Kinematics, stress, deformation and material behavior

Abstract

A compact review is given of some fundamentals of the theory of flow in materials and of the bulk behavior of experimentally deformed rocks. Kinematics is discussed first because it provides an easy introduction to second-order tensor quantities. These are explained as quantities linking the components of pairs of vectors to one another, for example velocity vectors to position vectors (the velocity gradient tensor) or stress vectors to plane-normal vectors (the stress tensor). The fundamental theorem of stress theory is derived from the requirement of force-balance at a point. Here and elsewhere the treatment is mostly two-dimensional. This saves space yet provides an introduction to principles that are important again in three dimensions. Mohr circles are used extensively to represent two-dimensional tensor quantities geometrically, including asymmetric velocity gradient and deformation tensors. The decomposition of a general deformation into components of translation, rotation and strain is explained, and this may lead to greater appreciation of such unfamiliar possibilities as coaxial accumulation of a simple shear deformation. The section on experimental deformation is concerned mainly with the measured strengths of rocks and how these can be extrapolated to strengths at geological strain-rates. The text is followed by a Glossary.