Constitutive models for elastoplasticity from a 4D thermodynamic construction and its applications to the simulation of large deformations

In the framework of the thermodynamic of irreversible processes, Eulerian constitutive models for elastoplasticity in large deformation are proposed. A formalism of four-dimensional equations derived from the Theory of Relativity is applied to ensure the generality and covariance of the proposed models. The Lie derivative is also chosen as a true time derivative. 3D models are derived from 4D equations and compared with classical ones by applying it to the simulations of forming processes.