Abstract
Using the variational point of view, the constitutive equations of an elastic one-dimensional string are deduced from the stress-strain relations of nonlinear three-dimensional elasticity, by passing to the limit when the other dimensions go to zero. The assumptions made on the three-dimensional model are not very restrictive.
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Acerbi, E., Buttazzo, G. & Percivale, D. A variational definition of the strain energy for an elastic string. J Elasticity 25, 137–148 (1991). https://doi.org/10.1007/BF00042462
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DOI: https://doi.org/10.1007/BF00042462