Basic Theory of Small-Amplitude Waves in a Constrained Elastic Body

Chadwick, P.; Whitworth, A. M.; Borejko, P.

doi:10.1007/978-3-642-61598-6_4

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…of constrained classical thermoelasticity, see equations (2.15) and (2.16) in the work by Chadwick and Scott [8], in place of the four field equations (7) of unconstrained classical thermoelasticity. The third part of equation ( 10) is simply the constraint equation ( 8) repeated.…”

Section: Constrained Classical Thermoelasticitymentioning

confidence: 99%

“…We define a stable wave as a wave whose amplitude remains bounded in the direction of propagation. For an isothermal or isentropic elastic material we recall that three stable waves may propagate in each direction and that only two stable waves propagate if a purely mechanical constraint operates, see Chadwick et al [7]. Thus the presence of a purely mechanical constraint removes one mode of propagation but maintains the stability of the system.…”

Section: Introductionmentioning

confidence: 99%

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Stability in constrained temperature-rate-dependent thermoelasticity

Alharbi

Scott

2017

Mathematics and Mechanics of Solids

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In an anisotropic temperature-rate-dependent thermoelastic material four plane harmonic waves may propagate in any direction, all dispersive and attenuated, and all stable in the sense that their amplitudes remain bounded in the direction of travel. In this paper, the material is additionally assumed to suffer an internal constraint of the deformation-temperature type, i.e. the temperature is a prescribed function of the deformation gradient. In this constrained thermoelastic material four waves continue to propagate but instabilities are now found. Constrained temperaturerate-dependent thermoelasticity is then combined with generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation. Four waves again propagate but instabilities are found as before. Anisotropic and isotropic materials are both considered.

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Section: Constrained Classical Thermoelasticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability in constrained temperature-rate-dependent thermoelasticity

Alharbi

Scott

2017

Mathematics and Mechanics of Solids

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“…Among other distinguished as well as popular works [1], Peter Chadwick made several contributions to the wave propagation problems in anisotropic models with different kinds of symmetries as well as those applicable to the theory of lattice defects [2][3][4][5][6][7][8]. His research into 2020 The Authors.…”

Section: Introductionmentioning

confidence: 99%

Scattering on a square lattice from a crack with a damage zone

Sharma

Mishuris

2020

Proc. R. Soc. A.

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A semi-infinite crack in an infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack tip is modelled by an arbitrarily distributed stiffness of the damaged links. While an open crack, with an atomically sharp crack tip, in the lattice has been solved in closed form with the help of the scalar Wiener–Hopf formulation (Sharma 2015 SIAM J. Appl. Math. , 75 , 1171–1192 ( doi:10.1137/140985093 ); Sharma 2015 SIAM J. Appl. Math. 75 , 1915–1940. ( doi:10.1137/15M1010646 )), the problem considered here becomes very intricate depending on the nature of the damaged links. For instance, in the case of a partially bridged finite zone it involves a 2 × 2 matrix kernel of formidable class. But using an original technique, the problem, including the general case of arbitrarily damaged links, is reduced to a scalar one with the exception that it involves solving an auxiliary linear system of N × N equations, where N defines the length of the damage zone. The proposed method does allow, effectively, the construction of an exact solution. Numerical examples and the asymptotic approximation of the scattered field far away from the crack tip are also presented.

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Basic Theory of Small-Amplitude Waves in a Constrained Elastic Body

Cited by 2 publications

References 13 publications

Stability in constrained temperature-rate-dependent thermoelasticity

Stability in constrained temperature-rate-dependent thermoelasticity

Scattering on a square lattice from a crack with a damage zone

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