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To describe the mathematics, mechanics and computer code that are involved in deriving the mechanical properties of a 3D composite material with a complicated internal architecture. To inform the reader how an application programming interface (API) can be used with a commercial FEA code to undertake the task. Finally to validate the process an demonstrate the versatility of the process.

The complex architecture of the composite is imported to an FEA environment and meshed. The special code is written in Pascal that applies six sets of constraints to simulate unit strain vectors on a cell of the composite. After six separate analyses are undertaken, the forces necessary to achieve the boundary constraints are summed to provide stresses and hence the necessary coefficients in the stress to strain relationship for the composite. After global FEA the strains in the homogenized material are used as input to the inverse homogenizer so that stress and strain levels in the individual ingredients of the composite can be calculated for the purposes of assessing failure.

The process of writing separate code to operate in conjunction with a commercial FEA code was found to be very reliable, time‐effective and can be of great benefit to engineers researching with composites.

At this state all the materials can only be stressed within their elastic limit. There is no logical impediment to extending the algorithm to increase stresses into the non‐linear range.

The use of the API environment allows third parties to develop application‐specific code that overcomes the increasing generality of commercial FEA codes. The author can easily make the research available to the whole engineering and materials community without losing any intellectual property.

The practical results of this research are now freely available to the whole community and the work demonstrates in a general way how researchers can make their work available without having to write any FEA code, only the things they have researched.

The purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.

The optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.

The optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.

The proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM).

The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied.

A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze.

By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance.

This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

The purpose of this research is to establish a robust numerical framework for the calibration of macroscopic constitutive parameters, based on the analysis of polycrystalline RVEs with computational homogenisation.

This framework is composed of four building-blocks: (1) the multi-scale model, consisting of polycrystalline RVEs, where the grains are modelled with anisotropic crystal plasticity, and computational homogenisation to link the scales, (2) a set of loading cases to generate the reference responses, (3) the von Mises elasto-plastic model to be calibrated, and (4) the optimisation algorithms to solve the inverse identification problem. Several optimisation algorithms are assessed through a reference identification problem. Thereafter, different calibration strategies are tested. The accuracy of the calibrated models is evaluated by comparing their results against an FE2 model and experimental data.

In the initial tests, the LIPO optimiser performs the best. Good results accuracy is obtained with the calibrated constitutive models. The computing time needed by the FE2 simulations is 5 orders of magnitude larger, compared to the standard macroscopic simulations, demonstrating how this framework is suitable to obtain efficient micro-mechanics-informed constitutive models.

This contribution proposes a numerical framework, based on FE2 and macro-scale single element simulations, where the calibration of constitutive laws is informed by multi-scale analysis. The most efficient combination of optimisation algorithm and definition of the objective function is studied, and the robustness of the proposed approach is demonstrated by validation with both numerical and experimental data.

The optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore, it is important to provide a novel multiscale topology optimization framework to tailor the topology of structure and the material to achieve specific applications. In comparison with porous materials, composites consisting of two or more phase materials are more attractive and advantageous from the perspective of engineering application. This paper aims to provide a novel concurrent topological design of structures and microscopic materials for thermal conductivity involving multi-material topology optimization (material distribution) at the lower scale.

In this work, the effective thermal conductivity properties of microscopic three or more phase materials are obtained via homogenization theory, which serves as a bridge of the macrostructure and the periodic material microstructures. The optimization problem, including the topological design of macrostructures and inverse homogenization of microscopic materials, are solved by bi-directional evolutionary structure optimization method.

As a result, the presented framework shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid macrostructures and material microstructures are obtained in terms of optimal thermal conductive path, which verify the effectiveness of the proposed mutliscale topology optimization method. Numerical examples adequately consider effects of initial guesses of the representative unit cell and of the volume constraints of adopted base materials at the microscopic scale on the final design. The resultant structures at both the scales with clear and distinctive boundary between different phases, making the manufacturing straightforward.

This paper presents a novel multiscale concurrent topology optimization method for structures and the underlying multi-phase materials for thermal conductivity. The authors have carried out the concurrent multi-phase topology optimization for both 2D and 3D cases, which makes this work distinguished from existing references. In addition, some interesting and efficient multi-phase material microstructures and macrostructures have been obtained in terms of optimal thermal conductive path.

This paper aims to provide a comprehensive review of the state-of–the-art design methods for additive manufacturing (AM) technologies to improve functional performance.

In this survey, design methods for AM to improve functional performance are divided into two main groups. They are design methods for a specific objective and general design methods. Design methods in the first group primarily focus on the improvement of functional performance, while the second group also takes other important factors such as manufacturability and cost into consideration with a more general framework. Design methods in each groups are carefully reviewed with discussion and comparison.

The advantages and disadvantages of different design methods for AM are discussed in this paper. Some general issues of existing methods are summarized below: most existing design methods only focus on a single design scale with a single function; few product-level design methods are available for both products’ functionality and assembly; and some existing design methods are hard to implement for the lack of suitable computer-aided design software.

This study is a useful source for designers to select an appropriate design method to take full advantage of AM.

In this survey, a novel classification method is used to categorize existing design methods for AM. Based on this classification method, a comprehensive review is provided in this paper as an informative source for designers and researchers working in this field.

The purpose of this paper is to define and solve the problem of an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling achievement of a maximum buckling load.

Two kinds of inclusions are considered: regular distribution of inclusions of different rigidities and non-uniform distribution of identical inclusions. It is shown that the optimal conditions are similar for both structural designs. The optimization problems are solved by using the homogenization method, and the target functions belong to the class of piece-wise continuous functions. Both optimized structures exhibit border zones free of any inclusions, and the largest amount of inclusions is localized in the central zone of the beams.

It has been shown that the final result of the carried out optimization of the internal structure for both studied types of FGM are similar. The relative increase in the buckling force of the FG beam with the optimized internal structure is on amount of 20 per cent while comparing it with the regular structure beam.

In contrary to a standard approach, this paper is aimed to detect and study a scenario of transition from heterogeneous to its counterpart homogeneous beam structure based on the consideration of the FGM inclusions. In addition, the problem of inversed transition from the optimized homogeneous structure to the optimal heterogeneous one is solved.

In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm.

The presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy.

As a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself.

This paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance of the used algorithm. In addition, some new and interesting material microstructural topologies have been obtained to provide wider possible solutions to the material design.

This paper aims to considered the problem of identification of temperature-dependent thermal conductivity in the nonstationary, nonlinear heat equation. To describe the heat transfer in the furnace charge occupied by a homogeneous porous material, the heat equation is formulated. The inverse problem consists in finding the heat conductivity parameter, which depends on the temperature, from the measurements of the temperature in fixed points of the material.

A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently developed.

The influence of different numerical scheme parameters on the accuracy of the identified conductivity coefficient is studied. The results of the experiment carried out on real measurements are presented. Their results confirm the ones obtained earlier by using other methods.

Novelty is in a new, easy way to identify thermal conductivity by known temperature measurements. This method is based on special finite-difference scheme, which gives a resolvable system of algebraic equations. The results sensitivity on changes in the method parameters was studies. The algorithms of identification in the case of a purely mathematical experiment and in the case of real measurements, their differences and the practical details are presented.