An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis

Abstract

An extended bond-based peridynamic (PD) approach is presented for quasi-static mechanical behavior and brittle failure analysis of materials and structures. A local artificial damping is introduced into the peridynamic equations of motion, and a step-by-step loading method and a non-equilibrium criterion are employed to calculate the elastic response quantitatively, simulate the crack initiation and propagation and predict the extreme failure load of structures. The effect of the magnitude of the local damping on the accuracy and efficiency of elastic calculation is investigated. In the proposed model, another important feature lies in the micromodulus of the pair-wise bond, which is described as a continuous function of the distance between two particles within the material horizon and is demonstrated to be more accurate when compared to the earlier PD models using a fixed stiffness constant to describe the interaction of particles. The qualitative and quantitative validity of the approach is established through simulating the mechanical response and fracture of a cantilever concrete beam, including the whole process from the earlier elastic deformation stage to crack initiation and propagation, and making comparisons to the analytical and other numerical data. To further demonstrate the capabilities of the proposed model, the crack propagation and fracture mechanism of a cantilever concrete beam with pre-existing notch is studied, and the effect of the notch location on the extreme failure load and fracture mode of the structure is examined.