Theoretical foundations of the grinding of heterogeneous materials

It is shown that a reduction in the energy consumption during the grinding of heterogeneous materials, including polymers, could be achieved by organizing the mechanochemical process of avalanche-like fracturing in such materials. An original classical Hamiltonian formalism based the approach to the description of crack propagation dynamics in homogeneous and heterogeneous solids is developed. The complete analytical dependences of the maximal (ultimate) velocity of supercritical crack propagation in homogeneous materials and the values of crack acceleration (retardation) in different components of stressed heterogeneous materials on the basic mechanical characteristics of such materials are obtained. The conditions of crack propagation, arrest, and multiplication in heterogeneous materials with different scales of heterogeneity are analyzed.