2023/07/24 by Sebastian Steinhäuser, Steinhäuser, Sebastian, Timm Treskatis +5
Chemical Engineering · Engineering · Materials Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Material Dynamics and Properties #Rheology and Fluid Dynamics Studies #Soft Condensed Matter (cond-mat.soft) #Structural Analysis of Composite Materials
paper · pdf · doi:10.48550/arxiv.2307.12764
openalex publication_date 2023/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.