Material forces in micromorphic fracture mechanics

Abstract

The physical foundation, the balance laws and the 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 solid, 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. It is shown that, at the crack front, material forces are reduced to generalized vectorial J‐integral. The calculation of material forces, due to the presence of inhomogeneities or cracks, by finite element analysis and meshless analysis is discussed. Finite element analysis is performed for a multiphase material 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. Numerical results, including Cauchy stresses, Eshelby stresses, and material forces, for a thin film of silicon subjected to thermal and/or mechanical loadings are obtained and discussed.