Failures of the three-dimensional patch test for large elastic deformations

Within the context of 3-D brick elements for nonlinear elastic materials it is well know that enhanced strain and incompatible mode methods can be used successfully to improve the accuracy of solutions for bending of thin structures. It is also known that these elements can exhibit unphysical hourglass instabilities in states of combined high compression and bending. Here, examples of large deformation uniaxial strain in tension indicate that the enhanced strain/incompatible mode elements in ABAQUS, ADINA and ANSYS predict negative eigenvalues in the stiffness matrix which can cause failure of the three-dimensional patch test. Specifically, the elements in ABAQUS and ANSYS predict unstable element response with multiple unphysical solutions for a constant value of stretch. In contrast, the Cosserat point element (CPE) analytically satisfies the three-dimensional patch test for all anisotropic nonlinear elastic materials and all reference element shapes. Copyright (C) 2009 John Wiley & Sons, Ltd.