This paper is concerned with a linear theory of thermopiezoelectricity in which the second gradient of the displacement, the second gradient of the electric potential and the second temperature ...gradient are included in the classic set of independent constitutive variables. The present paper is based on Green–Naghdi thermomechanics. The introduction of the entropy flux tensor leads to constitutive equations that depend on the second temperature gradient. The fundamental boundary-initial-value problems are formulated and the uniqueness of the solution is studied. Two applications of the theory are presented. We study the problem of a concentrated charge density acting in an unbounded region, as well as the effects of a concentrated heat source.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This paper deals with a linear theory of thermoviscoelasticity within the framework of Green–Naghdi thermomechanics. We use some notation and terminology introduced by Green and Naghdi, but instead ...of using the entropy balance law we employ an entropy production inequality. We introduce the entropy flux tensor and present a theory of materials of Kelvin–Voigt type in which the stress tensor depends on the temperature gradients. The theory leads to a fourth-order equation for temperature. The boundary conditions for thermal displacement are presented. In the dynamical theory of anisotropic solids, we formulate boundary-initial value problems and present a uniqueness theorem. We derive the continuous dependence of solutions upon initial data and supply terms. In the case of homogeneous and isotropic bodies, we establish a representation of the solution that is expressed in terms of two potentials and present an application of this result.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The deformation of the microstretch elastic solids is described by the displacement vector, the microrotation vector and the microstretch function. This paper is concerned with a theory of ...thermoelasticity for microstretch continua where the second-order displacement gradient is added to the classical set of independent constitutive variables. We establish the basic equations of the nonlinear theory and formulate boundary-initial-value problems. In the context of the linear theory, we present a reciprocity theorem and a uniqueness result. The effects of a concentrated heat source are investigated.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This paper is concerned with a linear theory of thermoelasticity without energy dissipation, where the second gradient of displacement and the second gradient of the thermal displacement are included ...in the set of independent constitutive variables. In particular, in the case of rigid heat conductors the present theory leads to a fourth order equation for temperature. First, the basic equations of the second gradient theory of thermoelasticity are presented. The boundary conditions for thermal displacement are derived. The field equations for homogeneous and isotropic solids are established. Then, a uniqueness result for the basic boundary-initial-value problems is presented. An existence theorem is established for the first boundary value problem. The problem of a concentrated heat source is investigated using a solution of Cauchy-Kowalewski-Somigliana type.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The interest in the gradient theory of elasticity is stimulated by the fact that this theory is adequate to investigate important problems related to size effects and nanotechnology. In this paper, ...we use the theory of microstretch solids and the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of porous thermoelastic bodies, which is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. A uniqueness theorem for the mixed problem is presented. In the case of isotropic solids we establish the continuous dependence of solutions upon initial data and body supplies. The problem of a concentrated heat source is also investigated.
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BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
This paper is concerned with the deformation of beams in the framework of the linear theory of micromorphic elastic solids. First, the plane strain of anisotropic and homogeneous elastic cylinders is ...investigated. Existence and uniqueness results are presented. Then, Saint-Venant’s problem for micromorphic beams is formulated. A method is established to reduce the extension, bending and torsion to the study of some plane problems. Finally, the deformation of beams loaded on the lateral surface is investigated. As a special case, the solution of the flexure problem is obtained. The method is used to study the deformation of a micromorphic rod subjected to a uniform pressure on the lateral surface.
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NUK, OILJ, SAZU, UKNU, UL, UM, UPUK
•The generalized plane strain of chiral materials in the gradient theory of elasticity is investigated.•Existence and uniqueness results are established.•The effects of concentrated body loads are ...studied.•The deformation of a circular cylinder which is subjected to a tangential displacement on the lateral surface is investigated.
The strain-gradient theory of elasticity is an adequate tool to describe the deformation of chiral elastic bodies. This paper is concerned with the generalized plane strain of homogeneous and isotropic chiral elastic solids in the equilibrium theory. First, existence and uniqueness results are presented. Then, the basic singular solutions are established. The generalized plane strain of a circular cylinder subjected to a tangential displacement on the lateral boundary is also studied. In contrast with the classical theory, the tangential displacement produces an axial extension.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A microstretch continuum is a material with microstructure in which the microelements can stretch and contract independently of their translations and rotations. This paper is concerned with the ...grade consistent theory of microstretch elastic solids, where the second-order displacement is added to the classical set of independent constitutive variables. We study the equilibrium of a homogeneous and isotropic elastic beam loaded by tractions distributed over its plane ends. First, the problem of bending and extension is investigated. It is shown that the solution of the problem can be expressed in terms of solutions of three plane strain problems. Then, we study the problem of torsion in the framework of the grade consistent theory of microstretch elastic solids. This problem is solved with the help of three torsion functions. The results are used to investigate the torsion of a right circular cylinder.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This paper is concerned with a theory of thermopiezoelectricity in which the second gradient of displacement and the second gradient of electric potential are included in the set of independent ...constitutive variables. First, the basic equations of a linear theory are derived. The field equations for homogeneous and isotropic solids are established and the boundary-initial-value problems are formulated. Then, a uniqueness result for the mixed boundary-initial-value problem and a reciprocity relation are presented. This relation forms the basis of a reciprocal theorem and a new uniqueness result. Finally, the fundamental solutions in the stationary theory and representations of Somigliana type are derived.
•We study a theory in which the second gradients of deformation and electric potential are taken into account.•We investigate the basic equations for homogeneous and isotropic solids.•We establish uniqueness and reciprocity theorems for anisotropic bodies.•Fundamental solutions and representations of Somigliana type are established.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This paper is concerned with the equilibrium theory of chiral porous elastic solids. We study the problem of torsion, bending and extension of chiral cylinders. First, it is shown that the solution ...can be found as a vector field which has the property that its partial derivative with respect to axial coordinate corresponds to a rigid deformation. Then, we reduce the problem to the study of some two-dimensional problems. With the help of these results we can investigate the bending by terminal couples and the problems of extension and torsion. The solution is used to study the torsion of a chiral circular cylinder.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
