A 3D visco-elasto-plastic damage constitutive model of concrete under long-term loads

Abstract

The present paper proposes a 3D coupled elasto-plastic damage model of concrete, incorporating long-term effects at the meso-scale. The model is able to capture permanent deformations, stiffness reduction and creep characteristics of concrete in a unified manner, including local confinement effects and stress concentrations of the cement matrix at the meso-scale. The modelling aspect related to plasticity is based on the pressure-dependent Menétrey–Willam plastic surface, extended to include a scalar damage variable accounting for the reduction in size of the elastic domain as concrete undergoes damage. The modelling aspect related to damage, on the other side, is inspired by the formulation of the isotropic damage by Mazars. Specifically, in the proposed formulation a stress-dependent damage variable is introduced to account for crack closure effects. The long-term effects are taken into account via the B3 creep model by Bažant and Baweja. Some challenging aspects related to the numerical implementation and interaction of the afore-mentioned models are addressed, amongst which the choice of a suitable loading scheme for the numerical implementation of the coupled model, and the mathematical derivation of the visco-elasto-plastic tangent operator. Numerical simulations are performed at the meso-scale, with the cement matrix being characterized by means of the visco-elasto-plastic damage constitutive model developed herein. The calibration of the model is discussed, and the numerical results at the meso-scale prove that the present model is fairly well capable of reproducing the creep failure of concrete materials, even when subjected to high loading levels.