Abstract
Concrete materials show a very complex macroscopic deformation behavior under tension and compression, accompanied by crack opening and crack closing phenomena under cyclic loading. The continuum damage mechanics offers a promising framework for the description of the damage deformation behavior. This paper proposes a continuum damage model, which is formulated based on energy equivalence using a unified equivalent strain. The evolution of isotropic damage is governed by two independent history variables to describe the crack opening and closing behavior, i.e., unilateral behavior, of concrete. The evolution of damage and inelastic strains are described by a single damage function and a modified failure surface, respectively. Moreover, the implicit gradient method is applied to the equivalent strains to achieve proper localization of deformation. The stiffness recovery and crack opening/closing mechanisms are simulated considering the thermodynamically consistent framework. Validation of numerical results with experimental data and the previous models demonstrates the efficiency of the model to simulate concrete behavior under monotonic and cyclic/reverse loadings.
Highlights
Concrete remains as a broadly used construction material in the field of civil engineering
A simplified constitutive model for concrete has been developed based on energy equivalence concept to take its distinct deformation behavior under monotonic and cyclic loading conditions into account
A unified equivalent strain is considered as the local measure of deformation driving the evolution of isotropic damage
Summary
Concrete remains as a broadly used construction material in the field of civil engineering. Most of the elastic damage or plastic damage models introduce two independent internal damage variables to represent the distinct behavior of concrete in tension as well as in compression The evolution of these damage variables is based on a damage surface. An effective damage could be considered as a function of two independent history deformation variables associated with two different loading surfaces [27] Thereby, these history variables are related to damage equivalent strains in tension and compression, respectively. The numerical predictions of Mazars’s unilateral model [27] are not smooth enough in the complex region, though this model offers good results with few differences near bisector of bicompression region It is witnessed from the experimental studies on concrete [16,20,26,32] that concrete exhibits inelastic/permanent deformation to some extent under direct cyclic loading or reverse cyclic loading even though this inelastic deformation is not as large as that observed in ductile materials like steel. The localization phenomena are illustrated using a numerical example
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