A variational approximation scheme for radial polyconvex elasticity that   preserves the positivity of Jacobians
  We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter. 
Alexey Miroshnikov, Athanasios E. Tzavaras
math.AP