Topological measure of brittle fragmentation (Q1317149)

A new approach for quantitative analysis of fragmentation for brittle materials is developed with the aid of axioms of continuum mechanics, fracture mechanics and topology. The principles of energy balance are used to establish the field equations for the surface and volume of a fragment which is homeomorphic to a sphere. The global and local geometric constraints on fragmentation are unveiled as a deterministic description of a crack network by use of the Euler theorem and energy transformation. A new physical parameter, the dissipative rate of surface energy, is derived which provides a theoretical basis for understanding the latest experimental results.