Analysis of 3D problems using a new enhanced strain hexahedral element

The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell nite elements, is here explored in a versatile 3D low-order element which is identi ed as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including nite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent sti ness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several nite strain tests. Some examples involve nite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples