The most commonly adopted method to test the strength of single sand particles is based on platen experiments. This setup tends to align the loading direction towards the particle minimum axis and provide an upper limit for the breakage stress. This paper numerically bypasses such limitation by using a combined finite and discrete element method (FDEM). FDEM was first validated via a mesh size analysis of a spherical particle and calibrated by in-situ experimental compressions of the single quartz sand particle, where the particle shape was obtained by X-ray micro-computed tomography (XCT) and then imported into the numerical model. Systematic point loading tests were recreated to explore the role of the curvature at contacting points on the breakage behaviour. The simulations allow to probe the same non-spherical particles, i.e., realistic quartz sand and ellipsoid particles, with multiple measurements highlighting the importance of the loading direction, which was inaccessible experimentally. Results show that FDEM can capture not only the crack initiation but also fracture patterns, while taking into account realistic shapes. It is found that the distance between two contact points and their combined curvedness reflecting the particle morphology are the two major factors governing fracture patterns and stresses. When loading is roughly parallel to the minimum principal dimension of particles, the obtained breakage stress and the number of fragments approach the upper limits.