ENERGY-MOMENTUM METHODS FOR NONLINEAR ELASTODYNAMICS RELYING ON POLYCONVEX STORED ENERGY FUNCTIONS

Abstract eng:
The present work deals with a mixed variational formulation of elastodynamics along with an energymomentum consistent discretization in space and time. The underlying continuum formulation relies on a polyconvex stored energy function [1]. In addition to the displacement field, further kinematic fields entering the polyconvex stored energy function are introduced by a newly proposed cascaded system of kinematic constraints. The corresponding mixed variational formulation is obtained by enforcing the kinematic constraints through a Hu-Washizu type variational functional. The newly proposed variational framework facilitates the design of new energy-momentum consistent discretizations in time. In addition to that, the mixed variational framework makes possible a wide variety of finite element discretizations in space. In the special case of a purely displacement-based discretization we obtain a new form of the algorithmic stress formula which is a typical feature of energy-momentum methods [2]. In particular, the new stress formula assumes a remarkably simple form when compared to previously proposed alternative stress formulas.

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