Damaged plasticity model for concrete using scalar damage variables with a novel stress decomposition

Abstract

In the presented work, a new plastic damage model for concrete is proposed with a novel stress decomposition, to account for shear induced damage. A consistent thermodynamic approach is used to derive the constitutive model. With the classical stress decomposition into positive and negative components, the novel stress decomposition is developed to further decompose tensile and compressive parts into pure biaxial shear and pure tensile/compressive biaxial stresses. This decomposition introduces four additional scalar damage parameters (ϕ±S, ϕ±EB). The additional damage parameters with classical damage parameters (ϕ+, ϕ−) are responsible for the different damages induced under loading. The two traditionally used, damage criteria (tensile/compressive) are further decomposed into four damage criteria (tensile/compressive shear, tensile/compressive pure) depending upon the formation of novel decomposition. The delayed damage growth, reduction in damage evolution and ductile behavior under triaxial confining stresses are captured by suppression of damage evolution and retardation of plastic hardening depending upon the confining stresses and minimum principal strain. The plasticity yield criteria and non-associative plastic flow rule with multiple hardening functions are presented in the effective stress space. Strain equivalency hypothesis is utilized for the transformation from effective configuration to damaged configuration. A Helmholtz free energy elastic-plastic function is described to define the relationship between the elastic-plastic-damage constitutive model and internal state variables. The damage-elastic-plastic consistent tangent operator is also derived.