Discontinuous Bifurcation Analysis in the Performance Dependent Model for Concrete

Abstract

This paper presents the predictions of different failure modes when concretes of arbitrary strength are subjected to different load scenarios. The discontinuous bifurcation analysis is performed in the Performance Dependent Model for concretes recently proposed by two of the authors, a constitutive
formulation valid for both normal and high strength concretes. Based on the incremental flow theory of plasticity, it depends on the three stress invariants, its maximum strength surface is defined by the Performance Dependent Failure Criterion, including a non uniform hardening law, an isotropic fracture energy based softening law and following a volumetric non associative flow rule.
Analytical and geometrical localization analysis is applied particularly for the case of uniaxial compression, based on the properties of the acoustic tensor. The results demonstrate the incidence of the relative brittleness of high strength concretes into the failure behavior in comparison with normal strength concretes.