Kinetic approach to the development of computational dynamic models for brittle solids

The paper presents an approach to developing the mathematical formalism of the discrete element method to numerically study the inelastic behavior and fracture of brittle materials under dynamic loading. The approach adopts the basic principles of the kinetic theory of strength which postulate the finite time of nucleation of discontinuities and relaxation of local stresses in the material. A general methodology is proposed for constructing dynamic (kinetic) models of the mechanical behavior of a discrete element based on quasi-static models and using three dynamic material parameters (time parameters). The physical meaning of these parameters is discussed, and a method is proposed for estimating the magnitude of the parameters for a considered material using standard experimental data on its mechanical characteristics. The approach is verified by a dynamic formulation of two-parameter models of inelasticity and strength of brittle materials within the method of simply deformable discrete elements. The proposed way to the dynamic generalization of conventional quasi-static mechanical models is applicable to various Lagrangian numerical methods and makes it possible to numerically study the dynamic behavior features and to predict the mechanical characteristics of brittle materials at different strain rates (up to strain rates 103 s−1) and different types of stress state.