On natural strain measures of the non-linear micropolar continuum

International Journal of Solids and Structures

Volumn 46, Issue 3-4, 2009, Pages 774-787

  Pietraszkiewicz, W ^a   Eremeyev, V A ^b  

^a INSTITUTE OF FLUID FLOW MACHINERY   (Poland)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Cosserat continuum; Micropolar continuum; Non linear elasticity; Strain measures; Wryness tensor

Indexed keywords

DEFORMATION; ELASTICITY; LAGRANGE MULTIPLIERS; STRESS ANALYSIS;

COSSERAT CONTINUUM; MICROPOLAR CONTINUUM; NON-LINEAR ELASTICITY; STRAIN MEASURES; WRYNESS TENSOR;

TENSORS;

EID: 58149349816     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.09.027     Document Type: Article

References (58)

1. Antman S.S. Nonlinear Problems of Elasticity. second ed. (2005), Springer Science Media Inc., New York
2. Atkin R.J., and Fox N. An Introduction to the Theory of Elasticity (1980), Longman, New York
3. Badur J., and Pietraszkiewicz W. On geometrically non-linear theory of elastic shells derived from pseudo-Cosserat continuum with constrained micro-rotations. In: Pietraszkiewicz W. (Ed). Finite Rotations in Structural Mechanics (1986), Springer-Verlag, Wien 19-32
4. Bertram A. Elasticity and Plasticity of Large Deformations (2005), Springer, Berlin
5. Bertram A., and Svendsen B. On material objectivity and reduced constitutive equations. Archives of Mechanics 53 6 (2001) 653-675
6. Besdo D. Ein Beitrag zur nichtlinearen Theorie des Cosserat-Kontinuums. Acta Mechanica 20 (1974) 105-131
7. Billington E.W. Introduction to the Mechanics and Physics of Solids (1986), Adam Hilger Ltd., Bristol
8. Chróścielewski, J., Makowski, J., Pietraszkiewicz, W., 2004. Statyka i dynamika powłok wielopłatowych. Nieliniowa teoria i metoda elementów skończonych. Warszawa, Wydawnictwo IPPT PAN.
9. Cosserat, E., Cosserat, F., 1909. Théorie des corps déformables, Herman et Flis, Paris, English translation: NASA TT F-11, 561, NASA, Washington, DC, 1968.
10. Dai T.-M. Renewal of basic laws and principles for polar continuum theories (I) - micropolar continua. Applied Mathematics and Mechanics 24 (2003) 1119-1125
11. Dłużewski P.H. Finite deformations of polar elastic media. International Journal of Solids and Structures 30 (1993) 2277-2285
12. Eremeyev V.A., and Pietraszkiewicz W. Local symmetry group in the general theory of elastic shells. Journal of Elasticity 85 (2006) 125-152
13. Eringen A.C., and Kafadar C.B. Polar field theories. In: Eringen A.C. (Ed). Continuum Physics vol. 4 (1976), Academic Press, New York 1-75
14. Eringen A.C. Microcontinuum Field Theory. I. Foundations and Solids (1999), Springer-Velag, New York
15. Grekova E., and Zhilin P. Basic equations of Kelvin's medium and analogy with ferromagnets. Journal of Elasticity 64 (2001) 29-70
16. Gurtin M.E. An Introduction to Continuous Mechanics (1981), Academic Press, New York
17. Kafadar C.B., and Eringen A.C. Micropolar media - I. The classical theory. International Journal of Engineering Science 9 (1971) 271-305
18. Le K.C., and Stumpf H. Strain measures, integrability condition and frame indifference in the theory of oriented media. International Journal of Solids and Structures 35 9-10 (1998) 783-798
19. Libai A., and Simmonds J.G. The Nonlinear Theory of Elastic Shells. second ed. (1998), Cambridge University Press, Cambridge, UK
20. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity. 4th ed. (1927), Cambridge University Press, Cambridge
21. Lurie A.I. Non-linear Theory of Elasticity (1990), North-Holland, Amsterdam
22. Lurie A.I. Theory of Elasticity (2005), Springer, Berlin
23. Makowski J., and Stumpf H. Buckling equations for elastic shells with rotational degrees of freedom undergoing finite strain deformation. International Journal of Solids and Structures 26 3 (1990) 353-368
24. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity (1983), Prentice-Hall, Englewood Cliffs, NJ
25. Maugin G.A. Acceleration waves in simple and linear viscoelastic micropolar materials. International Journal Engineering Science 12 (1974) 143-157
26. Maugin G.A. On the structure of the theory of polar elasticity. Philosophical Transactions of Royal Society London A 356 (1998) 1367-1395
27. Merlini T. A variational formulation for finite elasticity with independent rotation and Biot-axial fields. Computational Mechanics 19 (1997) 153-168
28. Murdoch A.I. Objectivity in classical continuum physics: a rationale for discarding the 'principle of invariance under superposed rigid body motions' in favour of purely objective considerations. Continuum Mechanics and Thermodynamics 15 (2003) 309-320
29. Muschik W., and Restuccia L. Changing the observer and moving materials in continuum physics: objectivity and frame-indifference. Technische Mechanik 22 2 (2002) 152-160
30. Naumenko K., and Altenbach H. Modeling of Creep for Structural Analysis (2007), Springer-Verlag, Berlin
31. Nikitin E., and Zubov L.M. Conservation laws and conjugate solutions in the elasticity of simple materials and materials with couple stress. Journal of Elasticity 51 (1998) 1-22
32. Nistor I. Variational principles for Cosserat bodies. International Journal of Non-linear Mechanics 37 (2002) 565-569
33. Noll W. A mathematical theory of the mechanical behavior of continuous media. Archive for Rational Mechanics and Analysis 2 1 (1958) 197-226
34. Ogden R.W. Non-linear Elastic Deformations (1984), Ellis Horwood, Chichester
35. Pabst W. Micropolar materials. Ceramics - Silikaty 49 (2005) 170-180
36. Pietraszkiewicz W., and Badur J. Finite rotations in the description of continuum deformation. International Journal of Engineering Science 21 (1983) 1097-1115
37. Pietraszkiewicz W., Chróścielewski J., and Makowski J. On dynamically and kinematically exact theory of shells. In: Pietraszkiewicz W., and Szymczak C. (Eds). Shell Structures: Theory and Applications (2005), Taylor & Francis, London 163-167
38. Ramezani S., and Naghdabadi R. Energy pairs in the micropolar continuum. International Journal of Solids and Structures 44 (2007) 4810-4818
39. Reissner E. On kinematics and statics of finite-strain force and moment stress elasticity. Studies in Applied Mathematics 52 (1973) 93-101
40. Reissner E. Note on the equations of finite-strain force and moment stress elasticity. Studies in Applied Mathematics 54 (1975) 1-8
41. Reissner E. A further note on the equations of finite-strain force and moment stress elasticity. ZAMP 38 (1987) 665-673
42. Scarpetta E. Some results on well-posedness for a nonlinear theory of micropolar elastostatics. Quarterly Journal of Mechanics and Applied Mathematics 42 (1989) 1-11
43. Simmonds J.G. The nonlinear thermodynamical theory of shells: descent from 3-dimensions without thickness expansion. In: Axelrad E.L., and Emmerling F.A. (Eds). Flexible Shells (1984), Springer-Verlag, Berlin 1-11
44. Shkutin L.I. Nonlinear models of deformable momental continua. Journal of Applied Mechanics and Technical Physics 6 (1980) 111-117 (in Russian)
45. Shkutin, L.I., 1988. Mechanics of Deformations of Flexible Bodies. Nauka, Novosibirsk (in Russian).
46. Sneddon J.N., and Berry D.S. The classical theory of elasticity. In: Flügge S. (Ed). Handbuch der Physik vol. VI (1958), Springer, Berlin
47. Steinmann P., and Stein E. A uniform treatment of variational principles for two types of micropolar continua. Acta Mechanica 121 (1997) 215-232
48. Stojanović R. Nonlinear micropolar elasticity. In: Nowacki W., and Olszak W. (Eds). Micropolar Elasticity (1972), CISM, Udine 73-103
49. Svendsen B., and Bertram A. On frame-indifference and form-invariance in constitutive theory. Acta Mechanica 132 (1999) 195-207
50. Toupin R.A. Theories of elasticity with couple-stress. Archives for Rational Mechanics and Analysis 17 (1964) 85-112
51. Truesdell C., and Noll W. The nonlinear field theories of mechanics. In: Flügge S. (Ed). Handbuch der Physik vol. III/3 (1965), Springer-Verlag, Berlin 1-602
52. Truesdell C., and Toupin R. The classical field theories. In: Flügge S. (Ed). Handbuch der Physik vol. III/1 (1960), Springer, Berlin 226-793
53. Wang C.-C., and Truesdell C. Introduction to Rational Elasticity (1973), Noordhoof Int. Publishing, Leyden
54. Yeremeyev V.A., and Zubov L.M. The theory of elastic and viscoelastic micropolar liquids. Journal of Applied Mathematics and Mechanics 63 (1999) 755-767
55. Zhilin P.A. Mechanics of deformable directed surfaces. International Journal of Solids and Structures 12 (1976) 635-648
56. Zubov L.M. Variational principles and invariant integrals for non-linearly elastic bodies with couple stresses. Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela 6 (1990) 10-16 (in Russian)
57. Zubov L.M. Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies (1997), Springer, Berlin
58. Zubov L.M., and Eremeev V.A. Equations for a viscoelastic micropolar fluid. Doklady Physics 41 (1996) 598-601