A new constitutive model of concrete developed in the framework of damage and multi-surface plasticity: Theory and verification

Abstract

Within this study, a new constitutive model of concrete for local analysis is formulated based on the uncoupled combination of the theory of plasticity and damage mechanics. The chosen yield function in the theory of plasticity part is uniquely adapted, with separate hardening variables corresponding to the compression and tension meridians in the principal stress space, aiming to describe independent material hardening under cyclic loading. An essential aspect of concrete behaviour, the closure and reopening of existing cracks under cyclic loading, is encompassed by introducing a secondary yield surface into the formulation. The damage mechanics part of the model is formulated by decomposing the stress tensor into positive and negative parts, introducing two damage variables for tension and compression. Introducing a specific exponential function for the damage evolution rule ensures an adequate model response on both the compression and tension sides of the softening response. This function is calibrated according to the concrete strength to simulate the more ductile behaviour of lower-grade concrete and the more brittle behaviour of higher-grade concrete without introducing additional model parameters. The model’s formulation ensures an objective response when modelling structures with different finite element mesh sizes.