Residual stresses couple microscopic and macroscopic scales

TL;DR

This paper presents a first-principles approach combining mode-coupling theory and finite-element methods to predict residual stresses in visco-elastic materials based on their flow history, linking microscopic dynamics to macroscopic features.

Contribution

It introduces a coupled FEM-MCT framework that models residual stresses from microscopic relaxation and flow history, advancing understanding of stress development in amorphous solids.

Findings

Predicts residual stress patterns in amorphous solids

Demonstrates dependence of material properties on processing history

Shows how microscopic dynamics influence macroscopic stresses

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.