Residual stresses couple microscopic and macroscopic scales

Abstract

We show how residual stresses emerge in a visco-elastic material as a signature of its past flow history, through an interplay between flow-modified microscopic relaxation and macroscopic features of the flow. Long-lasting temporal-history dependence of the microscopic dynamics and nonlinear rheology are incorporated through the mode-coupling theory of the glass transition (MCT). The theory's integral constitutive equation (ICE) is coupled to continuum mechanics in a finite-element method (FEM) scheme that tracks the flow history through the Finger tensor. The method is suitable for a calculation of residual stresses from a "first-principles" starting point following well-understood approximations. As an example, we calculate within a schematic version of MCT the stress-induced optical birefringence pattern of an amorphous solid cast into the shape of a slab with a cylindrical obstacle and demonstrate how FEM-MCT can predict the dependence of material properties on the material's processing history.