A finite-deformation anisotropic non-associative viscoplasticity/damage coupled thermodynamic model for ductile fracture of thick adhesive composite joint

Abstract This paper develops a finite-deformation anisotropic non-associative (visco)plasticity/ damage coupled model for thick adhesive composite joints within the framework of irreversible thermodynamics. First, a four-order damage tensor that is composed of a two-order damage tensor is introduced into the elastic constitutive model, the Drucker-Prager’s type yielding function and plastic potential function by considering the variable hydrostatic pressure and non-associative plasticity. The spectral decomposition of the second-order damage tensor is performed to derive the fourth-order damage tensor. Second, a damage potential function is also introduced to describe the coupled relationship between plastic deformation and damage evolution. Since the two-order damage tensor is related to the elastic strain tensor, plastic anisotropy and damage-induced anisotropy after plastic deformation interact. Third, both isotropic hardening and kinematic hardening are considered, represented by the back stress and the hardening stress as well as their conjugate relationships with the corresponding internal variables. They are derived by the Helmholtz free energy, and their evolved relationships are derived by the plastic potential function according to the Kuhn-Tucker loading-unloading consistency conditions for the rate-independent plasticity/damage coupled model. Fourth, an extended version of the Perzyna’s type model by introducing an over-stress function is developed to derive the consistency plasticity factor for the viscoplasticity/damage coupled model, regardless of the Kuhn-Tucker plastic loading-unloading consistency conditions. It is shown that the rate-independent plasticity model is just a particular case of the viscoplasticity model as viscous parameters tend to be zero. Fifth, all the thermodynamic forces and internal variables as well as the tangent modulus for the two models above are updated under the corotated configuration for finite deformation in the consistent integration procedure by implicit FEA. In order to simplify numerical computation, the stress and strain at time n + 1 are first updated using the frozen damage tensor and back stress tensor at time n, and then the latter two tensors are updated individually at time n + 1. Finally, the developed model and numerical algorithm by FEA are used to predict the stress, strain, and damage features of the dog-bone MMA ductile adhesive specimens under tensile loads and the thick MMA adhesive joint specimens under shear loads. It should be emphasized that numerical convergence and parameter identification in FEA should be addressed properly in order to lead to accurate and robust predictions of mechanical responses of structures.