The boundary element method (BEM) and discrete element method (DEM) are combined to calculate the internal stress and breakage paths of brittle granular materials. DEM is exerted to simulate the interaction between particles and the contact forces on each particle. Then

the calculation of the stress distribution inside the particle is conducted using BEM

during this procedure

the non-static or dynamic equilibrium of a particle is taken into consideration via treating the acceleration of particles as constant body force. Meanwhile

the body force leads to a domain integral in boundary integration equation (BIE)

to avoid BEM losing the traditional advantage

i.e.

dimension reduction

the domain integral is treated by the line integration method (LIM) and transformed into boundary integrals. In order to improve the computational efficiency of BEM

for particles with similar geometric shape

a random particle can be used as the template particle in the granular system

only the calculation of coefficient matrices of the template particle in the local coordinate system is needed

then

coefficient matrices of the rest particles can be obtained by mapping the solutions between the local and global coordinate systems. After the stress field is obtained

the Hoek-Brown criterion is applied to estimate whether particles are “broken” or not. Additionally

the breakage path that is assumed as a straight line can be obtained based on the least-squares fit.