When a material undergoes an elastic deformation, it means that it changes shape due to an applied load, but that when the load is removed, it recovers to its original shape. When a collision between objects is elastic, it means that the total kinetic energy of the objects is preserved (as kinetic energy - overall energy is conserved in all collisions). No macroscopic collisions are truly elastic, although some come close. A frequent cause of highly inelastic collisions is when one or more of the objects suffers a plastic deformation.
See also Elasticity (economics).
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