An adaptive, yet simple, single particle fracture model is developed within the context of a poly-ellipsoidal Discrete Element Method (DEM). The particle fracture model consists of two steps: (1) a criterion (such as maximum principal tensile stress) to sub-divide a parent poly-ellipsoidal particle into eight child sub-poly-ellipsoids, and (2) placement of rigid cohesive springs between the sub-poly-ellipsoids which when broken allow some or all of the sub-poly-ellipsoids to become individual particles. These individual sub-poly-ellipsoids may further sub-divide and break. This model has two main advantages: (a) it does not a-prior cluster sub-particles with bonds to in turn allow bond-breakage and clustered-particle fracture, which can become expensive computationally when considering realistic sand grain sizes in a region of interest (on the order of 100s of millions of particles, to possibly over 1 billion particles); and (b) the poly-ellipsoid particle shape allows minimal loss of mass and inter-particle contacts during the sub-division step (1). Main disadvantages are (i) even though better than spheres, the parent poly-ellipsoid and child sub-poly-ellipsoids are limited to the poly-ellipsoid particle shape approximation, and (ii) sub-poly-ellipsoid bonds occur along the principal axes of the parent poly-ellipsoid, which depends upon the geometric orientation of the particle, not its maximum principal stress plane. We consider spherical particles modeled as poly-ellipsoids currently to address this orientation effect. To demonstrate the efficacy of the DEM particle fracture model, high strain-rate split Hopkinson pressure bar (SHPB) experiments on silica sand are simulated with calibrated particle fracture parameters. Comparison with SHPB experimental data shows that the DEM particle fracture model can represent particle crushing under SHPB uniaxial strain conditions reasonably well.