Anisotropic Vertex Plasticity Formulation for Concrete In-Plane Stress

Abstract

Anisotropy due to directional loading in concrete has been observed not only in the postpeak range, but also before the peak strength is reached. The traditional isotropic description of a self-similar loading surface exhibits severe limitations when nonproportional or nonmonotonic load histories are considered. In this paper, we develop an anisotropic description of concrete using the vertex format of the Rankine criterion in which the strength values in each principal stress direction are assumed to fend for themselves. In biaxial tension, the two Rankine-type loading functions are fully decoupled, while in biaxial compression, the two complementary loading functions are interrelated. For the postpeak behavior, we adopt a fracture energy formulation, which distinguishes failure in terms of separate compressive and tensile components. Four internal state variables monitor the anisotropic evolution of the loading surface, whereby the increasing ductility in biaxial compression is taken into account. Nonassociated flow controls the amount of inelastic dilatancy, which has been observed in many concrete experiments in compression. In conclusion, we contrast the shortcomings of the classical isotropic description with the anisotropic formulation presented in this paper. Specifically, we examine the fracture energy concept with finite-element mesh size sensitivity studies of different height concrete specimens subjected to uniaxial compression.