3D cell-centered Lagrangian second order scheme for the numerical modeling of hyperelasticity system

Abstract The extension of the 3D cell-centered Finite Volume EUCCLHYD scheme to the hyperelasticity system is proposed here. This study is based on the left Cauchy-Green tensor B which enables to work in a fully updated Lagrangian formalism. The second order extension of this scheme is proposed using a MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) procedure combined with a GRP (Generalized Riemann Problem) approach. In particular, the limitation of the tensor fields is done in a component-wise manner. Moreover, the complete GRP procedure is proposed in the case of Neo-Hookean compressible solids. The scheme is validated on several test cases introducing small as well as large deformations. In particular, good results are found on the non trivial problems of oscillating and twisting beams.