SIMULATION OF SHEAR-BAND FORMATION IN PLANE-STRAIN TENSION AND COMPRESSION USING FEM

A phenomenological constitutive relation using the conventional J2-flo w isotropic hardening yield function as well as a threshold shear stre ss based yield function that governs a 'directionally preferred plasti c component' of shear strain, developed by the authors in an earlier w ork, is used for the simulation of the shear band formation. The const itutive relation which is expressed as an explicit function of elastic constants, deviatoric stress state, direction of the principal shear strain and material flow stresses, is shown to be fully capable of cap turing the formation of the shear band even under material hardening c onditions and does not demand any prior knowledge of the orientation o f the shear band. This dual yield constitutive relation is incorporate d in an FEM procedure capable of handling large strains and rotations and a numerical simulation of a tensile and compressive deformation of a plane strain specimen is performed. It is demonstrated that the for mation of the shear band can be captured more easily as a natural outc ome of the simulation, without resorting to any instability criterion or 'enriched' elements that are usually employed in the contemporary p rocedures. Nevertheless, the usefulness of a 'local instability criter ion' (Ortiz et al. (1987), Comp. Meth. Appl. Mech. Eng. 61, 189) is de monstrated in this study. The model is verified using the experimental data of Anand and Spitzig (1980, J. Mech. Phys. Solids 28, 113) and t he agreement between the results of the simulation and the experimenta l data is found to be reasonably good.