The numerical model of dynamic mechanical behavior of brittle materials based on the concept of the kinetic theory of strength

A model of the dynamic mechanical behavior of brittle materials based on the ideas of the kinetic theory of strength is developed. The proposed model is a generalization of the classical "quasi-static" Nikolaevsky plasticity model (non-associated flow law with the plasticity criterion in the form of Mises-Schleicher) to the strain rate interval corresponding to the dynamic loading. In contrast to the traditional approach to constructing dynamic models, in which the dependence of the model parameters on the strain rate is specified, the proposed model suggests to use the relaxation time and time of fracture as the key parameters. The presented model allows taking into account the change in the strength and rheological properties of brittle materials with an increase in the loading rate. This ensures a correct transition from the quasi-static regime of loading to the dynamic one in the range of strain rates within 10-33 s-1. Within the framework of the proposed model it is assumed that there exist the experimental data about the dependences of the strength and rheological characteristics of the material on the times of different scales discontinuities nucleation. However, in view of the complexity of obtaining this information, we propose a way of obtaining the estimates of these dependencies by transforming the dependences of the mechanical properties on the strain rate that can be gained with standard tests. The developed dynamic model can be implemented within various Lagrangian numerical methods using an explicit integration scheme (including the finite element and discrete element methods) and is relevant for solving a new class of applied problems related to natural and technogenic dynamic impacts to structures of artificial building materials, including concretes, ceramic elements of structures and natural rock materials.