Structural size effect in concrete using a micromorphic stress-based localizing gradient damage model

Abstract The presence of a nonlinear fracture process zone (FPZ) plays a crucial role in governing the failure response of a quasi-brittle structure. One such influence is the structural size and boundary effect phenomenon, where the growth and interaction of FPZ with the boundary has a considerable impact on the load-carrying capacity of the structure. In this article, a numerical study is conducted using a micromorphic stress-based localizing gradient damage model [1] , recently proposed by the authors, to capture the structural size effect phenomenon during quasi-brittle failure of geometrically similar concrete beams. The main objective is to reproduce the results of independent experimental investigations on the size effect in quasi-brittle structures using a single set of material and numerical parameters. Generally, a quasi-brittle fracture process starts with a diffuse network of microcracks, which eventually localizes in a narrow process zone before forming a macroscopic crack during the final stages of failure. To comply with this description, the micromorphic stress-based localizing gradient damage model incorporates evolving anisotropic nonlocal interactions throughout the loading process through an anisotropic interaction tensor and a damage dependent interaction function. A new arc-length control method based on rates of the internal and dissipated energy approach [2] is modified as per the localizing gradient damage formulation and implemented to trace the nonlinear behavior in numerical simulations. The damage model successfully reproduces the experimental results with localized damage profiles using low-order finite elements for both mode-I and mixed-mode cases.