Invariant characteristic representations for classical and micropolar anisotropic elasticity tensors
Bibliographic record
Abstract
No abstract is available for this record. The assistant can identify its topic from the title, but cannot infer the study’s results.
Source: Not provided · Quality: missing
Research context
OpenAlex topics: Elasticity and Material Modeling · Composite Material Mechanics · Nonlocal and gradient elasticity in micro/nano structures
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (37)
Show source-provided references
1. I.O. Tu, The decomposition of an anisotropic elastic tensor. Acta Cryst. A 24 (1968) 273?282.10.1107/S0567739468000458 ↗
2. T.P. Srinivasan and S.D. Nigam, Invariant elastic constants for crystals. J. Math. Mech. 19 (1969) 411?420.
3. G. Backus, A geometrical picture of anisotropic elastic tensors. Rev. Geophys. Space Phys. 8 (1970) 633?671.10.1029/RG008i003p00633 ↗
4. J. Jerphagnon, D. Chemla and R. Bonnevill, The description of the physical properties of condensed matter using irreducible tensors. Advances in Physics 27 (1978) 609?650.10.1080/00018737800101454 ↗
5. L.J. Walpole, Elastic behavior of composite materials: Theoretical foundation. Adv. Appl. Mech. 21 (1981) 169?242.10.1016/S0065-2156(08)70332-6 ↗
6. L.J. Walpole, Fourth-rank tensors of the thirty-two crystal classes: Multiplication tables. Proc. Roy. Soc. London A 391 (1984) 149?197.10.1098/rspa.1984.0008 ↗
7. E. Mochizuki, Spherical harmonic decomposition of an elastic tensor. Geophys. J. 93 (1988) 521?526.10.1111/j.1365-246X.1988.tb03878.x ↗
8. S.C. Cowin, Properties of the anisotropic elasticity tensor. Q. J. Mech. Appl. Math. 42 (1989) 249?266.10.1093/qjmam/42.2.249 ↗
9. R. Baerheim, Harmonic decomposition of the anisotropic elasticity tensor. Q. J. Mech. Appl. Math. 46 (1993) 391?418.10.1093/qjmam/46.3.391 ↗
10. H.T. Hahn, A derivation of invariants of fourth order tensors. J. Composite Materials 8 (1974) 2?14.10.1177/002199837400800101 ↗
11. T.C.T. Ting, Invariants of anisotropic elastic constants. Q. J. Mech. Appl. Math. 40 (1987) 431?448.10.1093/qjmam/40.3.431 ↗
12. S.C. Cowin and M.M. Mehrabadi, On the identification of material symmetry for anisotropic elastic materials. Q. J. Mech. Appl. Math. 40 (1987) 451?476.10.1093/qjmam/40.4.451 ↗
13. S.C. Cowin, Identification of elastic material symmetry by acoustic measurement. In: M.F. McCarthy and M.A. Hayes (eds), Elastic Wave Propagation. Amsterdam: North Holland (1989).
14. A.N. Norris, On the acoustic determination of the elasic moduli of anisotropic solids and acoustic conditions for the existence of planes of symmetry. Q. J. Meth. Appl. Math. 42 (1989) 413?426.10.1093/qjmam/42.3.413 ↗
15. A.N. Norris, Symmetry conditions for third order elastic moduli and implications in nonlinear wave theory. J. Elasticity 25 (1991) 247?257.10.1007/BF00040928 ↗
16. Y.Z. Huo and G. Del Piero, On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor. J. Elasticity 25 (1991) 203?246.10.1007/BF00040927 ↗
17. M.E. Gurtin, The linear theory of elasticity. In:Handbuch der Physik. Vol. VIa/2. Springer (1972).
18. M.E. Gurtin, A short proof of the representation theorem for isotropic, linear stress-strain relations. J. Elasticity 4 (1974) 243?245.10.1007/BF00049267 ↗
19. L.C. Martins and P. Podio-Guidugli, A new proof of the representation theorem for isotropic, linear constitutive relations. J. Elasticity 8 (1978) 319?322.10.1007/BF00130470 ↗
20. Z.H. Guo, The representation theorem for isotropic, linear asymmetric stress-strain relations. J. Elasticity 13 (1983) 121?124.10.1007/BF00041229 ↗
21. Z.H. Guo, An alternative proof of the representation theorem for isotropic, linear asymmetric stress-strain relations. Q. Appl. Math. 41 (1983) 119?123.10.1090/qam/700666 ↗
22. C. De Boor, A naive proof of the representation theorem for isotropic, linear asymmetric stress-strain relations. J. Elasticity 15 (1985) 225?227.10.1007/BF00041995 ↗
23. Lord Kelvin (W. Thomson), Elements of a mathematical theory of elasticity. Phil. Trans. Roy. Soc. Lond. 166 (1856) 481?498.
24. Lord Kelvin (W. Thomson), Encyclopedia Britanica 7 (1878) 796?825. 9th edn. London and Edinburgh.
25. I. Todhunter and K. Pearson, A History of the Theory of Elasticity. Vol. II, part II (1893). Reprinted by Dover: New York.
26. A.C. Pipkin, Constraints in linear elastic materials. J. Elasticity 6 (1976) 179?193.10.1007/BF00041785 ↗
27. J. Rychlewski, On Hooke's law. Prikl. Math. Mekh. 48 (1984) 303?314.
28. M.M. Mehrabadi and S.C. Cowin, Eigentensors of linear anisotropic elastic materials. Q. J. Mech. Appl. Math. 43 (1990) 15?41.10.1093/qjmam/43.1.15 ↗
29. S. Sutcliffe, Spectral decomposition of the elasticity tensor. J. Appl. Mech. 59 (1992) 762?773.10.1115/1.2894040 ↗
30. H. Xiao, Invariant characteristic representations for anisotropic material tensors. Ph.D. dissertation, Shanghai Institute of Appl. Math. & Mech. at Shanghai University (1990).
31. H. Xiao, Inequalities for micropolar elastic constants: cubic crystal classesO, O h , T d and hemitropic solids. Int. J. Engng Sci. 32 (1994) 385?393.10.1016/0020-7225(94)90010-8 ↗
32. J. Rychlewski, Decomposition of the elastic energy and limit criteria. Advances in Mechanics 7 (1984) 3, 51?80.
33. P.S. Theocaris and T.P. Philippidis, Variational bounds on the eigenangle ? of transversely isotropic materials. Acta Mech. 85 (1990) 31?26.
34. P.S. Theocaris and T.P. Philippidis, Spectral decomposition of compliance and stiffness fourthrank tensor suitable for orthotropic materials. Zeit. Angew. Math. Mech. 71 (1991) 161?171.10.1002/zamm.19910710104 ↗
35. J. Rychlewski and H. Xiao, Elasticity models of multidirectional composites with strong fibers. Advances in Mechanics 14 (1991) 1, 41?78.
36. J. Rychlewski, On thermoelastic constants. Arch. Mech. 36 (1984) 77?95.
37. L.B. Ilcewicz, M.N.L. Narasimhan and J.B. Wilson, Micro and Macro material symmetries in generalized continua. Int. J. Engng. Sci. 24 (1986) 97?109.10.1016/0020-7225(86)90152-7 ↗