A Physical Model for the Inelasticity of Concrete

Abstract

A physical model for the inelasticity of concrete is proposed in this paper. The main effects are attributed to microcracking and softening elastoplastic coupling. The composite nature of concrete is seen to influence decisively the process of microcracking, resulting, for instance, in stable crack growth under uniaxial compression, but unstable crack growth under uniaxial tension. A model is proposed that relates the degradation of the elastic compliances of the material to the extent of microcracking, as described by a set of internal variables that represent the sizes of the microcracks oriented along some selected directions. A thermodynamic approach to the inelasticity of concrete is then presented that proves advantageous in characterizing the coupling between the plasticity of the material and its elastic degradation, i. e. elastoplastic coupling. It is shown that a softening elastoplastic coupling may result in lack of normality and in unstable behaviour, in violation of Drucker’s postulates of classical plasticity. A suitable thermodynamic plastic stability criterion is proposed that generalizes Drucker’s second postulate in the presence of elastoplastic coupling allowing for unstable plastic behaviour. A specific model of elastoplastic coupling is then proposed that allows for the explicit generalization of the classical yield criteria when elastoplastic coupling is present. It is shown, with the aid of this model, how a general anisotropic distribution of microcracks renders the plastic yield criterion anisotropic. It is also shown that the plastic strain rates depart from isochoricity in the presence of microcracking, even if the uncracked material exhibits isochoric plasticity. The proposed thermodynamic criterion for the extension of microcracks is seen to generalize the Griffith criterion in the presence of elastoplastic coupling. It is shown that tensile plastic strains in the direction normal to a microcrack tend to decrease the critical stress for the extension of the microcrack, and that compressive plastic strains tend to increase it. Finally, the proposed model is seen to lead to rate-independent stress─strain incremental relations with symmetric tangent stiffness compliances.