Computational homogenisation of thermo-viscoplastic composites: Large strain formulation and weak micro-periodicity

Abstract

In this article, a first order two-scale finite element framework for fully coupled thermo-mechanical problems at finite deformations is considered. The scale bridging is achieved under application of Hill–Mandel condition based boundary conditions at the lower scale. Emphasis of the present article is on the extension of the concept of weak micro-periodicity to thermo-mechanically coupled problems. With this formulation at hand, uniform traction, respectively heat flux boundary conditions as well as the classic periodic boundary conditions are captured as well as a transition between them. The governing equations are summarised with a focus on the implementation of the weak periodic boundary conditions for thermo-mechanical problems. The performance of the proposed weak periodic boundary conditions in comparison to the classic boundary conditions is shown by means of simulations of a single representative volume element as well as by means of full multi-scale simulations.