Kinematic quantities of finite elastic and plastic deformation

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.

v5: minor changes, one section moved to an Appendix, 26 pages, 2 figures

References in corpus (3)

• Can material time derivative be objective?
• SO(3) invariance and covariance in mixtures of simple bodies
• Absolute Time Derivatives

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