Kinematic quantities of finite elastic and plastic deformation

TL;DR

This paper introduces a novel approach to defining kinematic quantities for finite elastic and plastic deformations directly on Galilean spacetime, avoiding auxiliary elements and explicitly accounting for inertial effects.

Contribution

It defines new elastic and plastic kinematic quantities based on metrics, providing a framework that does not depend on reference configurations or deformation gradients.

Findings

Elastic deformation measure compares current and relaxed metrics.

Plastic deformation rate is the change of the stressless metric.

Objective elastic or plastic quantities cannot be derived from deformation gradient.

Abstract

Kinematic quantities for finite elastic and plastic deformations are defined via an approach that does not rely on auxiliary elements like reference frame and reference configuration, and that gives account of the inertial-noninertial aspects explicitly. These features are achieved by working on Galilean spacetime directly. The quantity expressing elastic deformations is introduced according to its expected role: to measure how different the current metric is from the relaxed/stressless metric. Further, the plastic kinematic quantity is the change rate of the stressless metric. The properties of both are analyzed, and their relationship to frequently used elastic and plastic kinematic quantities is discussed. One important result is that no objective elastic or plastic quantities can be defined from deformation gradient.