Steinmann P. Geometrical Foundations of Continuum Mechanics: An Application to First- and Second-Order Elasticity and Elasto-Plasticity

Sptinger, 2015. — 534 p. — (Lecture Notes in Applied Mathematics and Mechanics 02). — ISBN: 978-3-662-46459-5.This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.Motivation: Linear Crystal Plasticity
Preliminaries
Geometry on Connected Manifolds
Geometry on Metric Manifolds
Representations in Four-, Three-, Two-Space
Continuum Kinematics
Elasticity
Elasto-Plasticity
Integrability and Non-Integrability in a Nutshell