Advanced general particle dynamics with nonlocal foundation for fracture analysis

Abstract

The general particle dynamics (GPD), which is based on the kernel approximation method and Navier–Stokes equation, was developed from smoothed‐particle hydrodynamics to simulate the fracture behaviors by using the collective of damage variable to describe the damage evolution behaviors. In this paper, an advanced GPD with a nonlocal foundation is proposed for better description of the solid mechanics. The nonlocal vector calculus and microscopic constitutive model are employed to derive the governing equations in the proposed theory. The novel GPD with a nonlocal core is a generalization, which permits the inclusion of the microscopic constitutive model and the multi‐scale modeling compared with the previous GPD. To accomplish this generalization, the relationship between GPD and the previous kernel‐based theory is established. The novel GPD is superior in the fracture problems and multi‐scale modeling. Some numerical experiments are launched to verify the ability of the novel GPD.

Hydromechanical coupling model for mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics

“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48…”

“…where ρ is density of rocks and the Kronecker delta, δ ij , values are 1 and 0, respectively, indicating whether the influence of hydrostatic pressure is considered. Considering a finite nonlocal influence domain, under the hydromechanical coupling condition, Equation 18 can be rewritten as 47,48…”

“…Considering a finite nonlocal influence domain, under the hydromechanical coupling condition, Equation 18 can be rewritten as 47,48 where w ( y ‐ x , Δ) is a kernel function, Δ is the radius of the influence domain, b ( x , t ) is the external force, and f is the nonlocal long‐range force under the hydromechanical coupling condition. In porous medium such as rocks, the nonlocal long‐force f considering the pore water pressure takes the following form based on Biot's theory 49 : where c xy is the micro‐elastic bond parameter, is the state function of a bond, α is Biot's coefficient, γ is the coefficient of pore water pressure, is the average pore water pressure on bond between particles and , is the stretch scalar vector, and and are, respectively, the current and initial bond.…”

“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48 where ρ [ v ( y ) + v ( x )] / 2 is defined as a nonlocal velocity divergence.…”

“…Moreover, the critical stretch can be expressed as 48 where μ is shear modules, κ is bulk modules, and is the critical energy release rate.…”