Diffuse and localized failure predictions of Perzyna viscoplastic models for cohesive-frictional materials

Abstract

Viscoplastic constitutive formulations are characterized by instantaneous tangent operators which do no exhibit degradation from the elastic properties. As a consequence Viscoplastic materials descriptions were often advocated to retrofit the shortcomings of the inviscid elastoplastic formulations such as loss of stability and loss of ellipticity. However, when the time integration of Viscoplastic material processes is considered within finite time increments, there exists an algorithmic tangent operator which may lead to loss of stability and loss of ellipticity similar to rate-independent elastoplastic materials. The algorithmic tangent operator follows from the consistent linearization process. Therefore, the numerical method considered for the time integration of the constitutive equations plays a fundamental role in failure analysis of Viscoplastic materials. This paper focuses in the performance of the conditions form diffuse and localized failure of two Perzyna-type Viscoplastic models, one of them based on the classical formulation and the other one based on a new proposal by Ponthot (1995) which includes a constrain condition representing a rate dependent generalization of the plasticity`s yield condition. Application of Backward Euler method form time integration of both Perzyna formulations leads to quite different form of the consistent tangent material operators. These stiffness tensors are obtained for Perzyna generalizations of the so called Extended Leon Model which is a fracture energy-based elastoplastic constitutive model for concrete. The results included in the paper illustrate the strong differences between the failure predictions of both Perzyna-type Viscoplastic formulations. In this regard, the classical formulation is unable to reproduce the predictions of the inviscid model when the viscosity approaches zero. This case leads to very small values of both failures indicators and their performances are characterized by strong oscillations and even discontinuities. On the other hand the so-called continuous formulation is associated with algorithmic tangent moduli which signals a smooth transition from the elastic operator to the elastoplastic algorithmic one, when the viscosity varies from very large to very small values.