A simple Python code for computing effective properties of 2D and 3D representative volume element under periodic boundary conditions

TL;DR

This paper presents a straightforward Python tool for calculating the effective mechanical properties of 2D and 3D composite RVEs under periodic boundary conditions, facilitating multiscale optimization and microstructure analysis.

Contribution

The paper introduces a simple, adaptable Python code based on Asymptotic Homogenization Theory for computing properties of complex microstructures in multiscale optimization.

Findings

Code accurately computes effective properties in 3D cases

Results align well with theoretical and experimental data

Platform supports various algorithms for microstructure optimization

Abstract

Multiscale optimization is an attractive research field recently. For the most of optimization tools, design parameters should be updated during a close loop. Therefore, a simple Python code is programmed to obtain effective properties of Representative Volume Element (RVE) under Periodic Boundary Conditions (PBCs). It can compute the mechanical properties of a composite with a periodic structure, in two or three dimensions. The computation method is based on the Asymptotic Homogenization Theory (AHT). With simple modifications, the basic Python code may be extended to the computation of the effective properties of more complex microstructure. Moreover, the code provides a convenient platform upon the optimization for the material and geometric composite design. The user may experiment with various algorithms and tackle a wide range of problems. To verify the effectiveness and reliability of the code, a three-dimensional case is employed to illuminate the code. Finally numerical results obtained by the code agree well with the available theoretical and experimental results