Application of a fractional step method to localization problems

Dynamic analysis of J′2 solids typically involves a huge number of degrees of freedom. Therefore, use of low cost elements such as linear triangles and tetrahedrals, is almost a requisite. However, the accuracy of these elements greatly deteriorates due to the incompressible behaviour of the material encountered in this type of problems. Besides, using mixed velocity–pressure formulations is precluded for these elements by the Babuska–Brezzi condition unless especial stabilization techniques are incorporated. This paper presents a stabilization technique allowing equal order of interpolation based on the operator splitting formulation used in the field of Fluid Dynamics with strong emphasis in the adequate treatment of the boundary conditions. The paper also describes its application to the solution of strain localization problems in J′2 rate dependent materials.