The evolution equation: An application of groupoids to material evolution

Víctor Manuel Jiménez; Manuel de León

doi:10.3934/jgm.2022001

Article Contents

2022, Volume 14, Issue 2: 331-348. Doi: 10.3934/jgm.2022001

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$ \infty $

-algebroids and adjoint representations Next Article Towards a 2-dimensional notion of holonomy

The evolution equation: An application of groupoids to material evolution

Víctor Manuel Jiménez^1, , and
Manuel de León^2,3,

1.
Universidad de Alcalá (UAH), Departamento de Física y Matemáticas, Av. de León, 4A, 28805 Alcalá de Henares, Madrid, Spain
2.
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C\Nicolás Cabrera, 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain
3.
Real Academia de Ciencias Exactas, Fisicas y Naturales, C/de Valverde 22, 28004 Madrid, Spain

^*Corresponding author: Víctor Manuel Jiménez
^*Corresponding author: Víctor Manuel Jiménez

To the memory of Kirill Mackenzie

Received: July 31, 2021

Published: June 2022

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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 material point and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.

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Mathematics Subject Classification: Primary: 74A20, 74B99, 74E99, 53C12, 18B40, 20L05; Secondary: 22A22, 58H05.

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