Third- and fourth-order weakly nonlinear theories of elasticity are widely used by applied mathematicians, physicists and acousticians. Although their introduction is traced back to a paper by Signorini dated 1930, some aspects related to the rigorous mathematical derivation of the strain energy for quasi-incompressible isotropic elastic solids are not satisfactorily clear. In this paper we address these aspects and use our results to discuss the incompressible limit of some fourth-order nonlinear constitutive parameters.
Some Remarks on the Weakly Nonlinear Theory of Isotropic Elasticity
Saccomandi G.;Vergori L.
2021
Abstract
Third- and fourth-order weakly nonlinear theories of elasticity are widely used by applied mathematicians, physicists and acousticians. Although their introduction is traced back to a paper by Signorini dated 1930, some aspects related to the rigorous mathematical derivation of the strain energy for quasi-incompressible isotropic elastic solids are not satisfactorily clear. In this paper we address these aspects and use our results to discuss the incompressible limit of some fourth-order nonlinear constitutive parameters.File in questo prodotto:
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