Simulation of shear band formation in plane and compression using FEM

A phenomenological constitutive relation using the conventional J2-fiow isotropic hardening yield function as well as a threshold shear stress based yield function that governs a 'directionally preferred plastic component' of shear strain, developed by the authors in an earlier work, is used for the simulation of the shear band formation. The constitutive 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 capturing the formation of the shear band even under material hardening conditions and does not demand any prior knowledge of the orientation of the shear band. This dual yield constitutive relation is incorporated 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 formation of the shear band can be captured more easily as a natural outcome of the simulation, without resorting to any instability criterion or 'enriched' elements that are usually employed in the contemporary procedures. Nevertheless, the usefulness of a 'local instability criterion' (Ortiz et al. (1987), Comp. Meth. AppL Mech. Eng. 61,189) is demonstrated in this study. The model is verified using the experimental data of Anand and Spitzig (1980, J. Mech. Phys. Solids 28, 113) and the agreement between the results of the simulation and the experimental data is found to be reasonably good.