A Shear Induced Damage of Concrete Using Local and Nonlocal Models

Abstract

Concrete is one of the most widely used construction material. Despite notable research, the concrete modeling is still complex task. To model unsymmetric concrete behavior under tensile and compressive loading, most of the researchers consider two types of damage in concrete i.e., tensile damage and compressive damage., which itself includes the shear damage in them. The shear damage is not separately considered under loading response of concrete. Therefore, 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. To capture shear damage, the concept of stress decomposition by utilizing fourth-order projector tensor is adopted. Two types of shear damage are considered in the proposed working, first one is shear-induced due to unequal same signed biaxial principal stresses, while the second one is due to opposite signed biaxial principal stresses. In the first approach, with the classical stress decomposition into positive (tensile) and negative (compressive) 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 damage 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. The 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. The model so far is local, with no interaction with neighboring integration points, which will eventually cause strain softening and damage localization under loading. The model is extended to nonlocal by using a gradient enhanced approach. The local model (which can handle directional dependency of damage, pure shear and biaxial damage, damage activation/deactivation, and microcracks opening/closure) is extended to a nonlocal model which can capture distinct behavior of concrete in tension, compression, and shear by utilizing three length scales (tension, compression, and shear). The model is implemented in Abaqus UEL-UMAT subroutine with eight noded quadrilateral user-defined element, having five degrees of freedom (u_x,u_y,▁eq^+,▁eq^-,▁eq^s) at corner nodes and two degrees of freedom at internal nodes (u_x,u_y). Five examples of mixed crack mode and mode-I cracking are modeled to show the performance of the model. In the second approach, a damage model for concrete is proposed with an extension of the stress decomposition (limited to biaxial cases), to capture shear damage due to the opposite signed principal stresses. To extract the pure shear stress, the assumption is made that one component of the shear stress is a minimum absolute of the two principal stresses. The opposite signed principal stresses are decomposed into shear stress and uniaxial tensile/compressive stress. A local model is implemented in Abaqus UMAT and it is further extended to a non-local model by utilization of the gradient theory. The concept of three length scales (tension, compression, and shear) and model implementation in Abaqus UEL-UMAT is kept the same as is described in the first approach. Some examples of a local model including uniaxial and biaxial loading are addressed. Also, five examples of mixed crack mode and mode-I cracking are presented to comprehensively show the performance of this model. The two different approaches, to extract shear stresses by projector tensor, and applying the concept of stress decomposition to capture shear damage are successfully applied, which will characterize each type of damage separately (tensile, compressive, and shear). There can be more ways to capture shear damage from tensile and compressive parts distinctly. However, here it is limited to two approaches by stress decomposition, which are due to unequal same signed principal biaxial stresses and due to opposite signed principal biaxial stresses. The purpose to capture shear-induced damage is that to predict the crack path based on principal stresses, from diffusive to localized for shear, tensile and compressive stresses independently (generally, pure shear crack is 45 degrees, tensile crack is orthogonal to the principal stresses, and compression crack is parallel to the principal stresses). Consequently, the work presented here is in a continuum damage framework. The above goal can be achieved in the future by merging continuum mechanics and fracture mechanics. The proposed models can capture well the numerical response. The response under normal loading (classical tensile and compressive) along with shear loading (using proposed models) gives good agreement with experimental results. The location of shear damage that affects the tensile and compressive damage is accurately predicted. Here, two different hypotheses are tested, and both give different shear locations depending on the type of stresses from which the shear damage evolve. The proposed models are adaptive, if the loading is classical (not including shear as per hypothesis), it will act as a traditional model and if the loading includes shear effect (as per hypothesis), it will present both effects (classical tensile/compressive and novel shear effect).