Kinetic Description
The virtual power principle in Virtual Power Principle will state equilibrium in terms of Cauchy true stresses and the conjugate virtual strain rate, the rate of deformation. It is worth noticing that, from the engineer's point of view, the Cauchy true stress is probably the only measure of practical interest because it is a direct measure of the traction being carried per unit area of any internal surface in the body under study. This is the reason why Radioss reports the stress as the Cauchy stress. The second Piola-Kirchhoff stress is, however, introduced here because it is frequently mentioned in standard textbooks.
Second Piola-Kirchhoff stresses have a simple physical interpretation. They correspond to a decomposition of forces in the frame coordinate systems convected by the deformation of the body. However, the stress measure is still performed with respect to the initial surface.