A non linear algorithm for the Maxwell-Norton-Hoff's model

The general framework of this study deals with numerical solution by the finite element method of boundary value problems relating to viscoplastic continuums complying with the Maxwell- Norton-Hoffs model. We develop, in a first part, the general equations of the space and time continuous problem. These equations are first discretized over finite time-steps, considering three assumptions. Then we give the variational formulation of the resulting time-discretized problems. In a second part we consider the Maxwell-Norton-Hoffs model. The constitutive equations are first integrated over a finite time-step, with the help of an original time discrete scheme. We obtain therefore a non linear correspondence between the increments of the stress and strain tensors. This tensorial relation is then linearized by using the Newton’s method and replaced in each of the previous time discretized variational problems. TTiese incremental problems are then solvable with a finite number of iterations.