Abstract
A continuous initial or initial—boundary value problem for an elastic viscoplastic string on an elastic viscoplastic foundation is formulated and an energy identity/inequality is deduced. Bounds in energy of the solutions are derived and the stress deviation of the viscoplastic model from the plastic one is estimated. As a farther limiting case similar results are derived for the rigid perfect plastic case. It is also shown that the energy identity/inequality is applicable to the discontinuous problem of impulsive loading of a rigid perfect plastic model when the horizontal motion of the string is neglected and that the total energy is preserved in this case.
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