Investigation of Mesh Dependence of Stochastic Simulations of Quasibrittle Fracture

Abstract

This paper presents a new crack band model for stochastic finite element (FE) simulations of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization and propagation. This study focuses on the case in which the finite element size is larger than the width of the localization band. A weakest link model is used to describe the probabilistic onset of damage localization inside the element, where the randomness of the location of the localization band is related to the random material strength. Meanwhile, the model also includes the regularization of fracture energy for the transition from damage initiation to localization. The proposed model is applied to analyze the probability distributions of nominal strength of quasibrittle structures of different geometries. The results show that, without a proper treatment of probability distributions of constitutive parameters, the direct application of the conventional crack band model for stochastic FE simulations would lead to mesh-sensitive results. The proposed model is able to effectively mitigate this issue of spurious mesh sensitivity.