Mesoscopic theory of microcracks

TL;DR

This paper develops a mesoscopic framework within continuum mechanics to model microcracks as penny-shaped entities, introducing statistical and dynamic descriptions of crack orientation and damage evolution.

Contribution

It extends continuum mechanics by incorporating mesoscopic variables and distribution functions to model microcracks and their dynamics.

Findings

Defined microcrack orientation parameters and derived their dynamic equations

Presented examples of crack growth and damage parameter definitions

Established a mesoscopic approach for complex material analysis

Abstract

The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. In our case microcracks are modelled as penny shaped and completely characterized by their diameter and the unit normal to the crack surface. Two examples of crack dynamics are given as well as a possible definition of a damage parameter. Orientational order parameters (fabric-alignment tensors) are defined and balance like dynamic equations for them are derived.