INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2003; 58:1637–1682 (DOI: 10.1002/nme.835) Analysis of 3D problems using a new enhanced strain hexahedral element P. M. A. Areias ∗; † , J. M. A. C esar de S a, C. A. Concei c˜ ao Ant onio and A. A. Fernandes Instituto de Engenharia Mecˆ anica (IDMEC); Faculdade de Engenharia da Universidade do Porto; Rua Dr. Roberto Frias s=n; 4200-465 Porto; Portugal SUMMARY 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. Copyright ? 2003 John Wiley & Sons, Ltd. KEY WORDS: nite elements; hexahedral element; nite strains; enhanced strains; brick element 1. INTRODUCTION The analysis of general solid mechanics problems from linear elastic beam bending to nite strain elasto-plastic problems can be accomplished with the use of solid 3D elements and, in particular, hexahedral elements. Objections to such a one-size ts all approach are related both to the cost of the analysis and its accuracy. In most commercial nite element codes, problems with beams or shells are analysed with special-purpose elements. In terms of cost of ∗ Correspondence to: P. M. A. Areias, Instituto de Engenharia Mecˆ anica (IDMEC), Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s=n, 4200-465 Porto, Portugal. † E-mail: simplas2002@netscape.net Contract=grant sponsor: Minist erio de Ciˆ encia e da Tecnologia, FCT; contract=grant number: PRAXIS XXI=BD= 18538=98 Received 9 September 2002 Revised 12 February 2003 Copyright ? 2003 John Wiley & Sons, Ltd. Accepted 14 March 2003