Simulation and visualization of solid deformation upon impact

Abstract

The use of adequate mathematical models to study the process of deformation of solids is an urgent issue for industrial engineering. It is known that under mechanical action the bodies are deformed and mechanical stresses arise in them, which, in turn, lead to destruction. Therefore, the simulation of deformation processes can be useful both in studying the issues of strength and reliability of equipment and for solving problems of fine grinding of solid fuels. Classical continuum models of continuum mechanics are useful for studying mechanical stresses in idealized environments and for bodies of regular shape. Their application in the analysis of heterogeneous structures and objects of complex shape encounters significant difficulties. In such cases, a number of simplifying assumptions have to be introduced, which reduces the adequacy of the models. A discrete model which considers a solid body as a set of local elements connected by elastic bonds is used in the research. A significant difference between the proposed approach and the one previously used is the following. In previous models, the separate local element of unit mass was a discretization step of space. In the new interpretation, the discretization step is consistent with the behavior of a system (set) of several interacting unit masses. An improved approach to the analysis of the process of deformation of a solid has been investigated. A model that allows studying not only axial deformations (compression – tension) but also the effects of changes in transverse dimensions (shear) has been proposed. It has been established that this approach to modeling can significantly simplify the visualization of the process at each step of the discrete time. The obtained results have made it possible to improve discrete approaches to simulation of solids deformation process. At the same time, it has become possible to model not only axial deformations (compression – tension), but also the effects of changes in transverse dimensions (shear). The discrete approach to modeling has enabled to significantly simplify the visualization of the process at each step of the discrete time. The study has shown that the discrete approach allows analyzing the stress state and visualizing the propagation of deformation waves in solids at free impact. The data on the propagation of elastic waves obtained by computer simulation coincide with the results of preceding physical experiments. The discrete approach does not create difficulties in analyzing the behavior of heterogeneous bodies of complex shape, since the design features are considered at the local level and do not require adjustment of the modeling algorithm.