ANALYSIS OF STRAIN LOCALIZATION IN STRAIN-SOFTENING HYPERELASTIC MATERIALS, USING ASSUMED STRESS HYBRID ELEMENTS

Newly developed assumed stress finite elements, based on a mixed varia tional principle which includes unsymmetric stress, rotation (drilling degrees of freedom), pressure, and displacement as variables, are pre sented. The elements are capable of handling geometrically nonlinear a s well as materially nonlinear two dimensional problems, with and with out volume constraints. As an application of the elements, strain loca lization problems are investigated in incompressible materials which h ave strain softening elastic constitutive relations. It is found that the arclength method, in conjunction with the Newton Raphson procedure , plays a crucial role in dealing with problems of this kind to pass t hrough the limit load and bifurcation points in the solution paths. Th e numerical examples demonstrate that the present numerical procedures capture the formation of shear bands successfully and the results are in good agreement with analytical solutions.