A mathematical model of network elastoplasticity

TL;DR

This paper presents a network-based mathematical model capturing both elasticity and plasticity of materials, using tension tensors and local graph moves to describe deformation behaviors.

Contribution

It introduces a novel network model that mathematically describes material elasticity and plasticity through tension tensors and graph transformations.

Findings

Tension tensor effectively models elasticity under deformation.

Local graph moves induce plasticity in the model.

Edge weights influence the plastic behavior of the network.

Abstract

We introduce a mathematical model, based on networks, for the elasticity and plasticity of materials. We define the tension tensor for a periodic graph in a Euclidean space, and we show that the tension tensor expresses elasticity under deformation. Plasticity is induced by local moves on a graph. The graph is described in terms of the weights of edges, and we discuss how these weights affect the plasticity.