Unified viscoplasticity constitutive equations are 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.