A model for damage of microheterogeneous kidney stones

In this paper, a theoretical framework is developed for the mechanics of kidney stones with an isotropic, random microstructure—such as those comprised of cystine or struvite. The approach is based on a micromechanical description of kidney stones comprised of crystals in a binding matrix. Stress concentration functions are developed to determine load sharing of the particle phase and the binding matrix phase. As an illustration of the theory, the fatigue of kidney stones subject to shock wave lithotripsy is considered. Stress concentration functions are used to construct fatigue life estimates for each phase, as a function of the volume fraction and of the mechanical properties of the constituents, as well as the loading from SWL. The failure of the binding matrix is determined explicitly in a model for the accumulation of distributed damage. Also considered is the amount of material damaged in a representative non-spherical collapse of a cavitation bubble near the stone surface. The theory can be used to assess the importance of microscale heterogeneity on the comminution of renal calculi and to estimate the number of cycles to failure in terms of measurable material properties.