Dissipation analysis on a large strain thermo-elasto-viscoplastic model us- ing the Finite Element Method

Resumo

We present a phenomenological large strain thermo-elasto-viscoplastic constitutive model using the multiplicative decomposition of the thermal, elastic and plastic deformation gradients. The laws of thermodynamics are used as basis to formulate the model and to obtain the heat equation, including the dissipation from the viscoplastic component. An isotropic expansion law in exponential form is used for the thermal part of the deformation, and a neo-Hookean model is used for the elastic part. Plasticity is considered based on the von Mises yield criterion with Perzyna model to account for the viscous behavior of the plastic component, Norton’s law for the
overstress function, and the Armstrong-Frederick model of kinematic hardening. For the numerical integration of the evolution laws, we employ an exponential map method that ensures the property of plastic incompressibility. The resulting constitutive model is applied in a position-based Finite Element framework to solve the mechanical problem. The thermal problem is also solved by the Finite Element Method, using temperatures as nodal parameters, and the thermo-mechanical coupling is performed as an iterative partitioned method. Finally, a representative numerical example is selected to show the characteristics of the constitutive model, with special focus on the heat generated due to plastic dissipation over different strain and stress rates.