Isogeometric analysis of finite deformation nearly incompressible solids

Abstract

This paper addresses the use of isogeometric analysis to solve finite deformationsolid mechanics problems, in which volumetric locking may be encountered. The current workis based on the foundation developed in the project ICADA for linear analysis, that herein isaugmented with additional capabilities such that nonlinear analysis of finite deformation prob-lems 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 variationalformulation, in which displacements, mean stress and volume change are independently approx-imated. The performance of the mixed forms is assessed by studying two numerical examplesinvolving large-deformation nearly incompressible elasticity and elastoplasticity. The resultsobtained with NURBS are shown to compare favorable with classical Lagrange finite elements.