Variational principles in the linear theory of viscoelastic media with microstructure

Author:
Kenneth A. Kline

Journal:
Quart. Appl. Math. **28** (1970), 69-80

MSC:
Primary 73.49

DOI:
https://doi.org/10.1090/qam/264888

MathSciNet review:
264888

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References | Similar Articles | Additional Information

**[1]**M. E. Gurtin,*Variational principles in the linear theory of viscoelasticity*, Arch. Rat. Mech. Anal.**13**, 179-191 (1963) MR**0214321****[2]**Hu Hai-Chang,*On some variational principles in the theory of elasticity and the theory of plasticity*, Sci. Sinica**4**, 33-54 (1955)**[3]**K. Washizu,*On the variational principles of elasticity and plasticity*, ASRL TR 25-18, Mass. Inst. Tech., Cambridge, Mass., 1955**[4]**R. D. Mindlin,*Microstructure in linear elasticity*, Arch. Rat. Mech. Anal.**16**, 51-78 (1964) MR**0160356****[5]**R. A. Toupin,*Theories of elasticity with couple-stress*, Arch. Rat. Mech. Anal.**17**, 85-112 (1964) MR**0169425****[6]**E. S. Suhubi and A. C. Eringen,*Nonlinear theory of microelastic solids. II*, Internat. J. Engrg. Sci.**2**, 389-404 (1964)**[7]**N. Fox,*A continuum theory of dislocations for polar elastic materials*, Quart. J. Mech. Appl. Math.**19**, 343 (1966)**[8]**A. E. Green, P. M. Naghdi and R. S. Rivlin,*Directors and multipolar displacements in continuum mechanics*, Internat. J. Engrg. Sci.**2**, 611-620 (1965)**[9]**M. E. Gurtin and E. Sternberg,*On the linear theory of viscoelasticity*, Arch. Rat. Mech. Anal.**11**, 291-356 (1962) MR**0147047****[10]**C. N. DeSilva and K. A. Kline,*Nonlinear constitutive equations for directed viscoelastic materials with memory*, Z. Angew. Math. Phys.**19**, 128-139 (1968)**[11]**K. A. Kline,*On thermodynamics of directed continuous media*, Z. Angew. Math. Phys.**19**, 793-802 (1968)**[12]**J. L. Ericksen and C. Truesdell,*Exact theory of stress and strain in rods and shells*, Arch. Rat. Mech. Anal.**1**, 295-323 (1958) MR**0099135****[13]**W. T. Koiter,*Couple-stresses in the theory of elasticity. II*, Nederl. Akad. Wetensch. Proc. Ser.**B 67**, 30-44 (1964) MR**0163469****[14]**P. M. Naghdi,*On a variational theorem in elasticity and its application to shell theory*, Trans. ASME Ser. F, J. Appl. Mech.**31**, 647-653 (1964) MR**0173390****[15]**W. Nowacki,*Couple-stresses in the theory of thermoelasticity. II*, Bull. Acad. Polon. Sci. Sér. Sci. Tech.**14**, 203-212 (1966)**[16]**E. Reissner,*On the foundations of the theory of elastic shells*, Proc. 11th Internat. Congr. of Appl. Mech. (Munich, 1964), Springer-Verlag, Berlin, 1966**[17]**W. Günther,*Zur Statik und Kinematik des Cosseratschen Kontinuums*, Abh. Braunschweig. Wiss. Ges.**10**, 195-213 (1958)**[18]**W. Nowacki,*Couple-stresses in the theory of thermoelasticity. III*, Bull. Acad. Polon. Sci. Sér. Sci. Tech.**14**, 505-513 (1966)**[19]**E. Reissner and F. Y. M. Wan,*A note on Günther's analysis of couple stress*, Proc. IUTAM Sympos. (1967),*Mechanics of generalized continua*, Springer-Verlag, Berlin, 1968**[20]**E. Reissner,*A note on variational principles in elasticity*, Internat. J. Solids Structures**1**, 93 (1965) MR**0096419****[21]**J. L. Ericksen,*Anisotropic fluids*, Arch. Rat. Mech. Anal.**4**, 231-237 (1960) MR**0110394****[22]**K. A. Kline, S. J. Allen and C. N. DeSilva,*A continuum approach to blood flow*, Biorheology**5**, 111-118 (1968)**[23]**O. D. Kellogg,*Foundations of potential theory*, Dover, New York, 1953**[24]**S. J. Allen, C. N. DeSilva and K. A. Kline,*Theory of simple deformable directed fluids*, Phys. Fluids**10**, 2551-2555 (1967)**[25]**A. E. Green and R. S. Rivlin,*On Cauchy's equations of motion*, Z. Angew. Math. Phys.**15**, 290-292 (1964) MR**0176650**

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DOI:
https://doi.org/10.1090/qam/264888

Article copyright:
© Copyright 1970
American Mathematical Society