Simple and accurate four-node axisymmetric element

Based on the assumed strain method, a simple four-node axisymmetric solid element is introduced. The assumed strain field is carefully selected to preserve the correct rank of the element stiffness matrix and to achieve high accuracy. The strain field is developed in conjunction with orthogonal projections and no matrix inversions are needed. The coarse mesh accuracy in bending and in typical axisymmetric load cases is excellent even for nearly incompressible materials. The strain-driven format obtained is well suited for materials with non-linear stress–strain relations. Several numerical examples are presented where the excellent performance of the proposed simple element is verified. Copyright © 2006 John Wiley & Sons, Ltd.     

Structure-preserving space-time discretization of a mixed formulation for quasi-incompressible large strain elasticity in principal stretches

In this paper, we propose an energy and momentum consistent time-stepping scheme for nonlinear elastodynamics. The algorithm is based on a mixed Hu-Washizu–type variational principle that is inspired by the concept of polyconvexity and relies on a tensor cross product of second-order tensors. In addition, we introduce a new algorithmic stress formula in its eigenvalue representation to model the transient behavior of hyperelastic bodies of Ogden-type materials. Finally, several numerical examples show the superior performance of the proposed formulation in terms of numerical robustness and stability.