Abstract
The simulation of dynamically created fractures in porous solids is a complex problem with important practical applications in areas such as hydraulic fracturing and enhanced geothermal systems. Peridynamics is a relatively recent formulation of solid mechanics which has attractive features in simulating fractures, both theoretical and in numerical implementation. The method is gridless, making the evolution of three-dimensional cracks in arbitrary topologies straightforward. To date it has been successful in simulating dynamic impact and fragmentation problems as well as in the delamination of composite materials, but its application to hydraulic fracture has not been reported. In this paper we report progress toward this goal, by elucidating a simple coupled formulation between fluid flow and fracture which may serve as a starting point for more advancedmodeling. Particular attention is paid to the communication of pressure forces on the newly formed faces of the crack.
1. INTRODUCTION
Peridynamics is a theory of continuum mechanics which has shown to be successful in applications of dynamic impact and fragmentation, as well as in delamination of composite materials [1, 2]. A basic idea of the theory is to consider pairwise interactions of material points interacting with one another over a small radius, called the horizon. The interactions can occur over several depths of neighbor particles, so the theory is termed non-local. There are no spatial gradients required in the theory, so in a fracture process the numerical behavior is stable. A drawback of original bond-based theory is that one is restricted to consider materials with a Poisson ratio of ¼ in three dimensions, and overall the constitutive behavior is limited (e.g. not able to capture plastic flow incompressibility). Even with these issues, the basic bond-based theory of peridynamics clearly has attractive properties in application to fracture simulations (e.g. more accurate crack patterns compared to other methods [2]). Recently, it has been applied to geomechanics problems [3], and its momentum will surely increase. Even aside from considering fractures, we find it also has well behaved numerical properties, and does not generally require special stabilization approaches like some other gridless methods, such as Smoothed Particle Hydrodynamics (SPH). Therefore, a desire tomodel dynamic crack growth in applications such as hydraulic fracturing makes peridynamics a strong candidate to consider.
