Linear Wave Motions in Continua with Nano-Pores

Giovine, Pasquale

doi:10.5772/50768

Cited by 7 publications

(5 citation statements)

References 42 publications

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“…The balance of moment of momentum in Eq. (8) assumes a more significant expression when we use the representation (1) for ; in fact we have skw PF 2 skw UY U Λ (10) where the tensor product between third-order tensors is so defined: We observe that the voids theories of Nunziato et al [2] and Capriz et al [23] are immediately recovered when the microstretch U is constrained to be spherical (see, also, §5 of Giovine [1]).…”

Section: Balance Equations and Jump Conditions For A Body With Ellipsmentioning

confidence: 99%

“…It is possible to use the balance Eqs. (7) and (10) and the relations (23) and (25) to eliminate the reactive parts of Eqs. (6) and (9) in order to arrive at a set of pure, that is reaction-free, consequences which alone are sufficient to study the evolution of our solid material with big pores.…”

Section: The Pure Field Equationsmentioning

confidence: 99%

“…The volume fraction of the pores in Nunziato et al [2] was not sufficient to describe the microdeformation of the holes when they are large: in fact, the linear voids theory of Cowin et al [7] does not predict size effects in torsion of bars in an isotropic material, while they occur both in bending and in torsion, as observed by Lakes [8] for bones and polymer foam materials. Instead the linear theory for a medium with ellipsoidal microstructure was used to find solutions of micro-vibrations, plane waves and macro-accelerations waves (see Giovine [9] and §3 of Giovine [10]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

Giovine¹

2017

JMEA

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The thermo-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-stretch bounded to the macro-deformation: in this case the microstructure disappears apparently (it becomes latent) and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies.

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Section: Balance Equations and Jump Conditions For A Body With Ellipsmentioning

confidence: 99%

Section: The Pure Field Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

Giovine¹

2017

JMEA

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“…The linear theory of elastic materials with voids was established by Cowin and Nunziato [15]. The theory of materials with voids has been extensively studied [16–18].…”

Section: Introductionmentioning

confidence: 99%

Deformation of chiral cylinders in the gradient theory of porous elastic solids

Ieşan

2016

Mathematics and Mechanics of Solids

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Chiral effects cannot be described by means of the classical theories of continua. In the context of the strain gradient theory of porous elastic solids we study the deformation of a chiral cylinder subjected to torsion, extension and bending by terminal couples. This work is motivated by recent interest in using the chiral continuum as a model for some auxetic materials, bones and carbon nanotubes. The problem is reduced to the study of some two-dimensional problems. We show that the torsion of a chiral cylinder is accompanied by extension, bending, and a variation of the volume fraction field. The solution is used to investigate the deformation of a circular cylinder.

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“…Introduction. In recent years considerable attention has been given to the mechanical behaviour of porous elastic solids (see, e.g., [9,16,33], and references therein). In [10,32] Nunziato and Cowin established a theory of elastic materials with voids for the treatment of porous solids.…”

mentioning

confidence: 99%

Strain gradient theory of porous solids with initial stresses and initial heat flux

Ieşan¹

2014

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper we present a strain gradient theory of thermoelastic porous solids with initial stresses and initial heat flux. First, we establish the equations governing the infinitesimal deformations superposed on large deformations. Then, we derive a linear theory of prestressed porous bodies with initial heat flux. The theory is capable to describe the deformation of chiral materials. A reciprocity relation and a uniqueness result with no definiteness assumption on the elastic constitutive coefficients are presented.

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Linear Wave Motions in Continua with Nano-Pores

Cited by 7 publications

References 42 publications

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

Strain Gradient Effects in a Thermo-Elastic Continuum with Nano-Pores

Deformation of chiral cylinders in the gradient theory of porous elastic solids

Strain gradient theory of porous solids with initial stresses and initial heat flux

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