Simulation of strength difference coupled to softening in elasto-plasticity for adhesive materials

Rubber-toughened adhesive materials exhibit a hardening regime with a pronounced strength difference between tension, torsion or combined loading. Furthermore a softening regime is observed, also dependent on the stress state of tension, torsion or combined loading. For simulation of these phenomena a yield function dependent on the first and second basic invariants of the related effective stress tensor in the framework of elasto-plasticity is used in this work. A plastic potential with the same mathematical structure is introduced to formulate the evolution equation for the inelastic strains. A softening function is proposed in a multiplicative way, which accounts for both, evolution of softening subject to deviatoric stress states and volumetric stress states. Furthermore thermodynamic consistency of the model equations is considered, thus rendering some restrictions on the material parameters. The resulting evolution equations are integrated with an implicit Euler scheme. Three examples are presented. The first example demonstrates the capability of the model equations to simulate the softening combined to strength difference between tension and torsion for an epoxy resin adhesive material. Two additional finite element simulations investigate the deformation evolution within an adhesive layer for a double-U-shaped specimen and a T-joint.