According to Love (Love, A.E.H., "A Treatise on the Mathematical Theory of Elasticity", 4th ed. Cambridge, 1927, p. 173), "The potential energy of deformation of a body, which is in equilibrium under given load, is equal to half the work done by the external forces, acting through the displacements from the unstressed state to the state of equilibrium." This is commonly known as Clapeyron's theorem in linear elasticity theory, first noted in 1833. In particular, this theorem implies that the accumulated elastic stored energy for a body in equilibrium accounts for only half of the work that is spent to distort the body. The remaining half of the work done to the body by the external forces is unaccounted for and apparently is lost somewhere in achieving the equilibrium state. It is natural, then, to question the whereabouts of this lost work. In this talk, we bring into evidence the richer dynamical theories of elasticity, viscoelasticity and thermoelasticity in order to shed light on the seemingly paradoxical and incomplete conclusion that is implicit in this classical and important theorem.
This talk is based on joint work with Lev Truskinovsky.
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