Representation of Material Elements and Geometry of Substructural Interactions

TL;DR

This paper explores the foundational aspects of modeling complex bodies, focusing on how substructural interactions influence overall behavior through geometric, energetic, and existence conditions.

Contribution

It provides a comprehensive framework for representing material elements and their interactions in the mechanics of complex bodies, emphasizing foundational geometric and energetic aspects.

Findings

Geometric description of material elements

Representation of substructural interactions

Conditions for ground state existence

Abstract

This paper collects some characteristic aspects of the general model-building framework of the mechanics of complex bodies, that are bodies in which the material substructure influences prominently the gross behavior through interactions conjugated with substructural changes. The emphasis in on issues that are foundational in nature: the geometrica description of the material elements, their energetic characterization, the representation of interactions, conditions for the existence of ground states in conservative setting.