FINITE ELEMENT IMPLEMENTATION OF AN ELASTOPLASTIC- VISCOPLASTIC CONSTITUTIVE LAW FOR TUNNELS

Resumo

The paper presents an efficient numerical integration scheme for coupled elastoplasticity-
viscoplasticity constitutive behavior with internal-state variables standing for irreversible processes. In

most quasi-static structural analyses, the solution to boundary value problems involving materials that
exhibit time-dependent constitutive behavior proceeds from the equations integration handled at two
distinct levels. On the one hand, the first or local level refers to the numerical integration at each
Gaussian point of the rate constitutive stress/strain relationships. For a given strain increment, the
procedure of local integration is iterated for stresses and associated internal variables until convergence
of the algorithm. On the other hand, the second or global level is related to structure equilibrium between
internal and external forces achieved by the Newton-Raphson iterative scheme. A review of the
elastoplastic and viscoplastic model will be shown, following the coupling between these models.
Particular emphasis is given in this contribution to address the first level integration procedure, also

referred to as algorithm for stress and internal variable update, considering a general elastoplastic-
viscoplastic constitutive behavior. The formulation is described for semi-implicit Euler schemes. The

efficacy of the numerical formulation is assessed by comparison with analytical solution derived for
deep tunnel in coupled elastoplasticity-viscoplasticity.