Advances in peridynamics modeling of deformation and fracturing of brittle geomaterials

Peridynamics (PD) is an emerging method that establishes a theoretical framework based on non-local theory to describe material mechanical behavior with spatial integral equations. It gives a unified expression of the medium including state transformation and characterization in different scales. It is showing great potential for evaluating the complicated mechanical behaviors of brittle solids. In the past two decades, peridynamics has been showing its great potential and advantages in modeling crackings of brittle materials although there are many challenges. The present paper summarizes firstly the theoretical framework and advantages of peridynamics for modeling fracturing. It introduces then the theoretical improvements to address challenges of peridynamics in modeling brittle solid crackings including the release of Poisson ratio limit, different fracture criteria, contact-friction models, coupled constitutive models, and computing accuracy. Afterward, the extension of peridynamics is introduced to the coupled modeling with the other methods such as finite element method, phase field method, and particle-like method before its applications in static and dynamic cracking as well as those under impacts. Meanwhile, some contents that require further exploration are briefly summarized. Finally, the blind spots and future development of peridynamics are analyzed and discussed for the deformation and fracturing modeling of brittle geomaterials. • Advances in peridynamics modeling for brittle geomaterials were introduced. • Fracture criteria and contact-friction models of cracking were classified and analyzed. • Eight kinds of physical field models and constitutive models were counted. • The simulation of mechanical behavior in static/dynamic/impact cracking was summarized. • The implementation and category of the existing coupling method were given.