ENERGY LOSSES IN NORMAL COLLISION OF 'RIGID' BODIES

摘要

For low to moderate speed collisions between elastic-plastic bodies, internal energy gained from work done by the contact force during compression is partially trapped in elastic waves, work done in plastic deformation and work done to overcome friction during sliding. These sources of kinetic energy loss in collisions depend on relative velocity at the contact point, material properties, inertia properties related to the impact configuration and geometric constraints on the deformation field. Hunter [1] showed that the energy losses due to elastic waves emanating from an impact point on a three-dimensional solid are less than 10% of the initial kinetic energy of normal relative motion. Using a similar method of analysis, present analysis indicates that in contrast, the energy loss due to elastic waves in a two-dimensional field (plane strain) is of the order of 40% if the colliding bodies are very dissimilar in size. If the colliding bodies are nearly equal in size, the energy loss to elastic waves is again negligibly small. Thus for similar bodies and impact conditions, the two-dimensional deformation fields (plane strain) dissipate substantially more energy than three-dimensional fields - the differences are due to elastic waves and plastic deformation. The results explain some anomalies present in two-dimensional finite element simulations of three-dimensional impact problems.