Continuum mechanics of the interaction of phase boundaries and dislocations in solids

TL;DR

This paper develops a continuum mechanics framework for line defects in solids, enabling analysis of phase boundaries, grain boundaries, and plasticity at the defect level, with a focus on kinematics and dissipation.

Contribution

It introduces a generalized continuum approach for line defects, incorporating differential geometry and constitutive laws respecting frame-indifference and dissipation constraints.

Findings

Derived constitutive laws for defect response.

Established a geometric interpretation of defect kinematics.

Highlighted the incompatibility of dissipation with strict deformation compatibility.

Abstract

The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase transformation, grain boundary, and plasticity-related phenomena at the level of individual line defects and domain walls. The continuously distributed defect approach is developed as a generalization of the discrete, isolated defect case. Constitutive guidance for equilibrium response and dissipative driving forces respecting frame-indifference and non-negative mechanical dissipation is derived. A differential geometric interpretation of the defect kinematics is developed, and the relative simplicity of the actual adopted kinematics is pointed out. The kinematic structure of the theory strongly points to the incompatibility of dissipation with strict deformation compatibility.