A velocity approach to finite element calculation of elastoplastic and viscoplastic deformation processes

The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.