Deformation.

Abstract

An introduction into the notion of deformation with reference to differentiable manifolds is presented. As measures of deformation tensores of type Green, Cauchy, Piola and Finger, strain tensors of type Green and Almansi, both as functionals of the displacement vector, are given. The Eulerian and the Lagrangean point of view is emphasized. Shifters transform reference frames from one manifold to the other. Length and angle changes, area and volume changes are studied from duality. Finally deformation is interpreted by means of polar decomposition. -from STAR, 22(7), 1984