Principal stress formulation of continua motion

Abstract

Principal stress coordinates are formulated for a material without tension, with the equations of motion projected onto a selected coordinate system. The translations are achieved by forming the local basis vector in correspondence with the local stress tensor. The principal stress coordinates are described as orthogonal and curvilinear, and the metric is defined. The kinematics and dynamics of the principal stress coordinates are analyzed, the latter in orthogonal coordinates, and an analytic formulation of the dynamics of a no-tension material is provided. Finally, elastic granular material such as sand, soil, etc., which are more complicated versions of no-tension material, are explored.