SUMMARY This article proposes a two‐scale formulation of fully coupled continuum thermomechanics using the finite element method at both scales. A monolithic approach is adopted in the solution of the momentum and energy equations. An efficient implementation of the resulting algorithm is derived that is suitable for multicore processing. The proposed method is applied with success to a strongly coupled problem involving shape‐memory alloys.Copyright © 2012 John Wiley & Sons, Ltd.

Abstract

This article proposes a continuum thermomechanical homogenization method inspired by the Irving-Kirkwood procedure relating the atomistic equations of motion to the balance laws of continuum mechanics. This method yields expressions for the macroscopic stress and heat flux in terms of microscopic kinematic and kinetic quantities. The resulting equation for macroscopic stress affords a rational comparison with the widely used Hill-Mandel stress-deformation condition, while the one for heat flux reduces, under certain assumptions, to a Hill-Mandel-like condition involving heat flux and the gradient of temperature.

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.

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