Galerkin-based energy-momentum time-stepping schemes for anisotropic hyperelastic materials

This paper is motivated by dynamic simulations of fiber-reinforced materials in light-weight structures, and has two goals. First of all, the introduction of energy-momentum schemes for nonlinear anisotropic materials, based on GALERKIN approximations in space and time, assumed strain approximations in time and superimposed algorithmic stress fields (compare [1]). Second, to show a variationally consistent design of energy-momentum schemes using a differential variational principle. We develop a discrete variational principle leading to energy-momentum schemes as discrete EULER-LAGRANGE equations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)