# Investigation of Dynamic Interactions of Solids by Methods of Mathematical Simulations

A.M. Lipanov, A.V. Vakhrouchev, A.Yu. FedotovHigh-speed impact loading of solids is widely used in engineering, industry, military affairs. In considering of this process the main problem is to study the level of destruction and fragmentation of interacting solids based on the calculation and analysis of stress-strain state. The destruction and fragmentation of obstacles, failure mode, the processes of spall fracture, the value of overload, integral resistance force introduction, the final depth of penetration rate in through the destruction of solids, studies of the effect of reinforcing the processes of destruction zone configuration shock interaction, movement solid in the barrier and free space are the main applied objectives of the study. The analysis of experimental data shows that the mechanisms of destruction are significantly change with variation in the parameters of the impacting body and barrier properties. Therefore, the simulation of these processes is a topical problem. The simulation of processes of penetration and destruction is usually performed using numerical methods: finite element method, and the method of smooth (antialiased) particles because of their complexity and interconnectedness. The paper describes the methodology of the processes of dynamic interaction of solids. A mathematical model of the interaction includes the laws of conservation of mass, momentum and energy equations of state, the model of the stress-strain state of the materials. The numerical model is based on an approximation of the fundamental laws of conservation of explicit Euler equations. Interacting bodies are considered as a collection of particles with certain physical and mechanical properties. This model is called a smoothed particle hydrodynamics(SPH) method and is widely used in intensive dynamic loading of bodies, where there is a significant change in the topology of modeled objects.Full text

- Keywords
- theory of deformable solids; simulation; smoothed particle hydrodynamics; SPH; dynamic effects.
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