigue fracture. It is revealed that the residual stress could considerably increase the susceptibility of plate fracture. The simulation results demonstrate that the pre-stresses induced by screw tightening are more substantial than that from plate bending during the surgical procedure. The finding is of important clinical implications for surgeons who are commonly involved in selecting and preparing different forms of fixation plates for mandibular reconstruction. This study helps elucidate the key factors contributing on the failure of reconstruction plates and guide the development of more robust and durable mandibular reconstruction systems.

While ceramic additive manufacturing (AM) technologies have shown great promise to create functional scaffolds with tailored biomechanical properties, the true potential of these advanced techniques has not been fully exploited yet due to lack of practical design optimisation approaches. To address this challenge, a machine learning (ML)-based design approach is proposed herein where ceramic 3D printing techniques are combined to fabricate functionally graded tissue scaffolds composed of Triply Periodic Minimal Surfaces (TPMS), aiming to fulfil the anticipated biomechanical requirements for the target bone regeneration outcomes. The proposed ML based design strategy couples a Bayesian optimisation (BO) algorithm to enable time-dependent mechano-biological optimisation of the 3D printed ceramic scaffolds at a reasonably low computational cost. For a representative example relating to bone scaffolding in a segmental defect of sheep tibia, the simulated results demonstrate that the optimised functionally graded scaffolds significantly enhance bone ingrowth outcomes. Furthermore, a Lithography-based Ceramic Manufacturing (LCM) technique is employed to fabricate the optimised scaffolds based on the proposed ML-based design framework, followed by micro-CT analyses of the additively manufactured ceramic scaffolds to assess their geometric qualities. This study is expected to gain new insights into mechanical sciences on design for varying material conditions and provide an effective design tool for ceramic additive manufacturing.

Phase field models have gained growing popularity in fracture analysis. However, phase field modelling remains lacking for complex real-life applications such as structural crushing analyses to date. The novelty of this study is to propose an explicit phase field modelling framework considering complex loading history to predict the crushing behaviour of additively manufactured metallic structures. First, the explicit phase field model is formulated by considering stress state dependent fracture initiations with non-proportional loading. Then, five types of material specimens with a wide range of stress states are experimentally tested to calibrate material parameters for additively manufactured 316L steel and Ti-6Al-4V titanium. Last, the square tubes are 3D-printed and tested under three-point bending and axial compression to demonstrate the capacity of the proposed model. The modelling results unveil that the crushing behaviour of both materials could be properly reproduced in terms of force-displacement curves and crack paths. Finally, the fracture mechanism of crushing deformation is analysed. For the three-point bending of Ti-6Al-4V tubes, cracks are mainly induced by the medium stress triaxiality tension and shear loading. For the axial compression of 316L tubes, the stress states of critical elements are relatively diverse yet slightly concentrated at the shear, compression-shear, and high stress triaxiality tension regions. Remarkably, non-proportional loading is significant in crushing deformation as a material point may experience a significant change in stress state with loading. By considering a non-proportional loading dependent threshold, the proposed phase field model can predict the crushing behaviour of structures even when the fracture initiations do not locate on the fracture locus. This study provides an effective explicit phase field framework featured with an insightful fracture mechanism for quasi-static crushing of additively manufactured metallic materials.

Combining design optimization and additive manufacturing (AM) enables the full exploitation of the potential for heightening the performance of carbon fiber reinforced plastic (CFRP) structures. This study simultaneously conducts topology optimization and fiber path design by employing the radial basis function (RBF) based level set function (LSF). Fiber paths are determined instinctively for the inherent advantages of the LSF, and fiber orientations are parameterized accordingly. Manufacturing drawbacks such as gaps and overlaps can be avoided by introducing a fast-marching method. To verify the effectiveness of the optimization method, three groups of optimized and empirical designs are fabricated by the AM technique, respectively, and the experimental tests are further carried out. Finite element (FE) models are also reconstructed based on the printing schemes, and then the FE simulation is validated by the experimental tests. With the proposed optimization method, stiffnesses for all three groups of the optimal samples are significantly improved compared with the empirical counterparts. The FE modeling technique is capable of reproducing the experimental results. This study paves a new way to develop an integrated framework of optimization, additive manufacturing, experimentation, and validation to deliver high-performance CFRP structures.

The present study aims at developing reusable metamaterials fabricated by 4D printing technology. Honeycomb metamaterials were manufactured via fused deposition modeling (FDM) with shape memory polymers (SMPs). The reusability of these metamaterials was determined through cyclic cold programming experiments, where each cycle involved a loading-unloading-heating (shape recovery)-cooling process. The novelty of this paper lies not only in experimentally demonstrating the recoverability of metamaterials by reversing plastic deformation based on the shape memory effect of SMPs, but also in studying their reusability of SMP metamaterials under cyclic programming and the effect of printing materials and unit-cell types on the mechanical degradation. The results reveal that, under one single compression cycle, the polylactic acid (PLA) hexagonal honeycomb dissipated 22% more energy than the polyethylene terephthalate glycol (PETG) counterpart because the higher elastic modulus of PLA leads to a larger critical buckling load for segments in honeycomb structures. Furthermore, the PETG re-entrant honeycomb dissipated 25% more energy than the hexagonal counterpart due to its negative Poisson's ratio and the overall uniform deformation pattern. More importantly, it is found that under multiple compression cycles, the PETG hexagonal honeycomb maintained an energy dissipation capacity of 78.3% at Cycle 6, nearly 3.5 times that of the PLA counterpart as a result of the better ductility of PETG. Moreover, the PETG re-entrant honeycomb could be reused for 17 cycles, while the hexagonal counterpart could only be reused for 12 cycles. This is because the re-entrant unit cells are failure-resistant and of less concentration in plastic deformation. The results demonstrate that the constituent materials with better ductility and the unit-cells with more failure resistance can reduce mechanical degradation, thereby exhibiting better reusability of metamaterials.

Tissue scaffolds have emerged as a promising solution for treatment of critical size bone defects, offering significant advantages over conventional strategies. One of the key functionalities of bone scaffolds is their ability to promote long-term bone ingrowth effectively. To enhance this functionality, we develop a novel dynamic optimisation framework to customise bone scaffolds for achieving maximum bone ingrowth outcomes over a certain period in this study. To improve the design efficiency, we extensively leverage machine learning (ML) techniques within our proposed dynamic optimisation framework. Specifically, two neural networks are integrated into a dynamic bone growth model, and another neural network is coupled with a genetic algorithm for dynamic optimisation process. To demonstrate the effectiveness and efficiency of the approach, we employ a sheep mandible reconstruction for treating a critical size bone defect as an illustraive example. To validate the finite element (FE) model established, we first conduct a mechanical test on the sheep mandible assembled with a tailored 3D printed scaffold made of Polyetherketone (PEK) material. Then, we compare three different optimisation schemes, namely uniform design, lateral gradient design, and vertical gradient design, with an empirical design under the same biomechanical conditions. A 18.5 % enhancement is found in the long-term bone ingrowth when the optimised scaffold is adopted in comparison with the empirical design, which is attributed to the fine-tuning of strut sizes within lattice scaffold structures for facilitating bone regeneration in the gradient regions. This study proposes a novel design framework by combining ML and time-dependent topology optimisation, which provides a new methodology for developing innovative tissue scaffolds with better clinical outcomes.

Fiber-reinforced plastic (FRP) composites exhibit significant potential in lightweight and multifunctionality due to its superior designability, which have been extensively employed in leading-edge industries, including automotive, aerospace, maritime, sports and wearable devices. Dynamic problems with certain frequency responses arise in these practical situations, in which even a small excitation force could result in severe deformation in composite structures, thereby largely affecting the performance. To address this critical design issue, we propose a novel topology optimization approach for controlling dynamic responses of FRP structures. A discrete material and thickness optimization (DMTO) method is developed for parameterization of topological and fiber orientation variables, in which the Heaviside penalization of polynomial interpolation scheme (HP-PIS) and rational approximate material penalization (RAMP) method are adopted for variable discretization, respectively. A new frequency response analysis (for short nFRA) method is implemented and a decoupled sensitivity analysis is incorporated in the optimization process. The design aims to minimize the dynamic displacement responses of FRP composites under given volume fraction. To verify the computational efficiency and accuracy of the optimization process, a comparative study is first conducted with the conventional mode displacement method (MDM), mode acceleration method (MAM), and original adjoint variable method (AVM) through a benchmark example. The generality and robustness of the proposed optimization procedure are further validated through the several numerical problems for a given excitation frequency and frequency band. The results demonstrate considerable potential of the proposed method for solving the frequency based dynamic topology optimization of FRP composite structures.

Finding ideal materials remains a crucial challenge in the aerospace, automotive, construction, and biomedical industries. Moreover, a growing concern about environmental burden and fuel consumption has triggered strong demand for lightweight materials with high-performance multifunctional characteristics. Composite lattices exploiting topological and constituent materials are of particular interest thanks to their excellent mechanical properties and lightweight that can ideally meet critical design requirements. However, composite lattices are integrated with high complexity in their geometries, which creates challenges in their manufacturing in practice. Additive manufacturing (AM) technologies have been extensively developing to provide more freedom in manufacturing to support the growing interest in fabricating these innovative materials with intricate geometry. This paper reviews current studies on additively manufactured composite lattices. First, AM and post-treatment techniques and their capability for fabricating complex structural materials are discussed. Then, several types of structural configurations and characteristics of AM composite lattices are reviewed. Further, the mechanical properties of these composite lattices are analyzed and the role of reinforcing phases is discussed in detail. Finally, the review highlights some potential future research directions and opportunities of 3D printed composite lattices for energy absorption, recoverability, specific strength and stiffness, and weight lightening.

In the past three decades, biomedical engineering has emerged as a significant and rapidly growing field across various disciplines. From an engineering perspective, biomaterials, biomechanics, and biofabrication play pivotal roles in interacting with targeted living biological systems for diverse therapeutic purposes. In this context, in silico modelling stands out as an effective and efficient alternative for investigating complex interactive responses in vivo. This paper offers a comprehensive review of the swiftly expanding field of machine learning (ML) techniques, empowering biomedical engineering to develop cutting-edge treatments for addressing healthcare challenges. The review categorically outlines different types of ML algorithms. It proceeds by first¿assessing their applications in biomaterials, covering such aspects as data mining/processing, digital twins, and data-driven design. Subsequently, ML approaches are scrutinised for the studies on mono-/multi-scale biomechanics and mechanobiology. Finally, the review extends to ML techniques in bioprinting and biomanufacturing, encompassing design optimisation and in situ monitoring. Furthermore, the paper presents typical ML-based applications in implantable devices, including tissue scaffolds, orthopaedic implants, and arterial stents. Finally, the challenges and perspectives are illuminated, providing insights for academia, industry, and biomedical professionals to further develop and apply ML strategies in future studies.

The role of the biomechanical stimulation generated from soft tissue has not been well quantified or separated from the self-regulated hard tissue remodeling governed by Wolff's Law. Prosthodontic overdentures, commonly used to restore masticatory functions, can cause localized ischemia and inflammation as they often compress patients' oral mucosa and impede local circulation. This biomechanical stimulus in mucosa is found to accelerate the self-regulated residual ridge resorption (RRR), posing ongoing clinical challenges. Based on the dedicated long-term clinical datasets, this work develops an in-silico framework with a combination of techniques, including advanced image post-processing, patient-specific finite element models and unsupervised machine learning Self-Organizing map algorithm, to identify the soft tissue induced RRR and quantitatively elucidate the governing relationship between the RRR and hydrostatic pressure in mucosa. The proposed governing equation has not only enabled a predictive simulation for RRR as showcased in this study, providing a biomechanical basis for optimizing prosthodontic treatments, but also extended the understanding of the mechanobiological responses in the soft-hard tissue interfaces and the role in bone remodeling.

Triply periodic minimal surface (TPMS) structures have been extensively studied for their exceptional mechanical characteristics. However, numerical analysis of their fracture behaviour remains insufficient due to the complexity of the fracture mechanism. This study aims to utilise a new phase field model to predict the mechanical responses and analyse the fracture mechanism of TPMS gyroid (G) and primitive (P) structures. Firstly, the G and P structures were additively manufactured using Ti-6Al-4 V titanium and tested under both axial and oblique compression. Secondly, an explicit phase field model was developed by incorporating the Bao-Wierzbicki fracture model to capture damage initiations. It was found that the developed explicit phase field model enables accurate reproduction of experimental force-displacement responses, deformation modes, crack initiations and propagations for G and P structures under both loading conditions. It was found that medium stress triaxiality tension was the dominant stress state to trigger material damage, regardless of structure and loading condition. Moreover, compared with axial compression, oblique loading introduced a more non-proportional loading history, leading damage initiation points far away from the fracture locus. Further, in comparison with the G structure, the P structure involved more medium and high stress triaxiality tension induced fracture initiations, resulting in more damaged material points. This study offers valuable insight into the fracture mechanism of TPMS structures, which is beneficial to improving the design of these structures.

Lightweight materials and structures have been extensively studied for a wide range of applications in design and manufacturing of more environment-friendly and more sustainable products, such as less materials and lower energy consumption, while maintaining proper mechanical and energy absorption characteristics. Additive manufacturing (AM) or 3D printing techniques offer more freedom to realize some new designs of novel lightweight materials and structures in an efficient way. However, the rational design for desired mechanical properties of these materials and structures remains a demanding topic. This paper provides a comprehensive review on the recent advances in additively manufactured materials and structures as well as their mechanical properties with an emphasis on energy absorption applications. First, the additive manufacturing techniques used for fabricating various materials and structures are briefly reviewed. Then, a variety of lightweight AM materials and structures are discussed, together with their mechanical properties and energy-absorption characteristics. Next, the AM-induced defects, their impacts on mechanical properties and energy absorption, as well as the methods for minimizing the effects are discussed. After that, numerical modeling approaches for AM materials and structures are outlined. Furthermore, design optimization techniques are reviewed, including parametric optimization, topology optimization, and nondeterministic optimization with fabrication-induced uncertainties. Notably, data-driven and machine learning-based techniques exhibit compelling potential in design for additive manufacturing, process-property relations, and in-situ monitoring. Finally, significant challenges and future directions in this area are highlighted. This review is anticipated to provide a deep understanding of the state-of-the-art additively manufactured materials and structures, aiming to improve the future design for desired mechanical properties and energy absorption.

Crack-direction-based decomposition of elastic strain energy could effectively control the propagation of tensile and shear cracks in a phase field modelling context. The objective of the proposed double-phase field model is to extend the crack-direction-based decomposition strategy from 2D brittle fracture to complex mixed-mode crack modelling in a 3D setting, with plastic deformation incorporated. Both effective (undamaged) stress and plastic strain are split in the crack-orientation-based coordinate system. The decomposed tensile/shear stress contribute to tensile/shear damage evolution, respectively. The plastic contribution is coupled by relating the decomposed tensile/shear plastic strain to the corresponding tensile/shear crack energy release rates. Crack surface normal direction, represented by two orientation variables in 3D spatial domains, is determined by the F-criterion. The proposed model is implemented via ABAQUS subroutines with a staggered scheme for two phase field variables and crack direction. The simulation of a single-edge notch specimen under shear loading demonstrates that the ratio between shear and tensile crack energy release rates plays a significant role in the crack mode and mechanical response. Numerical results of a group of uniaxial tension, simple shear and tension shear specimens show good agreement with the experimental data in terms of the force¿displacement curve and crack path, exhibiting the validity of the proposed model for capturing different crack modes. This model has also been proven effective for complex 3D problems via the third Sandia Challenge example.

The bone-periodontal ligament-tooth (BPT) complex is a unique mechanosensing soft-/hard-tissue interface, which governs the most rapid bony homeostasis in the body responding to external loadings. While the correlation between such loading and alveolar bone remodelling has been widely recognised, it has remained challenging to investigate the transmitted mechanobiological stimuli across such embedded soft-/hard-tissue interfaces of the BPT complex. Here, we propose a framework combining three distinct bioengineering techniques (i, ii, and iii below) to elucidate the innate functional non-uniformity of the PDL in tuning mechanical stimuli to the surrounding alveolar bone. The biphasic PDL mechanical properties measured via nanoindentation, namely the elastic moduli of fibres and ground substance at the sub-tissue level (i), were used as the input parameters in an image-based constitutive modelling framework for finite element simulation (ii). In tandem with U-net deep learning, the Gaussian mixture method enabled the comparison of 5195 possible pseudo-microstructures versus the innate non-uniformity of the PDL (iii). We found that the balance between hydrostatic pressure in PDL and the strain energy in the alveolar bone was maintained within a specific physiological range. The innate PDL microstructure ensures the transduction of favourable mechanobiological stimuli, thereby governing alveolar bone homeostasis. Our outcomes expand current knowledge of the PDL's mechanobiological roles and the proposed framework can be adopted to a broad range of similar soft-/hard- tissue interfaces, which may impact future tissue engineering, regenerative medicine, and evaluating therapeutic strategies. Statement of significance: A combination of cutting-edge technologies, including dynamic nanomechanical testing, high-resolution image-based modelling and machine learning facilitated computing, was used to elucidate the association between the microstructural non-uniformity and biomechanical competence of periodontal ligaments (PDLs). The innate PDL fibre network regulates mechanobiological stimuli, which govern alveolar bone remodelling, in different tissues across the bone-PDL-tooth (BPT) interfaces. These mechanobiological stimuli within the BPT are tuned within a physiological range by the non-uniform microstructure of PDLs, ensuring functional tissue homeostasis. The proposed framework in this study is also applicable for investigating the structure-function relationship in broader types of fibrous soft-/hard- tissue interfaces.

Despite significant advances in the design optimization of bone scaffolds for enhancing their biomechanical properties, the functionality of these synthetic constructs remains suboptimal. One of the main challenges in the structural optimization of bone scaffolds is associated with the large uncertainties caused by the manufacturing process, such as variations in scaffolds' geometric features and constitutive material properties after fabrication. Unfortunately, such non-deterministic issues have not been considered in the existing optimization frameworks, thereby limiting their reliability. To address this challenge, a novel multiobjective robust optimization approach is proposed here such that the effects of uncertainties on the optimized design can be minimized. This study first conducted computational analyses of a parameterized ceramic scaffold model to determine its effective modulus, structural strength, and permeability. Then, surrogate models were constructed to formulate explicit mathematical relationships between the geometrical parameters (design variables) and mechanical and fluidic properties. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to generate the robust Pareto solutions for an optimal set of trade-offs between the competing objective functions while ensuring the effects of the noise parameters to be minimal. Note that the nondeterministic optimization of tissue scaffold presented here is the first of its kind in open literature, which is expected to shed some light on this significant topic of scaffold design and additive manufacturing in a more realistic way.

The mechanical stimuli generated by body exercise can be transmitted from cortical bone into the deep bone marrow (mechanopropagation). Excitingly, a mechanosensitive perivascular stem cell niche is recently identified within the bone marrow for osteogenesis and lymphopoiesis. Although it is long known that they are maintained by exercise-induced mechanical stimulation, the mechanopropagation from compact bone to deep bone marrow vasculature remains elusive of this fundamental mechanobiology field. No experimental system is available yet to directly understand such exercise-induced mechanopropagation at the bone-vessel interface. To this end, taking advantage of the revolutionary in vivo 3D deep bone imaging, an integrated computational biomechanics framework to quantitatively evaluate the mechanopropagation capabilities for bone marrow arterioles, arteries, and sinusoids is devised. As a highlight, the 3D geometries of blood vessels are smoothly reconstructed in the presence of vessel wall thickness and intravascular pulse pressure. By implementing the 5-parameter Mooney¿Rivlin model that simulates the hyperelastic vessel properties, finite element analysis to thoroughly investigate the mechanical effects of exercise-induced intravascular vibratory stretching on bone marrow vasculature is performed. In addition, the blood pressure and cortical bone bending effects on vascular mechanoproperties are examined. For the first time, movement-induced mechanopropagation from the hard cortical bone to the soft vasculature in the bone marrow is numerically simulated. It is concluded that arterioles and arteries are much more efficient in propagating mechanical force than sinusoids due to their stiffness. In the future, this in-silico approach can be combined with other clinical imaging modalities for subject/patient-specific vascular reconstruction and biomechanical analysis, providing large-scale phenotypic data for personalized mechanobiology discovery.

Although additive manufacturing has offered substantially new opportunities and flexibility for fabricating 3D complex lattice structures, effective design of such sophisticated structures with desired multifunctional characteristics remains a demanding task. To tackle this challenge, we develop an inventive multiscale topology optimisation approach for additively manufactured lattices by leveraging a derivative-aware machine learning algorithm. Our objective is to optimise non-uniform unit cells for achieving an as uniform strain pattern as possible. The proposed approach exhibits great potential for biomedical applications, such as implantable devices mitigating strain and stress shielding. To validate the effectiveness of our framework, we present two illustrative examples through the dedicated digital image correlation (DIC) tests on the optimised samples fabricated using a powder bed fusion (PBF) technique. Furthermore, we demonstrate a practical application of our approach through developing bone tissue scaffolds composed of optimised non-uniform iso-truss lattices for two typical musculoskeletal reconstruction cases. These optimised lattice-based scaffolds present a more uniform strain field in complex anatomical and physiological condition, thereby creating a favourable biomechanical environment for maximising bone formation effectively. The proposed approach is anticipated to make a significant step forward in design for additively manufactured multiscale lattice structures with desirable mechanical characteristics for a broad range of applications.

In this paper, a complete optimization design verification process is proposed and a novel structure of connecting brackets is presented, solving the fatigue failure of chassis connecting brackets operating on harsh roads. First, an endurance road test and fatigue life analysis were applied to the truck equipped with the original brackets, verifying the fatigue damage of the structure. Based on the solid isotropic material with penalization method, a novel lightweight connecting bracket layout was obtained by using the method of moving asymptotes (MMA) for topology optimization under multiple working conditions with multiple performance constraints. Moreover, the derivatives of objective and constraint functions concerning design variables were applied for the MMA. Considering manufacturability and functionality, the improved model based on the topology optimization results was further optimized by size optimization. Finally, fatigue life analysis and an endurance road test were conducted using the optimal design. Compared with the original structure, the novel brackets showed better stiffness, strength and fatigue performance while reducing the total mass by 15.2%. The whole optimization and validation process can provide practical ideas and value for developing multi-performance suspensions in the pre-product development stage.

To investigate bone remodelling responses to mandibulectomy, a joint external and internal remodelling algorithm is developed here by incorporating patient-specific longitudinal data. The primary aim of this study is to simulate bone remodelling activity in the conjunction region with a fibula free flap (FFF) reconstruction by correlating with a 28-month clinical follow-up. The secondary goal of this study is to compare the long-term outcomes of different designs of fixation plate with specific screw positioning. The results indicated that the overall bone density decreased over time, except for the Docking Site (namely DS1, a region of interest in mandibular symphysis with the conjunction of the bone union), in which the decrease of bone density ceased later and was followed by bone apposition. A negligible influence on bone remodeling outcome was found for different screw positioning. This study is believed to be the first of its kind for computationally simulating the bone turn-over process after FFF maxillofacial reconstruction by correlating with patient-specific follow-up.

Phase field approaches have been developed to analyze the failure behavior of ductile materials. In the previous phase field models, a constant critical energy or strain threshold is commonly introduced to the formulation of the driving force, aiming to avoid damage initiation at a low level of elastic and plastic deformations. However, it may not suffice to describe complex ductile fracture behavior of materials subject to various stress states. In this study, a new phase field approach is proposed to consider the effects of stress triaxiality and Lode angle, by incorporating phenomenological ductile fracture criteria. The proposed models are formulated using variational principles and implemented numerically in the finite element framework. Analytical homogeneous solutions for uniaxial tension, simple shear, and equibiaxial tension loads are derived to demonstrate the effectiveness of the proposed models. Three groups of numerical examples, covering a wide range of stress states, are utilized to further examine the proposed models. The results show that the models can reproduce the experimental response of the specimen in terms of force versus displacement curve, crack initiation, and crack propagation under various loading conditions. The proposed models are able to capture the stress-state dependence of fracture behavior of ductile materials.

This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.

Background and objective: The fibula free flap (FFF) has been extensively used to repair large segmental bone defects in the maxillofacial region. The reconstruction plate plays a key role in maintaining stability and load-sharing while the fibula unites with adjacent bone in the course of healing and remodeling. However, not all fibula flaps would fully unite, and fatigue of prosthetic devices has been recognized as one major concern for long-term load-bearing applications. This study aims to develop a numerical approach for predicting the fatigue life of the reconstruction plate by taking into account the effect of ongoing bone remodeling. Methods: The patient-specific mandible reconstruction with a prosthetic system is studied in this work. The 3D finite element model with heterogeneous material properties obtained from clinical computerized tomography (CT) data is developed for bone, and eXtended Finite Element Method (XFEM) is adopted for the fatigue analysis of the plate. During the remodeling process, the changing apparent density and Young's modulus of bone are simulated in a step-wise fashion on the basis of Wolff's law, which is correlated with the specific clinical follow-up. The maximum biting forces were considered as the driving force on the bone remodeling, which are measured clinically at different time points (4, 16 and 28 months) after reconstruction surgery. Results: Under various occlusal loadings, the interaction between fatigue crack growth and bone remodeling is investigated to gain new insights for the future design of prosthetic devices. The simulation results reveal that appropriate remodeling of grafted bone could extend the fatigue life of fixation plates in a positive way. On the other hand, the rising occlusal load associated with healing and remodeling could lead to fatigue fracture of fixation plate and potentially cause severe bone resorption. Conclusion: This study proposes an effective approach for more realistically predicting fatigue life of prosthetic devices subject to a tissue remodeling condition in-silico. It is anticipated to provide a guideline for deriving an optimal design of patient-specific prosthetic devices to better ensure longevity.

This study develops a topology optimization approach for design of carbon fiber reinforced plastic (CFRP) laminated components with different failure criteria to reduce the risk of structural failure. The discrete material and thickness optimization (DMTO) method is adopted to parameterize the design variables of thickness and orientation of CFRP composites, which is driven by the Method of Moving Asymptote (MMA) algorithm. A large number of local constraints associated with the failure criteria are aggregated in terms of a p-norm function. Analytical sensitivities are derived with respect to the design variables. In this study, a battery hanging structure in electrical vehicle (EV) is exemplified; and a DMTO based design is prototyped and validated through the in-house experimental tests first. To prevent different failure modes, the Hashin, Hoffman and Tsai-Wu failure criteria are then imposed as the design constraints together with manufacturing requirements in the optimization. A comparative study is performed for the design with and without such failure criteria. The results demonstrate that the maximum failure index of the optimized structure with the Tsai-Wu failure criterion decreases the most by 40%; and follows by the Hashin and Hoffman criteria by 24% and 33%, respectively. Finally, the CFRP structure is also optimized to design a so-called double-double laminates for demonstrating the generality of the proposed method. The study is anticipated to gain in-depth understanding of how the failure criteria would affect the design of fiber reinforced composite structures to ensure structural integrity.

Scaffold-based bone tissue engineering has been extensively developed as a potential means to treatment of large bone defects. To enhance the biomechanical performance of porous tissue scaffolds, computational design techniques have gained growing popularity attributable to their compelling efficiency and strong predictive features compared with time-consuming trial-and-error experiments. Nevertheless, the mechanical stimulus necessary for bone regeneration, which characterizes dynamic nature due to continuous variation in the bone-scaffold construct system as a result of bone-ingrowth and scaffold biodegradation, is often neglected. Thus, this study proposes a time-dependent mechanobiology-based topology optimization framework for design of tissue scaffolds, thereby developing an ongoing favorable microenvironment and ensuring a long-term outcome for bone regeneration. For the first time, a level-set based topology optimization algorithm and a time-dependent shape derivative are developed to optimize the scaffold architecture. In this study, a large bone defect in a simulated 2D femur model and a partial defect in a 3D femur model are considered to demonstrate the effectiveness of the proposed design method. The results are compared with those obtained from stiffness-based topology optimization, time-independent design and typical scaffold constructs, showing significant advantages in continuing bone ingrowth outcomes.

This study proposes a machine learning (ML) based approach for optimizing fiber orientations of variable stiffness carbon fiber reinforced plastic (CFRP) structures, where neural networks are developed to estimate the objective function and analytical sensitivities with respect to design variables as a substitute for finite element analysis (FEA). To reduce the number of training samples and improve the regression accuracy, an active learning strategy is implemented by successively supplying effective samples along with the suboptimal process. After proper training of neural networks, a quasi-global search strategy can be applied by implementing a large number of initial designs as starting points in the optimization. In this article, a mathematical example is first presented to show the superiority of the active learning strategy. Then a benchmark design example of a CFRP plate is scrutinized to compare the proposed ML-based with the conventional FEA-based discrete material optimization (DMO) method. Finally, topology optimization of fiber orientations is performed for design of a CFRP engine hood, in which the structural performance generated from the proposed ML-based approach achieves 12.62% improvement compared with that obtained from the conventional single-initial design method. This article is anticipated to demonstrate a new alternative for design of fiber-reinforced composite structures.

In this paper, a recently-developed phase-field damage model is incorporated into the topology optimization framework to take into account crack initiation and propagation in a path-dependent fashion. The proposed topological design can enhance fracture resistance of structures made of brittle materials such as advanced ceramics. For the first time, a path-dependent shape derivative is developed in a step-wise manner during the nonlinear fracture analysis, which enables to drive the topology optimization properly. To measure the fracture resistance of structure, a p-norm function is formulated to aggregate the phase-field variables into a single constraint. To demonstrate the effectiveness of the presented topology optimization procedure, three 2D benchmark examples with single-phasic material and one 3D biomedical example with biphasic materials are studied here. The comparison with the topological designs based upon conventional linear elastic finite element analysis without the damage model indicates that the proposed method can significantly improve the fracture resistance of structures with more efficient use of materials. The proposed method is anticipated to provide an effective approach for sophisticated path-dependent topological design of structures reducing severe stress concentration and high risks of fracture failure.

While prosthetic devices have been extensively used to treat a wide range of human diseases and injuries, failure of these devices due to fatigue under cyclic loading has been recognized as a primary concern on therapeutic longevity. Experimental testing has long been a dominant approach to characterizing the fatigue behavior of prosthetic devices. However, experimental methods could be of multiple shortcomings such as their restrictive nature in-vivo in medical studies and limitations of extrapolating the testing results. This study develops a numerical approach for modeling fatigue failure in some commonly-used osteofixation devices that are implanted to support various major bone defects/trauma and fractures. The eXtended Finite Element Method (XFEM) is employed herein to model fatigue crack formation and propagation as per level set functions to suppress the need for re-meshing. For validation purpose, a benchmark problem involving a modified compact tension structure is first carried out, in which the modeling results are compared with the relevant experimental data to demonstrate the effectiveness of the proposed XFEM approach. Further, two representative orthopedic examples are studied for characterizing the fatigue behavior of a femoral osteofixation plate and a mandibular reconstruction mini-plate, respectively. The results reveal that healing/remodeling of grafted bone as well as tissue ingrowth to the scaffold have significant bearing on fatigue life of fixation plates. This study showcases a valuable approach for predicting fatigue failure of prosthetic devices in-silico, thereby providing an effective tool for design optimization of patient-specific prosthetic devices to ensure their longevity.

Computational modeling methods combined with non-invasive imaging technologies have exhibited great potential and unique opportunities to model new bone formation in scaffold tissue engineering, offering an effective alternate and viable complement to laborious and time-consuming in vivo studies. However, existing numerical approaches are still highly demanding computationally in such multiscale problems. To tackle this challenge, we propose a machine learning (ML)-based approach to predict bone ingrowth outcomes in bulk tissue scaffolds. The proposed in silico procedure is developed by correlating with a dedicated longitudinal (12-month) animal study on scaffold treatment of a major segmental defect in sheep tibia. Comparison of the ML-based time-dependent prediction of bone ingrowth with the conventional multilevel finite element (FE2) model demonstrates satisfactory accuracy and efficiency. The ML-based modeling approach provides an effective means for predicting in vivo bone tissue regeneration in a subject-specific scaffolding system.

Biomaterials have been extensively used in prosthetic applications for their proven biocompatibility and osseointegration characteristics. Nevertheless, one of the critical issues of some synthetic biomaterials is brittleness prone to experience fracture failure due to low tensile strength and low fracture toughness. This study aims to employ a recently-developed phase-field model to simulate the crack propagation in brittle biomaterials. Unlike discrete fracture modeling methods, the phase-field approach allows simulating crack path in a continuous manner, thereby avoiding remeshing that may not be trivial for complicated fracture surfaces and facilitate iterative procedure commonly required for structural optimization. The phase-field model is formulated to treat the fracture path as a localized region of diffusive damage that can be described in terms of a phase-field function, in which the discreteness in cracked materials is assumed to be smeared. In this study, three representative case studies from the biomedical context, namely a zirconia-based dental bridge (or namely fixed partial denture (FPD)), a ceramic tissue scaffold and an analog saw-bone femur, are employed as illustrative examples. The phase-field modeling results are compared with the in-house experimental tests, demonstrating the effectiveness of the phase-field technique for predicting brittle fracture failure in several typical biomedical case scenarios. The phase-field model provides a useful tool for the computational fracture analysis and design optimization of other brittle biomaterials.

Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level-set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase-field fracture model is formulated herein to simulate crack initiation and propagation, in which a staggered algorithm is developed to solve such time-dependent crack propagation problems. In line with diffusive damage of the phase-field approach for fracture; topological derivatives, which provide gradient information for the topology optimization in a LS framework, are derived for fracture mechanics problems. A reaction-diffusion equation is adopted to update the LS function within a finite element framework. This avoids the reinitialization by overcoming the limitation to time step with the Courant-Friedrichs-Lewy condition. In this article, three numerical examples, namely, a L-shaped section, a rectangular slab with predefined cracks, and an all-ceramic onlay dental bridge (namely, fixed partial denture), are presented to demonstrate the effectiveness of the proposed LS based topology optimization for enhancing fracture resistance of multimaterial composite structures in a phase-field fracture context.

Bone plates have been widely used for the treatment of bone defects and trauma. These fixation plates can stabilize or replace bone tissue to restore appropriate load-bearing functionality. Nevertheless, the use of bone plates may lead to the stress shielding, thereby weakening prosthetic bone substitutes (e.g. bone graft or scaffolds) due to significant change in the biomechanical environment after implantation. To address this issue, we propose a time-dependent topology optimization procedure for the design of bone plates by taking into account bone remodeling. A solid isotropic material penalization (SIMP) model is used to interpolate design variables. The objective is to maximize total bone density within a reconstruction area at the final stage of bone remodeling, subject to a volume constraint of the bone plate and maximum allowable compliance of the prosthetic system. The sensitivity of bone density at the final stage is derived with respect to the topological variables of the plate in a step-wise manner. To facilitate sensitivity analysis, a bone remodeling rule is formulated in two different ways to accommodate a C1continuity. A jaw reconstruction problem is exemplified in this study to demonstrate the effectiveness of the proposed approach. Through this specific case, the non-differentiability issue due to the lazy zone of a remodeling rule is smoothed; and the proposed approach is also compared with that of a time-independent design. The effects of volume fraction and compliance constraints are also investigated to gain further insights into the design of prosthetic substitutes. Together with additive manufacturing technology, the proposed time-dependent topology optimization procedure is expected to form a useful tool for the design of implantable devices ensuring favorable long-term treatment outcomes.

Phase-field methods for fracture have been integrated with plasticity for better describing constitutive behaviours. In most of the previous phase-field models, however, the length-scale parameter must be interpreted as a material property in order to match the material strength in experiments. This study presents a phase-field model for fracture coupled with plasticity for quasi-brittle materials with emphasis on insensitivity of the length-scale parameter. The proposed model is formulated using variational principles and implemented numerically in the finite element framework. The effective yield stress is calibrated to vary with the length-scale parameter such that the tensile strength remains the same. Moreover, semi-analytical solutions are derived to demonstrate that the length-scale parameter has a negligible effect on the stress¿displacement curve. Five representative examples are considered here to validate the phase-field model for fracture in quasi-brittle materials. The simulated force¿displacement curves and crack paths agree well with the corresponding experimental results. Importantly, it is found that the global structural response is insensitive to the length scale though it may influence the size of the failure zone. In most cases, a large length-scale parameter can be used for saving the computational cost by allowing the use of a coarse mesh. On the other hand, a sufficiently small length-scale parameter can be selected to prevent overly diffusive damage, making it possible for the proposed phase-field model to simulate the fracture behaviour with G-convergence.

The phase field modelling has been extended from brittle fracture to ductile fracture by incorporating plasticity. However, the effects of plastic yield functions and hardening on the fracture behaviour have not been examined systematically to date. The phase field fracture coupled with multi-surface plasticity is formulated in the variational framework for the unified yield criterion, which is able to facilitate the study on different yield surfaces. First, the homogeneous solutions of fracture in elasto-plastic solids are derived analytically for 1D and 2D cases. The results show that a greater hardening modulus would lead to an ascending branch of the stress versus strain curve; and the yield function may significantly affect the stress state and phase field damage. Second, the finite element (FE) technique is implemented for modelling the phase field fracture in elasto-plastic solids, in which the stress update and consistent tangent modular matrix are derived for the unified yield criterion. Finally, three numerical examples are presented to explore the effects of the yield function and material hardening. It is found that the yield function and material hardening could significantly affect the crack propagation and the final fracture pattern. In particular, the Tresca yield function tends to create a straight crack path orthogonal to the first principal stress, while the other yield functions show no sizeable difference in their crack paths.

The structures in thermal environment often suffer from severe thermal expansion, potentially leading to buckling failure. This study aims to address this issue by proposing multi-material topology optimization for thermomechanical buckling problems. The density-based model with the rational approximation of material properties (RAMP) is adopted here for parameterization of multiple materials. The sensitivities of thermomechanical compliance and buckling are derived through the adjoint technique. The globally convergent version of the method of moving asymptotes (GCMMA) is employed to solve the non-monotonic topology optimization problem. In this study, two numerical examples are presented to illustrate the effectiveness of the proposed method, in which the total volume of multi-materials is minimized subject to thermoelastic compliance and buckling constraints. The examples exhibit significant difference in the final topologies for mechanical buckling and thermomechanical buckling optimization. The study demonstrates the importance of thermomechanical buckling criteria for the design of structures operating in a temperature-varying environment.

Phase field modelling for fracture has been extended from elastic solids to elasto-plastic solids. In this study, we present the implementation procedures of a staggered scheme for phase field fracture of elasto-plastic solids in commercial finite element software Abaqus using subroutines UEL and UMAT. The UMAT is written for the constitutive behaviour of elasto-plastic solids, while the UEL is written for the phase field fracture. The phase field and displacement field are solved separately using the Newton-Raphson iteration method. In each iteration, one field is computed by freezing the other field at the last loading increment. A number of benchmark examples are tested from one single element up to 3D problems. The correctness of the staggered scheme is verified analytically in terms of the stress-strain curve and the evolution of the phase field in the one single element example. In the 2D and 3D problems, the fracture behaviour of elasto-plastic solids can be reproduced in terms of reaction force curve and crack propagation, which exhibit good agreement with the experimental observations and numerical results in literature. Not only can the proposed implementation help attract more academic researchers, but also engineering practitioners to take the advantages of phase field modelling for fracture in elasto-plastic solids. The Abaqus subroutine codes can be downloaded online from Mendeley data repository linked to this work (The link is provided in Supplementary material).

This study developed a discrete topology optimization procedure for the simultaneous design of ply orientation and thickness for carbon fiber reinforced plastic (CFRP)-laminated structures. A gradient-based discrete material and thickness optimization (DMTO) algorithm was developed by using casting-based explicit parameterization to suppress the intermediate void across the thickness of the laminate. A benchmark problem was first studied to compare the DMTO approach with the sequential three-phase design method using the free size, ply thickness, and stacking sequence of the laminates. Following this, the DMTO approach was applied to a practical design problem featuring a CFRP-laminated engine hood by minimizing overall compliance subject to volume-related and functional constraints under multiple load cases. To verify the optimized design, a prototype of the CFRP engine hood was created for experimental tests. The results showed that the simultaneous discrete topology optimization of ply orientation and thickness was an effective approach for the design of CFRP-laminated structures.

This study proposes a non-deterministic robust topology optimization of ply orientation for multiple fiber-reinforced plastic (FRP) materials, such as carbon fiber¿reinforced plastic (CFRP) and glass fiber¿reinforced plastic (GFRP) composites, under loading uncertainties with both random magnitude and random direction. The robust topology optimization is considered here to minimize the fluctuation of structural performance induced by load uncertainty, in which a joint cost function is formulated to address both the mean and standard deviation of compliance. The sensitivities of the cost function are derived with respect to the design variables in a non-deterministic context. The discrete material optimization (DMO) technique is extended here to accommodate robust topology optimization for FRP composites. To improve the computational efficiency, the DMO approach is revised to reduce the number of design variables by decoupling the selection of FRP materials and fiber orientations. In this study, four material design examples are presented to demonstrate the effectiveness of the proposed methods. The robust topology optimization results exhibit that the composite structures with the proper ply orientations are of more stable performance when the load fluctuates.

The discrete material and thickness optimization (DMTO) algorithm was adopted to achieve the optimization. Ply orientations and thicknesses of composite laminates and the metal reinforcement thickness were considered as the design variables simultaneously while the casting constraints such as symmetrical shape, contiguity constraint and preventing intermediate void were introduced. The commercial finite element software (Abaqus) was employed to obtain the strain vectors so as to solve the sensitivity issues and the optimization for carbon fiber reinforced plastic (CFRP) battery hanging point was finished in Matlab with gradient-based algorithm. The results demonstrated that the total mass of the composite material battery hanging point after optimal design is 0.447 kg, which reduces by 41.2%, compared with the steel structure without sacrificing the mechanical properties.

This study addresses the design of ply orientation for a CFRP vehicle door by implementing a Discrete Material Optimization (DMO) method in a general-purpose commercial finite element code (ABAQUS) and mathematical analysis tool (MATLAB). To accommodate multiple loading conditions, the weighted mean compliance of the CFRP vehicle door was taken as the objective function, subject to the constraints on the local displacements, primary natural frequency and manufacturability. The sensitivities of objective and constraints were calculated by using the strain vectors, which is a more general method than using element stiffness matrices and allows extracting local displacements from the commercial finite element code. A gradient-based algorithm was employed in the DMO approach to tackle the large-scale problem. In the discrete topology optimization, four material penalization schemes were attempted in this study. The proposed DMO approach was compared with the empirical design and the existing method in commercial software. The results demonstrated that the proposed method is able to produce a more competent solution than the empirical design and other optimization methods efficiently.