A micro-potential based Peridynamic method for deformation and fracturing in solids: A two-dimensional formulation

Abstract

A two-dimensional micro-potential based Peridynamic (MPPD) formulation is proposed to investigate deformation and fracturing in solid materials. To this end, square measure of the bond length change is applied and a generalized Peridynamic (PD) strain for plane stress and strain problems is developed to decompose the bond length change into two parts, one resulting from the volumetric PD strain and the other from the deviatoric PD strain. The micro-potential generated in the deformed bond is postulated as a function of both length change components. The nonlocal elastic strain energy density (NESED) at a material point is computed by the integral of the bond potential over the horizon. Through the Frechet derivative of the NESED, a general constitutive relation depending on the micro-potential function is well formulated. The model parameters are calibrated through the equivalence of the NESED with the linear elastic strain energy density. Several specific micro-potential functions and their corresponding constitutive force densities are carefully discussed. The discussions reveal that the proposed MPPD model not only can retrieve the well-known bond based PD model, but also allows specific materials with any Poisson ratio to be represented. Moreover, one failure criterion based on the total micro-bond potential is developed for the present model. The reliability and efficiency of the MPPD model is demonstrated through numerical tests. Simulation results show that the proposed model is capable of investigating deformation and cracking in solids.