Hyperelasticity and physical shear buckling of a block predicted by the Cosserat point element compared with inelasticity and hourglassing predicted by other element formulations

摘要

This paper examines the response of 18 nonlinear “hyperelastic” elements which are available in the computer codes ABAQUS, ADINA, ANSYS and FEAP. Simulations are proposed to test inelasticity of element formulations caused by potential path-dependence of the external work done on the element. All elements tested based on full integration produce hyperelastic response for these simulations. Most modified elements produce inelastic response for these simulations and one generates energy. One incompatible mode element in ADINA and one enhanced strain element in FEAP exhibit hyperelastic response in these simulations. However, both of these elements predict unphysical hourglass buckling modes for plane strain compression of a block. The Cosserat point element has been proven analytically to be hyperelastic for all deformations. The example problems indicate that the Cosserat point element is robust, does not exhibit typical locking phenomena and predicts a physical shear buckling mode for plane strain compression of a block.