Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 12
60
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Transmission problems in the theory of elastic hemitropic materials

, , &
Pages 1463-1508 | Received 29 Sep 2007, Accepted 30 Sep 2007, Published online: 21 Nov 2007

References

  • Aero , EL and Kuvshinski , EV . 1963 . Continuum theory of asymmetric elasticity. Microrotation effect . Solid State Physics , 5 ( 9 ) : 2591 – 2598 . (in Russian) (English translation: Soviet Physics–Solid State, 5 (1964), 1892–1899)
  • Aero , EL and Kuvshinski , EV . 1964 . Continuum theory of asymmetric elasticity. Equilibrium of an isotropic body . Solid State Physics , 6 ( 9 ) : 2689 – 2699 . (in Russian) (English translation: Soviet Physics–Solid State, 6 (1965), 2141–2148)
  • Cosserat , E and Cosserat , F . 1898 . Sur les équations de la théorie de l'élasticité . Comptes Rendus de l’ Academic des Sciences, Paris , 126 : 1129 – 1132 .
  • Eringen , AC . 1999 . Microcontinuum Field Theories. I: Foundations and Solids , New York : Springer-Verlag .
  • Lakes , RS and Benedict , RL . 1982 . Noncentrosymmetry in micropolar elasticity . International Journal of Engineering Science , 29 : 1161 – 1167 .
  • Lakes , RS . 2001 . Elastic and viscoelastic behavior of chiral materials . International Journal of Mechanical Science , 43 : 1579 – 1589 .
  • Lakes , RS and Yang , JFC . 1978 . Transient study of couple stress effects in compact bone. Torsion . J. Biomechanical Engng. , 103 : 275 – 279 .
  • Dyszlewicz , J . 2004 . Micropolar Theory of Elasticity, Lecture notes in applied and Computational Mechanics , Vol. 15 , Berlin : Springer-Verlag .
  • Haijun , Z and Zhong-can , O . 1998 . Bending and twisting elasticity: a revised Marko-Sigga model on DNA chirality . Physical Review E , 58 ( 4 ) : 4816 – 4821 .
  • Lakhtakia , A . 1994 . Beltrami Fields in Chiral Media , Singapore : World Scientific .
  • Mura , T . 1987 . Micromechanics of Defects in Solids , Hague, , Netherlands : Martinus Nijhoff .
  • Mura , T . 2000 . Some new problems in the micromechanics . Materials Science and Engineering A (Structural Materials: Properties, Microstructure and Processing) , A285 ( 1–2 ) : 224 – 228 .
  • Nowacki , W . 1986 . Theory of Asymmetric Elasticity , Oxford : Pergamon Press; Warsaw: PWN–Polish Scientific Publishers .
  • Nowacki , JP . 1977 . Green function for a hemitropic micropolar continuum . Bulletin de l’ Academic Polonaise des Sciences, Sér. Sci. Techn. , 25 : 235 – 241 .
  • Nowacki , JP . 1977 . Some dynamical problems of hemitropic micropolar continuum . Bulletin de l’ Academic Polonaise des Sciences, Sér. Sci. Techn. , 25 : 207 – 216 .
  • Nowacki , JP and Nowacki , W . 1977 . Some problems of hemitropic micropolar continuum . Bulletin de l’ Academic Polonaise des Sciences, Sér. Sci. Techn. , 25 : 151 – 159 .
  • Ro , R . 1999 . Elastic activity of the chiral medium . Journal of Applied Physics , 85 ( 5 ) : 2508 – 2513 .
  • Sharma , P . 2004 . Size-dependent elastic fields of embedded inclusions in isotropic chiral solids . International Journal of Solids and structures , 41 : 6317 – 6333 .
  • Yang , JFC and Lakes , RS . 1982 . Experimental study of micropolar and couple stress elasticity in compact bone bending . Journal of Biomechanics , 15 ( 2 ) : 91 – 98 .
  • Natroshvili , D , Giorgashvili , L and Stratis , IG . 2003 . Mathematical problems of the theory of elasticity of chiral materials . Applied Mathematics, Informatics, and Mechanics , 8 ( 1 ) : 47 – 103 .
  • Natroshvili , D and Stratis , IG . 2006 . Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains . Mathematical Methods in the Applied Sciences , 29 ( 4 ) : 445 – 478 .
  • Natroshvili , D , Giorgashvili , L and Zazashvili , S . 2005 . Steady state oscillation problems of the theory of elasticity of chiral materials . Journal of Integral Equations and Applications , 17 ( 1 ) : 19 – 69 .
  • Eshelby , JD . 1959 . The elastic field outside an ellipsoidal inclusion . Proceedings of the Royal Society of London , A, A252 : 561 – 569 .
  • Eshelby , JD . 1961 . “ Elastic inclusions and inhomogeneities ” . In Progress in Solid Mechanics , Edited by: Sneddon , IN and Hill , R . Vol. 2 , 89 – 140 . Amsterdam : North Holland .
  • Weitsman , Y . 1967 . Initial stress and skin effects in a hemitropic Cosserat continuum . Journal of Applied Mathematics , 349 : 160 – 164 .
  • Lakhtakia , A , Varadan , VK and Varadan , VV . 1988 . Elastic wave propagation in noncentrosymmetric isotropic media: dispersion and field equations . Journal of Applied Physics , 64 : 5246 – 5250 .
  • Lakhtakia , A , Varadan , VK and Varadan , VV . 1990 . Reflection of elastic plane waves at a planar achiral–chiral interface . Journal of the Acoustical Society of America , 87 : 2314 – 2318 .
  • Lakhtakia , A , Varadan , VV and Varadan , VK . 1992 . Elastic wave scattering by an isotropic noncentrosymmetric sphere . Journal of the Acoustical Society of America , 91 : 680 – 684 .
  • Triebel , H . 1978 . Interpolation Theory, Function Spaces, Differential Operators , Amsterdam : North Holland .
  • Triebel , H . 1983 . Theory of Function Spaces , Basel, , Boston, Stuttgart : Birkhäuser Verlag .
  • Lions , J-L and Magenes , E . 1968 . Problèmes aux limites non homogènes et applications , Vol. 1 , Paris : Dunod .
  • Fichera , G . 1973 . “ Handb. der Physik, Bd. 6/2 ” . In Existence Theorems in Elasticity , Heidelberg : Springer Verlag .
  • McLean , W . 2000 . Strongly Elliptic Systems and Boundary Integral Equations , Cambridge : Cambridge University Press .
  • Nečas , J . 1967 . Méthodes Directes en Théorie des Équations Élliptiques , Paris : Masson Éditeur .
  • Dautray , R and Lions , JL . 1990 . “ Integral equations and numerical methods ” . In Mathematical Analysis and Numerical Methods for Science and Technology , Vol. 4 , Berlin, , Heidelberg : Springer Verlag .
  • Gachechiladze , R , Gwinner , I and Natroshvili , D . 2006 . A boundary variational inequality approach to unilateral contact with hemitropic materials . Memoirs on Differential Equations and Mathematical Physics , 39 : 69 – 103 .
  • Kupradze , VD , Gegelia , TG , Basheleishvili , MO and Burchuladze , TV . 1979 . “ North Holland Series in Applied Mathematics and Mechanics ” . In Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , Vol. 25 , New York, , Oxford : Amsterdam North Holland Publishing Company .
  • Eskin , G . 1981 . “ Translation of Mathematical Monographs ” . In Boundary Value Problems for Elliptic Pseudodifferential Equations , Vol. 52 , Providence, , Rhode Island : American Mathematical Society .
  • Seeley , RT . 1966 . Singular integrals and boundary value problems . American Journal of Mathematics , 88 : 781 – 809 .
  • Natroshvili , D . 1984 . Investigation of boundary value and initial boundary value problems of the mathematical theory of anisotropic elasticity and thermoelasticity by means of potential methods , : 1 – 325 . Doct. Thesis, A. Razmadze Math. Inst. of the Georgian Academy of Sciences, Tbilisi
  • Natroshvili , D . 1995 . Mixed interface problems for anisotropic elastic bodies . Georgian Mathematical Journal , 2 ( 6 ) : 631 – 652 .
  • Natroshvili , D . 1997 . Boundary integral equation method in the steady state oscillation problems for anisotropic bodies . Mathematical Methods in the Applied Sciences , 20 ( 2 ) : 95 – 119 .
  • Burchuladze , TV and Gegelia , TG . 1985 . Development of Potential Methods in the Theory of Elasticity , Tbilisi : Metsniereba .
  • Mikhlin , SG and Prössdorf , S . 1986 . Singular Integral Operators , Berlin : Springer-Verlag .
  • Duduchava , R , Natroshvili , D and Shargorodsky , E . 1990 . Boundary value problems of the mathematical theory of cracks . Proceedings of I. Vekua Institute of Applied Mathematics Tbilisi State University , 39 : 68 – 84 .
  • Duduchava , R , Natroshvili , D and Shargorodsky , E . 1995 . Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts, I, II . Georgian Mathematical Journal , 2 ( 2 ) : 123 – 140 . 2(3), 259–276
  • Natroshvili , D , Chkadua , O and Shargorodsky , E . 1990 . Mixed boundary value problems of the anisotropic elasticity . Proceedings of I. Vekua Institute of Applied Mathematics Tbilisi State University , 39 : 133 – 181 .
  • Natroshvili , D , Djagmaidze , A and Svanadze , M . 1986 . Problems of the Linear Theory of Elastic Mixtures , Tbilisi : Tbilisi University .
  • Jentsch , L and Natroshvili , D . 1999 . Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, I . Memoirs on Differential Equations and Mathematical Physics , 17 : 7 – 126 .
  • Jentsch , L and Natroshvili , D . 1999 . Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, II . Memoirs on Differential Equations and Mathematical Physics , 18 : 1 – 50 .
  • Costabel , M and Wendland , WL . 1986 . Strong ellipticity of boundary integral operators . Journal für die Reine and Angewandte Mathematik , 372 : 34 – 63 .
  • Duduchava , R . 2001 . The Green formula and layer potentials . Integral Equations and Operator Theory , 41 : 127 – 178 .
  • Buchukuri , T , Chkadua , O , Natroshvili , D and Sändig , A-M . 2005 . Solvability and regularity results to boundary-transmission problems for metallic and piezoelectric elastic materials , Stuttgart University, Institut für Angewandte Analysis und Numerische Simulation, Preprint No. 004, pp. 1–56. (To appear in : Mathematische Nachrichlen) .
  • Costabel , M . 1988 . Boundary integral operators on Lipschitz domains: elementary results . SIAM Journal of Mathematical Analysis , 19 : 613 – 626 .
  • Shamir , E . 1967 . Elliptic systems of singular integral operators, I . Transactions of the American Mathematical Society , 127 : 107 – 124 .
  • Grubb , G . 1990 . Pseudodifferential boundary problems in Lp spaces . Communications in Partial Differential Equations , 15 ( 3 ) : 289 – 340 .
  • Shargorodsky , E . 1993 . Boundary value problems for elliptic pseudodifferential operators: the halfspace case . Proceedings of A Razmadze Mathematical Institute , 99 : 44 – 80 .
  • Shargorodsky , E . 1993 . Boundary value problems for elliptic pseudodifferential operators on manifolds . Proceedings of A Razmadze Mathematical Institute , 105 : 108 – 132 .
  • Shargorodsky , E . 1994 . An Lp -analogue of the Vishik-Eskin theory . Memoirs on Differential Equations and Mathematical Physics , 2 : 41 – 148 .
  • Jentsch , L and Natroshvili , D . 1996 . Non–classical mixed interface problems for anisotropic bodies . Mathematische Nachrichten , 179 : 161 – 186 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.