Isogeometric analysis of finite deformation nearly incompressible solids

Abstract

This paper addresses the use of isogeometric analysis to solve finite deformation solid mechanics problems, in which volumetric locking may be encountered. The current work is based on the foundation developed in the project ICADA for linear analysis, that herein is augmented with additional capabilities such that nonlinear analysis of finite deformation problems in solid mechanics involving material and geometrical nonlinearities may be performed.In particular, we investigate two mixed forms based on a three-field Hu-Washizu variational formulation, in which displacements, mean stress and volume change are independently approximated. The performance of the mixed forms is assessed by studying two numerical examples involving large-deformation nearly incompressible elasticity and elastoplasticity. The results obtained with NURBS are shown to compare favorable with classical Lagrange finite elements.