3D behaviour of a 4 parameter isotropic nonlinear hardening plasticity model for concrete

Abstract

In general, concrete is a highly nonlinear material with great dependence on the confining stresses, a type of behaviour also common in other granular and quasi-brittle materials. The CEB-FIP Model Code [1] recommends the use of a four-parameter failure criterion to estimate the strength of concrete under multiaxial states of stress. This failure criterion is also known as the Ottosen failure criterion, and it captures with high accuracy the behaviour of these materials, as demonstrated by several researchers, performing experimental test programs. The concrete strength estimation takes into account, with great precision, the effect of the increase in the confining stresses. In order to simulate the monotonic quasi-static multiaxial behaviour of concrete, one possible strategy is to introduce in this failure criterion a hardening parameter and the corresponding evolution law, under the isotropic behaviour framework. In the present work, the concrete compressive strength in the Ottosen failure criterion is assumed as the hardening parameter, and the CEB-FIP Model Code 90 law for the uniaxial nonlinear behaviour of concrete is used to derive the hardening law. In this case, the loading surface is not explicitly defined as a function of the hardening parameter, as in the other more common and simpler isotropic models. As a consequence, some difficulties may emerge, mainly of a numerical nature. In this context, the formulation of the model in a thermodynamically consistent framework is presented. The general behaviour of this model is accessed by the simulation of the monotonic multiaxial loading of concrete elements, and its numerical efficiency is discussed.