In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the external forces computed assuming these forces had remained constant from the initial state to the final state.
[1] It is named after the French scientist Émile Clapeyron.
For example, consider a linear spring with initial length L0 and gradually pull on the spring until it reaches equilibrium at a length L1 when the pulling force is F. By the theorem, the potential energy of deformation in the spring is given by: The actual force increased from 0 to F during the deformation; the work done can be computed by integration in distance.
Clapeyron's equation, which uses the final force only, may be puzzling at first, but is nevertheless true because it includes a corrective factor of one half.
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