2007
DOI: 10.1007/s10778-008-0012-7
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On universal deformations in analysis of Signorini’s nonlinear theory of hyperelastic media

Abstract: It is shown that uniform compression/tension and simple shear as universal deformations are quite useful in studying Signorini's nonlinear theory of hyperelastic materials. They make it possible to formulate restrictions for the elastic constants of the theory and to explain the Poynting effect Keywords: Signorini's hyperelastic model, universal deformations, simple shear, uniform compression/ tension, restrictions for elastic constants, Poynting effect 1. Introduction. During the development of materials mech… Show more

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Cited by 5 publications
(8 citation statements)
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“…Assume that U is a family of solutions to (10a) (13a) as in Proposition 1, depending smoothly on the parameter X , and that (10b) (13b) admits a solution V , square integrable in Y and jointly smooth in (X 2 , X ). (18) where J is the (real) constant given by…”
Section: Surface Wavesmentioning
confidence: 99%
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“…Assume that U is a family of solutions to (10a) (13a) as in Proposition 1, depending smoothly on the parameter X , and that (10b) (13b) admits a solution V , square integrable in Y and jointly smooth in (X 2 , X ). (18) where J is the (real) constant given by…”
Section: Surface Wavesmentioning
confidence: 99%
“…It results to be a nonlocal generalization of the inviscid Burgers' equation of the same type studied by Hunter [15,16] and Benzoni-Gavage [17]. As a reference for the second-order elasticity theory, we cite [5,18].…”
Section: Introductionmentioning
confidence: 99%
“…We will focus on the evolution of the waveprofile. Solutions (65) and (94) Thus, the first difference is that plane and cylindrical waves in a Murnaghan material are analyzed using different approaches.…”
Section: Propagation Of Plane and Cylindrical Hyperelastic Waves In Mmentioning
confidence: 99%
“…Then the form of the linear part suggests that the cylindrical wave looks like a longitudinal plane wave with three more specific differences (than those mentioned above): the amplitude quickly decreasing with distance traveled and the phase variable k r t L --w p ( / ) 3 4 with nonzero shift ( / ) 3 4 p and high uncertainty at small radius. We revert to solutions (65) and (94). Noteworthy is the fact that formula (65) describes two main nonlinear effects for a longitudinal plane wave in a quadratic nonlinear elastic medium: self-generation and second-harmonic generation.…”
Section: Propagation Of Plane and Cylindrical Hyperelastic Waves In Mmentioning
confidence: 99%
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