Continuum Kinematics with Incompatible-Compatible Decomposition

TL;DR

This paper introduces a new framework for analyzing the kinematics of materials undergoing anelastic deformation, capturing phenomena like plasticity and fracture through a unique incompatible-compatible decomposition.

Contribution

It proposes a novel geometric decomposition method that unambiguously separates incompatible and compatible deformation factors, extending standard elastic-plastic analysis.

Findings

Provides a unified geometric framework for anelastic deformation

Includes standard elastic-plastic decomposition as a special case

Applicable to phenomena like plasticity, fracture, and discontinuities

Abstract

Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities, and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors which includes the standard elastic-plastic decomposition in plasticity.