Research on consistent tangent modulus for unified viscoplastic constitutive equations

Unified viscoplasticity constitutive equations arc a system of integral or incremental equations with implied internal variables. So, it is difficult to provide a well-defined expression of the consistent tangent modulus. Based on the backward Euler's integral for unified viscoplasticity constitutive equations, a new expression of consistent tangent modulus was derived for rate-dependent plasticity. The constitutive equations and consistent tangent modulus expression were implemented in a commercial finite element code-MARC. The numerical examples of finite elements verify the feasibility of consistent tangent modulus.