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Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
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. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
2004 On the propagation of plane waves in typeIII thermoelastic
 A
"... The propagation of plane waves in infinite, threedimensional, typeIII thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low and highfrequency asymptotic expressions are given, smallcoupling limit ..."
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The propagation of plane waves in infinite, threedimensional, typeIII thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low and highfrequency asymptotic expressions are given, smallcoupling limit results are derived, and special/limiting cases, including those corresponding to thermoelastic media of types II and I, are noted. Computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters. Of the findings presented, the following are most significant: (i) the determination of critical values of the physical parameters and their impact on the wavefields; (ii) ascertaining that typeIII media behave, essentially, like typeII (respectively, typeI) media with respect to low (respectively, high) frequency plane waves; (iii) establishing the Whitham stability of plane waves in typeIII media; and (iv) the determination of the dispersion characteristics of typeIII media.
ON THE FLEXURAL AND EXTENSIONAL THERMOELASTIC WAVES IN ORTHOTROPIC PLATES WITH TWO THERMAL RELAXATION TIMES
, 2003
"... Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and fl ..."
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Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases. 1.
Director
, 2005
"... This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Doctor of Philosophy. ..."
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This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Doctor of Philosophy.
The threedimensional steadystate thermoelastodynamic problem of moving sources over a half space
, 2002
"... A procedure based on the Radon transform and elements of distribution theory is developed to obtain fundamental thermoelastic threedimensional (3D) solutions for thermal and/or mechanical point sources moving steadily over the surface of a half space. A concentrated heat flux is taken as the therma ..."
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A procedure based on the Radon transform and elements of distribution theory is developed to obtain fundamental thermoelastic threedimensional (3D) solutions for thermal and/or mechanical point sources moving steadily over the surface of a half space. A concentrated heat flux is taken as the thermal source, whereas the mechanical source consists of normal and tangential concentrated loads. It is assumed that the sources move with a constant velocity along a fixed direction. The solutions obtained are exact within the bounds of Biots coupled thermoelastodynamic theory, and results for surface displacements are obtained over the entire speed range (i.e. for subRayleigh, superRayleigh/subsonic, transonic and supersonic source speeds). This problem has relevance to situations in Contact Mechanics, Tribology and Dynamic Fracture, and is especially related to the wellknown heat checking problem (thermomechanical cracking in an unflawed halfspace material from highspeed asperity excitations). Our solution technique fully exploits as auxiliary solutions the ones for the corresponding planestrain and antiplane shear problems by reducing the original 3D problem to two separate 2D problems. These problems are uncoupled from each other, with the first problem being thermoelastic and the second one pure elastic. In particular, the auxiliary planestrain problem is completely analogous to the original problem, not only with regard to the field equations but also with regard to the boundary conditions. This makes the technique employed here more advantageous than other techniques, which require the prior determination of a fictitious auxiliary planestrain problem through solving an integral equation.
th AIMETA Congress of Theoretical and Applied Mechanics STRUCTURAL INTERFACES IN ELASTICITY
"... Viene introdotto il concetto di interfaccia strutturale e vengono descritte possibili applicazioni nel campo della bioingegneria. L'attenzione e posta in particolare su due tipi di interfaccia strutturale: il legamento parodontale e la cartilagine articolare. Si discute, inne, la possibilita di ..."
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Viene introdotto il concetto di interfaccia strutturale e vengono descritte possibili applicazioni nel campo della bioingegneria. L'attenzione e posta in particolare su due tipi di interfaccia strutturale: il legamento parodontale e la cartilagine articolare. Si discute, inne, la possibilita di utilizzare questo modello nello studio dell'interazione recettorelegante tra proteine. The concept of structural interface is introduced and potential applications to bioengineering are presented. In particular, two structural interfaces in biological systems are identied, namely, the periodontal ligament in the toothbone system and the articular cartilage in diarthrodial joints. Speculations on possible applications in the modelling of receptorligand binding between proteins close this paper. 1.
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"... (This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors i ..."
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(This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Acta Mech 224, 657–674 (2013) DOI 10.1007/s007070120776z
"... Abstract In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain vali ..."
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Abstract In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a firstorder linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the firstorder differential system follows. On this basis, the Rayleightype surface waves are studied, and the dispersion condition is found. 1
MAGNETOVISCOELASTIC PLANE WAVES IN ROTATING MEDIA IN THE GENERALIZED THERMOELASTICITY II
, 2004
"... A study is made of the propagation of timeharmonic magnetothermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of KelvinVoigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The gene ..."
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A study is made of the propagation of timeharmonic magnetothermoviscoelastic plane waves in a homogeneous electrically conducting viscoelastic medium of KelvinVoigt type permeated by a primary uniform external magnetic field when the entire medium rotates with a uniform angular velocity. The generalized thermoelasticity theory of type II (Green and Naghdi model) is used to study the propagation of waves. A more general dispersion equation for coupled waves is derived to ascertain the effects of rotation, finite thermal wave speed of GN theory, viscoelastic parameters and the external magnetic field on the phase velocity, the attenuation coefficient, and the specific energy loss of the waves. Limiting cases for low and high frequencies are also studied. In absence of rotation, external magnetic field, and viscoelasticity, the general dispersion equation reduces to the dispersion equation for coupled thermal dilatational waves in generalized thermoelasticity II (GN model), not considered before. It reveals that the coupled thermal dilatational waves in generalized thermoelasticity II are unattenuated and nondispersive in contrast to the thermoelastic waves in classical coupled thermoelasticity (Chadwick (1960)) which suffer both attenuation and dispersion. 1.