The evolution equation: an application of groupoids to material evolution

TL;DR

This paper introduces a novel groupoid-based framework to model the intrinsic evolution of individual material points, capturing phenomena like remodeling and aging.

Contribution

It develops a new mathematical approach using groupoids to describe the evolution of material points, focusing on intrinsic properties rather than the entire body.

Findings

Groupoid construction encodes intrinsic properties of material points.

Defines an evolution equation based on the groupoid framework.

Addresses phenomena such as remodeling and aging in materials.

Abstract

The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the particle and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.