Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Abstract

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.