Cross-scale optimization of advanced materials for micro and nano structures based on strain gradient theory

Recently developed cross-scale optimization methods are mainly the macro equivalent calculation of performances based on the traditional homogenization method. However, the traditional homogenization is limited to the classic continuum of Cauchy-Boltzmann. Therefore, it is inadequate to interpret the size dependence of the optimal result. Hence, a new cross-scale optimization is proposed based on Wei-Hutchinson strain gradient theory by employing the non-local homogenization model, which could describe and explain the size dependence during optimization process when considering micro structures. The topological optimization procedure simultaneously has the ability of coupled computing by using subdomain parameterized coarse meshes. The numerical computations involved in the entire model can be solved in one iteration, which helps to eliminate mesh dependencies and greatly reduce the computation time. It is shown that the final stiffness of the optimized periodic structure can be significantly increased by considering the strain gradient theory compared with the classic homogenization scheme in the process of cross-scale optimization. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

Recently developed cross-scale optimization methods based on traditional homogenization method realize macro equivalent calculation of performances. However, the traditional homogenization method is limited to Cauchy-Boltzmann continuum and cannot explain the size dependence of the optimum result. Therefore, a new cross-scale optimization method is proposed based on Wei-Hutchinson strain gradient theory and non-local homogenization model to consider the size dependence during the optimization process, especially when micro structures are involved. The topological optimization procedure achieves coupled computing using subdomain parameterized coarse meshes, and the entire model can be solved in one iteration, eliminating mesh dependencies and greatly reducing computation time. The results show that the final stiffness of the optimized periodic structure can be significantly increased by considering the strain gradient theory compared to the classic homogenization scheme in the cross-scale optimization process.