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

## Palavras-chave:

Constitutive models, Elastoplasticity, Viscoplasticity, Deep Tunnel, Finite Element Method## 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.