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This paper aims at developing an efficient finite element based computational procedure for the topology design of heat conducting fields. To evaluate the temperature change in a specific position, due to varying the conducting material distribution in other regions, a discrete temperature sensitivity is derived for an evolutionary topology optimization method. In the topology optimization of the conducting fields, the thermal conductivity of an individual finite element is considered as the design variable. By removing or degenerating the conductive material of the elements with the most negative sensitivity, the temperature objective at the control point can be most efficiently reduced. Illustrative examples are presented to demonstrate this proposed approach. [Copyright &y& Elsevier]

• The reusability of metamaterials is studied through cyclic cold programming. • The effect of materials and unit-cell configurations on reusability is investigated. • PETG honeycombs show better reusability than PLA honeycombs due to better ductility. • Re -entrant honeycombs show better reusability than hexagonal and hybrid honeycombs. 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. [Display omitted] [ABSTRACT FROM AUTHOR]

• Topology and filament path of CFRP structures were optimized simultaneously. • Filament paths can be obtained directly, which suit the non-open-source 3D printer. • Behaviors of optimal structures were better than those of the empirical designs. • Simulations matched well with the test results after reconstructing FE models. 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. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: Most structures in the real life are subject to multiple load cases. This paper aims at extending the evolutionary structural optimization (ESO) algorithm to optimal contact shape design for elastic bodies under the multiple load cases. To evaluate the reference stresses of each contact node in a finite element framework, an extreme stress criterion (the worst case design) and a weighted average criterion (Pareto design) are presented. In the extreme stress method, the highest nodal contact stress under all load cases is adopted as the reference level. In the weighted average method, the weighted sum of nodal contact stresses over all the load cases is regarded as the reference. It is found that these two criteria can produce different results. In this paper, the examples are presented to demonstrate some new features of contact shape optimization in the presence of the multiple load cases. [Copyright &y& Elsevier]

• A novel explicit phase field model was developed for crushing behaviour. • Non-proportional loading should be considered for crushing behaviour. • Material samples and tubal structures were 3D-printed and tested. • Experimental global response and crack paths of tubes were properly reproduced. • The mechanism of crushing behaviour was analyzed. 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. [Display omitted] [ABSTRACT FROM AUTHOR]

• A phase field model is proposed for laser powder bed fusion printed metals. • Transversely isotropic plasticity and fracture models are incorporated. • The phase field model considers stress-state and orientation-dependent responses. • Phase field model is experimentally validated through various specimens. • Crack propagation patterns are perfectly predicted by the phase field model. Phase field models have been extensively studied in the analysis of ductile fracture. However, few have been explored to simulate additively manufactured materials and validated by experimental data to date. This study aims to develop a phase field framework for modelling complex mechanical behaviours of laser powder bed fusion printed metallic materials. To consider the laser powder bed fusion induced microstructural orientation, transversely isotropic Hill48 and modified Mohr-Coulomb constitutive models are incorporated here to depict the plastic and fracture behaviours, respectively. Five types of material specimens representing a wide spectrum of stress states are designed to identify the material parameters of plasticity and fracture. Three groups of crack propagation specimens are also tested to demonstrate the capacity of the developed model. The numerical results divulge that, by considering the stress state-dependent crack initiation, the proposed phase field model is able to better reproduce force-displacement responses of all specimens. Remarkably, the complex cracking sequences, including crack initiation, propagation and final rupture, can be properly captured by the proposed phase field model. More importantly, it is necessary to apply a transversely isotropic fracture model to characterise the orientation-dependent fracture behaviour; otherwise, the crack path would be predicted incorrectly, resulting in unacceptable global force-displacement responses. This study offers an effective phase field modelling framework for the sophisticated constitutive characterisation of laser powder bed fusion fabricated metallic materials. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The success of GA-based topology optimisation methods for continuum structures has been limited. Though a number of methods exist, the results are far from comparable to solutions from more established methods in terms of quality and fidelity. This had led many structural optimisation researchers to dismiss the GA as a viable method for topology optimisation of continuum structures. The authors believe however that the deficiencies of previous applications lie not in the GA but in the manner in which it was applied. Based on insights gained from these applications, a new GA-based method for the continuum topology optimisation problem is herein presented which yields high-fidelity solutions comparable to those produced through more well-known and established methods. The method is centred on a number of novel concepts, most notably the simultaneous use of multiple genetic algorithms, and the use of a high-level string coding based on structural response information. In this work, the basis and methodology of the multi-GA approach are explained, and key algorithms detailed. The method was also applied to a number of structural problems to show its efficacy, and the results presented and discussed. [Copyright &y& Elsevier]

The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the “nibbling” technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges. [Copyright &y& Elsevier]

• A nonlinear topology optimization enhances fracture resistance of structures. • Clear topological boundaries are guaranteed by a level-set approach. • A p-norm phase-field constraint controls risks of fracture failure. • Path dependent shape derivatives improve the accuracy of design sensitivity. • 2D benchmark examples and a 3D real dental implant design are illustrated. 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. [ABSTRACT FROM AUTHOR]

• Different failure modes in terms of the Hashin, Hoffman and Tsai-Wu failure criteria are imposed as constraint functions • Different failure criteria result in different topological configurations of CFRP, including both the ply orientations and material thickness layout • Of these three failure criteria considered, the Tsai-Wu criterion is found most conservative whilst the Hashin counterpart is least • From the perspective of maximum failure index, the best strength performance appears in the structure based upon the Tsai-Wu criterion 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. [Display omitted] [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]