An enhanced local damage model for 2D and 3D quasi-brittle fracture: ABAQUS-FEM implementation and comparative study on the effect of equivalent strains

In this paper, the initiation and propagation of cracks in quasi-brittle materials are characterized by an enhanced local damage model. The model is implemented using UMAT, an ABAQUS user-subroutine platform, for fracture in two- and three-dimensional media. As usual, the material state is represented by a damage parameter $D$ ranging from 0 (intact) to 1 (completed failure). Different from the conventional local damage models (Kachanov [1], 1999), (Lemaitre [2], 1985) both fracture energy and characteristic length of the element are incorporated into the calculation of the damage parameter, hence the inherent issue of mesh-dependency is mitigated. A comparative study on the effect of equivalent strain on the prediction of crack path as well as load–displacement curve under mixed-mode condition is conducted. For that purpose, three types of equivalent strain are adopted based on three models: the modified von Mises model, the Ottosen criterion model, and the new Mazars model (named after the work of Mazars et al., [3] (2015) in this paper). The accuracy and performance of the developed codes and proposed damage approach in association with the three types of equivalent strain are demonstrated by comparison of the computed results with experimental data as well as other numerical results reported in the literature. The experimental data is well-fit by the simulation results. A detailed description of implementation in UMAT subroutine is also provided. The source codes are provided for free, and users can amend them for their own purpose.