A Deformable Solid

Abstract

The system is a deformable solid. Both the equations of motion and the constitutive laws are investigated. Predictive theories differ mainly by the fact that they either involve torques or do not. The symmetry of the stress tensor is related to this property. The three first theories take volume torques into account. The third one accounts for volume and surface torques. There are different ways to introduce the equations of motion for deformable solids. We describe some of them: the first one is a sophisticated theory involving three velocities of deformation: the gradient of the velocity, the symmetric strain rate and the angular velocity; the second one involves two velocities of deformation: the gradient of the velocity and the angular velocity; the third theory is an upgrading of the second one introducing the gradient of the angular velocity as a new velocity of deformation; the last one involves only one velocity of deformation: the symmetric gradient of the velocity, the classical strain rate. This theory is the classical one widely used in engineering.