Failure analysis of elastoviscoplastic material models

One of the open questions is the performance of rate-independent versus rate-dependent constitutive formulations when failure is evaluated at the material and the finite-element levels. In the case of rate-independent descriptions, the underlying tangential material operator exhibits singularities and material branching at limit points of the response regime. In addition discontinuous bifurcation can take place in the form of localization concomitant with the formation of spatial discontinuities. In contrast, rate-dependent descriptions resort to an instantaneous elastic stiffness operator that remains normally positive definite, while degradation is introduced through the time history of inelastic eigenstrains. In fact when the inelastic process does not contribute to the instantaneous material operator one speaks of elastic-inelastic decoupling. As a consequence viscoplastic material descriptions are often advocated to retrofit loss of stability, loss of uniqueness, and loss of ellipticity of rate-independent, inviscid material descriptions. In this paper the failure predictions of viscoplastic Duvaut-Lions and viscoplastic Perzyna material formulations are analyzed and compared with the inviscid elastoplastic formulation. Our attention will be focused on the loss of material stability and on discontinuous bifurcation in the form of localization. The results on the material and on the finite-element level indicate that Duvaut-Lions regularization fails in the limit, when we consider viscoplastic processes with relaxation times approaching zero. In this case, there exists an algorithmic tangent operator for the Newton-Raphson solution of implicit time integration procedures that exhibits loss of stability, loss of uniqueness, and loss of ellipticity in the form of discontinuous bifurcation similar to rate-independent elastoplasticity. On the other hand, localization at the material level indicates that Perzyna viscoplasticity does suppress localization for the entire range of viscosities and thus provides stronger regularization than the Duvaut-Lions viscoplastic overstress model at the cost of excessive degradation when the viscosity approaches zero. These theoretical observations are confirmed with computational simulations of dynamic failure of a flexural member.