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The paper presents the development of recently proposed kinetic model of dynamic mechanical behavior of brittle solids. The model uses the ideas of kinetic theory of strength to describe the inelastic deformation and fracture. The main feature of the modified dynamic model is the introduction of two relaxation times, which determine the patterns of inelastic deformation under dynamic loading, including the dependences of the values of the cohesion and strain hardening coefficient on the strain rate. These relaxation times have the meaning of a generation time of damage of the smallest ranks and a characteristic time of formation of a system of local damage and cracks of the greatest rank. The advantage of a developed dynamic model is the possibility of its implementation within different conventional models of inelasticity of brittle solids. In the paper we implemented the kinetic model within the classical “quasi-static” Nikolaevsky’s plasticity model (non-associated plastic flow rule with the plasticity criterion in the form of Mises– Schleicher). We verified the model and determined its parameters by the example of high-strength concrete. The developed dynamic model can be implemented within the framework of various Lagrangian numerical methods (including finite and discrete element methods) using an explicit integration scheme. [ABSTRACT FROM AUTHOR]

Earlier the authors developed a discrete element based numerical model of dynamic mechanical behavior of brittle materials. The model is based on the concept of kinetic theory of strength. An important problem in the application of the proposed model to the study of features of dynamic response of real materials is lack of information about the dependence of model parameters on stress relaxation times (including time of fracture development). The present paper proposes an analytical approach to determining these dependencies for different brittle materials. [ABSTRACT FROM AUTHOR]

2D and 3D models of mechanical behavior of brittle porous material under uniaxial compression loading were developed in the framework of the movable cellular automaton method. The considered material was characterized by pore size distribution function having two maxima. On the basis of simulation results the dependence of the strength properties of brittle porous material on its total porosity and partial porosities corresponding to pores with different size was revealed. The change in internal structure of material in a wide range of mentioned parameters was analyzed. The main structural factors influencing compression strength of the material at various combinations of values of porosity parameters were identified. [ABSTRACT FROM AUTHOR]

In the framework of the movable cellular automata method we have developed a plane/2D model of mechanical behavior of brittle porous material under shear loading. The work considers the material characterized by a function of pore size distribution with two maxima. Based on simulation results, the authors proposed the analytical estimation of the dependence of strength and elastic properties of the material on its total porosity and partial porosities that correspond to the pores with different sizes. [ABSTRACT FROM AUTHOR]

In the present paper the multiscale approach to the construction of rheological models of brittle materials with heterogeneous internal structure is implemented within the numerical method of movable cellular automata. An example of application of the implemented approach to determine the mechanical properties (including parameters of the rheological model and strength) of brittle materials with complicated internal structure at both macroscopic and mesoscopic scales is described. The effect of strain rate on brittle materials behavior under uniaxial compression and tension is analyzed. [ABSTRACT FROM AUTHOR]