Toward realization of computational homogenization in practice

TLDR

The paper presents a computational homogenization approach compatible with conventional finite element codes and urges practitioners and commercial vendors to adopt and integrate it into their analysis and design processes. The authors implement the approach in ABAQUS by using existing facilities for linear unit‑cell analysis and a Python script invoked during coarse‑scale stress updates for nonlinear problems. They provide a seamless ABAQUS implementation, including Python scripts, validation examples, and a web link to download the scripts, subroutines, and input files. © 2007 John Wiley & Sons, Ltd.

Abstract

Abstract We present a computational homogenization approach for linear and non‐linear solid mechanics problems, which is fully compatible with conventional finite element code architecture. A seamless implementation in ABAQUS is presented including Python script, validation problems and a web‐link where script files, user‐defined subroutines and input files can be accessed. For linear problems, we demonstrate how to utilize ABAQUS existing facilities to develop analysis attributes required for solving a unit‐cell problem. For non‐linear problems, a Python script invoked by a coarse‐scale stress update procedure is introduced to carry out the scale bridging. The purpose of this paper is twofold: (i) to motivate practitioners to adopt the computational homogenization as an integral part of their analysis and design process; and (ii) to encourage commercial code vendors to seamlessly integrate the architectures proposed in their legacy codes. Copyright © 2007 John Wiley & Sons, Ltd.