Material forces in micromorphic thermoelastic solids

Abstract

The physical foundation, balance laws and constitutive relations of microcontinuum field theories are briefly reviewed. The concept of material forces, which may also be referred as Eshelbian mechanics, is extended to micromorphic theory. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum and material forces are derived. It is found that, for micromorphic thermoelastic solids, the material forces are due to (1) body force and body moment, (2) temperature gradient and (3) the material inhomogeneities in density, microinertia and elastic coefficients. Finite element analysis is performed for a polycrystalline, which is composed of randomly distributed and oriented grains and in between the grain boundaries in its amorphous phase. Each grain is modeled as a single crystal by specialized micromorphic theory. The grain boundaries are modeled with a thin and finite width by classical continuum mechanics. A thin film of silicon, cooling down from the process temperature at 400°C to room temperature at 25°C, is numerically simulated. Thermally induced stresses, Eshelby stresses and material forces are obtained. Discussions about the application of material forces in multiphase materials are presented.

Acknowledgement

The support to this work by National Science Foundation under Award Number CMS-0301539 is gratefully acknowledged.