A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians (Q357491)

The paper deals with the equations describing the dynamics of radial motions for isotropic elastic materials. The authors construct a variational approximations scheme, by considering a particular form of polyconvex stored energy, that on the hand preserves the positivity of the determinants and the other produces a time-discretized variant of entropy dissipation. They prove a existence, uniqueness and regularity of minimizers. Moreover the minimizer satisfies the time-discretized version of a specific entropy dissipation inequality.