Representations and Hyperelastic Bodies
D.a. Hyperelastic Bodies
In (A.13) we have shown that the rate at which energy is stored in a body during a given deformation from reference body B(0), assuming no heat loss, is given by
where S is the second Piola-Kirchhoff stress tensor, E is the Lagrange deformation tensor (2.69), and the integral is over the fixed reference body B (0). The entire integrand is not necessarily the time derivative of a function. The stress tensor S is generally a complicated function of the ...