A nonlocal damage model for concrete with three length scales

Abstract

In the presented work, a nonlocal gradient enhanced damage model for concrete is proposed with a stress decomposition, to account for shear induced damage. The nonlocal model is an extension of the recently proposed local plasticity damage model by the authors, which can handle directional dependency of damage, pure shear and biaxial damage, damage activation/deactivation and microcracks opening/closure. The gradient enhanced approach is utilized for the extension of the local model. Due to the distinct behavior of concrete in tension, compression and shear, three length scales (tension, compression and shear) are incorporated, depending on local damage variables. The model is implemented in Abaqus UEL-UMAT subroutine with eight node quadrilateral user defined element, having five degrees of freedom $$ \left( {{\text{u}}_{x} ,{\text{u}}_{y} ,\underline{\text{eq}}^{ + } ,\underline{\text{eq}}^{ - } ,\underline{\text{eq}}^{s} } \right) $$ at corner nodes and two degrees of freedom at internal nodes $$ \left( {{\text{u}}_{x} ,{\text{u}}_{y} } \right) $$ . Five examples of mixed crack mode and mode-I cracking are modeled to show the performance of the model.