Simulation of strength difference for adhesive materials in finite deformation elasto-plasticity

The experimental investigation of certain adhesive materials reveals elastic strains, plastic strains and hardening, respectively. Additionally a pronounced strength difference between tension, torsion or combined loading is observed. The purpose of this work is the simulation of these phenomena in the framework of large strain elasto-plasticity. To this end a yield function dependent on the first and second basic invariants of the Cauchy stress tensor is introduced. Furthermore, a plastic potential with the same mathematical structure is used to formulate the evolution equations under the assumption of small elastic strains. Upon considering thermodynamic consistency of the model equations some restrictions on the material parameters are derived. Furthermore numerical aspects are addressed concerning the integration of the constitutive relations and the finite element equilibrium iteration. In the numerical examples, firstly, we compare simulated and experimental results exhibiting the yield strength difference between tension and torsion for the adhesive material Betamate 1496. A second example investigates the deformation evolution of a compact tension specimen with an adhesive zone.