# Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

Abstract: A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above...

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50 citations

### Cites background from "Nonlocal theory of thermoelastic ma..."

...This shows that x ¼ xc acts as a cutoff frequency for the existing transverse wave, a conclusion in accordance with that earlier mentioned by Sarkar and Tomar [14]....

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...(24), we see that the speed of transverse wave in thermoelastic medium with voids reduces to the classical transverse wave speed, a result recently obtained by Sarkar and Tomar [14] in the relevant medium when r 6¼ 1....

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...Within the framework of Eringen’s theory of nonlocal elasticity [1], the constitutive relations for thermoelastic solid with voids are given by [12,14] 1 e2r2 ð Þsij 1⁄4 sij 1⁄4 2leij þ kekk þ b/ ch ð Þdij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / n/ bekk þmh; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk þ ahþm/; (4)...

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...Bachher and Sarkar [12] established a nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer....

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...Biswas and Sarkar [13] reported fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model....

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43 citations

40 citations

### Cites background from "Nonlocal theory of thermoelastic ma..."

...Other symbols have their usual meanings and borrowed from [50]....

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...Field equations and constitutive relations Within the framework of Eringen’s theory of nonlocal elasticity [2], the constitutive relations for thermoelastic solid with voids are given by [50] 1 e2r2 ð Þtij 1⁄4 t ij 1⁄4 2leij x ð Þ þ kekk x ð Þ þ b/ x ð Þ ch x ð Þ 1⁄2 dij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i x ð Þ; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / x ð Þ n/ x ð Þ bekk x ð Þ þmh x ð Þ; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk x ð Þ þ ah x ð Þ þm/ x ð Þ; (4) where the quantities tL ij; h L i ; g L and ðqgÞ correspond the local thermoelastic solid with voids....

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37 citations

### Cites background from "Nonlocal theory of thermoelastic ma..."

...[70] M. Bachher, N. Sarkar, Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer, Waves in Random and Complex Media, pp. 1-19, 2018....

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...Bachher and Sarkar [70] established a new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative to study transient wave propagation in an infinite thermoelastic material....

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36 citations

### Cites background from "Nonlocal theory of thermoelastic ma..."

...where n = 5 and αj and Kj are complex numbers and given as [45,46]....

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##### References

4,124 citations

### "Nonlocal theory of thermoelastic ma..." refers methods in this paper

...Laplace transform [45] together with an eigenvalue approach [33,46] technique is employed to obtain the closed form solutions in the transform domain....

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1,870 citations

1,525 citations

592 citations

### "Nonlocal theory of thermoelastic ma..." refers background in this paper

...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....

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...Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....

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416 citations

### "Nonlocal theory of thermoelastic ma..." refers background in this paper

...In the last few years, fractional calculus has been successfully applied to extend generalized thermoelasticity theories to fractional order generalized thermoelasticity by Bachher et al. [33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc. Rossikhin and Shitikova [44] applied fractional calculus to various problems of mechanics of solids....

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...[33,34], Povstenko [35,36], Sherief [37], Youssef [38], Ezzat and his co-workers [39–43] etc....

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