On the Theory of Two-Temperature Thermoelasticity with Two Phase-Lags

REFERENCES

• M. A. Biot , Thermoelasticity and Irreversible Thermodynamics , J. Appl. Phys , vol. 27 , pp. 240 – 253 , 1956 .
   Web of Science ®Google Scholar
• H. W. Lord and Y. Shulman , A Generalized Dynamical Theory of Thermoelasticity , J. Mech. Phys. Solid , vol. 15 , pp. 299 – 309 , 1967 .
   Web of Science ®Google Scholar
• A. E. Green and K. A. Lindsay , Thermoelasticity, J. Elast. , vol. 2, pp. 1–7, 1972.
   Google Scholar
• D. Y. Tzou , A Unified Field Approach for Heat Conduction from Macro to Micro-Scales , ASME J. Heat Transf. , vol. 117 , pp. 8 – 16 , 1995 .
   Web of Science ®Google Scholar
• D. S. Chandrasekharaiah , Hyperbolic Thermoelasticity: A Review of Recent Literature , Appl. Mech. Rev. , vol. 51 , pp. 705 – 729 , 1998 .
   Google Scholar
• R. Quintanilla and R. Racke , A Note on Stability of Dual Phase-Lag Heat Conduction , Int. J. Heat. Mass Transf. , vol. 49 , pp. 1209 – 1213 , 2006 .
   Web of Science ®Google Scholar
• R. Quintanilla and R. Racke , Qualitative Aspects in Dual Phase-Lag Heat Conduction , Proc. Royal Soc. A. , vol. 463 , pp. 659 – 674 , 2007 .
   Google Scholar
• P. J. Chen and M. E. Gurtin , On a Theory of Heat Involving Two Temperatures , J. Appl. Math. Phys. (ZAMP). , vol. 19 , pp. 614 – 627 , 1968 .
   Web of Science ®Google Scholar
• P. J. Chen , M. E. Gurtin , and W. O. Williams , A Note on Non-Simple Heat Conduction , J. Appl. Math. Phys. (ZAMP). , vol. 19 , pp. 969 – 970 , 1968 .
   Web of Science ®Google Scholar
• P. J. Chen , M. E. Gurtin , and W. O. Williams , On the Thermodynamics of Non-Simple Materials with Two Temperatures , J. Appl. Math. Phys. (ZAMP). , vol. 20 , pp. 107 – 112 , 1969 .
   Web of Science ®Google Scholar
• D. Iesan , On the Linear Coupled Thermoelasticity with Two Temperatures , J. Appl. Math. Phys. (ZAMP). , vol. 21 , pp. 583 – 591 , 1970 .
   Web of Science ®Google Scholar
• R. Quintanilla , On Existence, Structural Stability, Convergence and Spatial Behavior in Thermoelasticity with Two Temperatures , Acta Mech. , vol. 168 , pp. 61 – 73 , 2004 .
   Web of Science ®Google Scholar
• H. M. Youssef , Theory of Two-Temperature-Generalized Thermoelasticity , IMA J. Appl. Math. vol. 71 , pp. 383 – 390 , 2006 .
   Web of Science ®Google Scholar
• A. Magana and R. Quintanilla , Uniqueness and Growth of Solution in Two Temperature Generalized Thermoelastic Theories , Math. Mech. of Solids , vol. 14 , pp. 622 – 634 , 2008 .
   Web of Science ®Google Scholar
• R. Kumar , R. Prasad , and S. Mukhopadhyay , Variational and Reciprocal Principles in Generalized Two-temperature Thermoelasticity , J. Therm. Stresses , vol. 33 , pp. 161 – 171 , 2010 .
   Web of Science ®Google Scholar
• H. M. Youssef and E. A. Al-Lehaibi , State-Space Approach of Two-Temperature Generalized Thermoelasticity of One Dimensional Problem , Int. J. Eng. Sci. , vol. 44 , pp. 1550 – 1562 , 2007 .
   Google Scholar
• H. M. Youssef and A. H. Al Harby , State-Space Approach of Two-Temperature Generalized Thermoelasticity of Infinite Body with a Spherical Cavity Subjected to Different type of Thermal Loading , Arch. Appl. Mech. , vol. 77 , pp. 675 – 687 , 2007 .
   Web of Science ®Google Scholar
• R. Kumar and S. Mukhopadhyay , Effects of Thermal Relaxation Parameter on Plane Wave Propagation under Two-Temperature Thermoelasticity , Int. J. Eng. Sci. , vol. 48 , pp. 128 – 139 , 2010 .
   Web of Science ®Google Scholar
• S. Mukhopadhyay and R. Kumar , Thermoelastic Interaction on Two Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity , J. Therm. Stresses , vol. 32 , pp. 341 – 360 , 2009 .
   Web of Science ®Google Scholar
• R. Quintanilla , A Well Posed Problem for the Dual-Phase-Lag Heat Conduction , J. Therm. Stresses , vol. 31 , pp. 260 – 269 , 2008 .
   Web of Science ®Google Scholar
• S. Chirita and M. Ciarletta , Reciprocal and Variational Principles in Linear Thermoelasticity without Energy Dissipation , Mech. Res. Comm. , vol. 37 , pp. 271 – 275 , 2010 .
   Web of Science ®Google Scholar
• M. E. Gurtin , Variational Principles for Linear Elastodynamics , Arch. Rat. Mech. Anal. , vol. 16 , pp. 34 – 50 , 1964 .
   Web of Science ®Google Scholar
• M. E. Gurtin , The Linear Theory of Elasticity . in Flugge , S. (ed.) , Encyclopedia of Physics , pp. 1 – 295 , vol. VIa, no. 2, Mechanics of Solids II, vol. II , Springer-Verlag , Berlin-Heidelberg-New York , 1972 .
   Google Scholar
• R. Nickell and J. Sackman , Variational Principles for Linear Coupled Thermoelasticity , Quart. Appl. Math. , vol. 26 , pp. 11 – 26 , 1968 .
   Web of Science ®Google Scholar