Deformation

Abstract

This section introduces various deformation, stretch and strain tensors to describe the deformation behaviour of a solid during an arbitrary motion. Their definitions are essentially based on the deformation gradient and the stretch variables introduced by the polar decomposition theorem. Emphasis is given to the eigenvalue problems of stretches presenting a suitable background for the definition of various strain measures within a unified concept. Attention is then dedicated to pull-back and push-forward operations which are of major importance for the construction of the LIE-derivatives. Finally the rate of the deformation tensor and the spin tensor are introduced and their geometrical interpretations are given.