Characteristic foliations of material evolution: from remodeling to aging

TL;DR

This paper introduces a mathematical framework using material groupoids and distributions to model and analyze the evolution of material properties, including remodeling and aging, in complex materials.

Contribution

It develops a unified approach employing material groupoids and distributions to handle non-uniform material evolution, extending previous models to more general cases.

Findings

Defines the material groupoid for evolution materials.

Introduces the material distribution for non-Lie groupoid cases.

Provides a unified framework for modeling material aging and remodeling.

Abstract

For any body-time manifold $\mathbb{R} \times \mathcal{B}$ there exists a groupoid, called material groupoid, encoding all the material properties of the evolution material. A smooth distribution, the material distribution, is constructed to deal with the case in which the material groupoid is not a Lie groupoid. This new tool provides a unified framework to deal with general non-uniform evolution materials.