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In this paper the reduced parameter dependence in linear plane elasticity with eigenstrains (transformation strains) is studied. The focus is on simply connected inhomogeneous materials and two-phase materials with perfectly bonded interfaces. In the analysis we rely on the result of Cherkaev, Lurie and Milton (Proc. Roy. Soc. Lond. A 438, 519-529, 1992), and we show that the stress field is invariant under a shift in area bulk and shear compliances, if the eigenstrains obey certain conditions. The analysis can be extended to multiply connected inhomogeneous materials and materials with slipping interfaces.
Czasopismo
Rocznik
Tom
Strony
425--437
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, U.S.A.
autor
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, U.S.A.
Bibliografia
- 1. T. Mura, Micromechanics of defects in solids, 2nd ed., Martinus Nijhoff, Dordrecht 1987.
- 2. J. H. Michell, On the direct determination of stress in an elastic solid, with application to the theory of plates, Proc. Lond. Math. Soc. 31, 100-125, 1899.
- 3. J. Dundurs, Effect of elastic constants on stress in a composite under plane deformation, J. Compos. Mater. 1. 310-322, 1967.
- 4. J. Dundurs, Discussion of paper by D.B. Bogy, J. Appl. Mech. 36, 650-652, 1969.
- 5. J.M. Neumeister, On the role of elastic constants in multiphase contact problems, J. Appl. Mech. 59, 328-334, 1992.
- 6. A. Cherkaev, K. Lurie, G.W. Milton, Invariant properties of the stress in plane elasticity and equivalence classes of composites. Proc. R. Soc. Lond. A 438, 519-529, 1992.
- 7. M. F. Thorpe, I. Jasiuk, New results in the theory of elasticity for two-dimensional composites. Proc. R. Soc. Lond. A438, 531-544, 1992.
- 8. J. Dundurs, X. Markenscoff, Invariance of stresses under a change in elastic compliances, Proc. R. Soc. Lond. A 443, 289-300, 1993.
- 9. B. Moran, M. Gosz, On the constitutive response of fiber composites with imperfect interfaces. In Advanced Composites: Design, Materials and Processing Technologies (Proc. 8th Annual ASM/ESD Advanced Composites Conference), pp. 261 266. ASM International 1992.
- 10. B. Moran, M. Gosz, Stress invariance m plane anisotropic elasticity, Modelling Simul. Mater. Sci. Engng. 2, 677-688, 1994.
- 11. Q.-S. Zheng, K.C. Hwang, Reduced dependence of defect compliance on matrix and inclusion elastic properties in two-dimensional elasticity, Proc. R. Soc. Lond. A 452, 2493-2507, 1996.
- 12. Q.-S. Zheng, K.C. Hwang, Two-dimensional elastic compliances of materials with holes and microcracks, Proc. R. Soc. Lond. A 453, 353-364, 1997.
- 13. J. Dundurs, I. Jasiuk, Effective elastic moduli of composite materials: Reduced parameter dependence, Appl. Mech. Rev., 50 (Part 2), S39-S43, 1997.
- 14. I. Jasiuk, J. Dundurs, M. Jiang, On the reduced parameter dependence of the Mon- Tanaka theory, Mater. Sci. & Engng. A, 285, 130 135, 2000.
- 15. X. Markenscoff, I. Jasiuk, On multiple-connectivity and the reduction of constants for composites with body forces, Proc. R. Soc. Lond. A 454, 1357 1369, 1998.
- 16. M. Ostoja-Starzewski, I. Jasiuk, Stress invariance in planar Cosserat elasticity, Proc. R. Soc. Lond. A 451, 453-470, 1995.
- 17. T. Chen, Further results on mvanant properties of the stress in plane elasticity and its extension to piezoelectricity, Mech. Res. Comm. 22, 251-256, 1995.
- 18. Q.-S. Zheng, T. Chen, Generalized plane deformation of electromagnetic thermoelastic solids I. Correspondence and invariance shifts, Proc. R. Soc. Lond. A 455, 1283-1299, 1999.
- 19. Q.-S. Zheng, T. Chen, Generalized plane deformation of electromagnetic thermoelastic solids II. Further results on invariance shifts and reduced dependencies, Proc. R. Soc. Lond. A 455, 1301-1314, 1999.
- 20. A. N. Norris, Stress invariance and redundant moduli in three-dimensional elasticity, Proc. R. Soc. Lond. A 455, 4097-4116, 1999.
- 21. G. K. Hu, G. J. Weng, A new derivative on the shift property of effective elastic compliances for planar and three-dimensional composites, Proc. R. Soc. Lond. A 457, 1675 1684, 2001.
- 22. A. Hoger, On the residual stress possible in an elastic body with material symmetry, Arch. Rat. Mech. Anal. 88, 271-289, 1985.
- 23. J. Dundurs, Boundary conditions at Interface. In Micromechanics and inhomogeneity, The Toshio Mura Anniversary Volume, G.J. Weng, M. Taya and H. Abe |Eds.|, pp. 109 -114. New York: Springer-Verlag, 1990.
- 24. X. Markenscoff, A note on strain jump conditions and Cesaro integrals for bonded and slipping inclusions, J. Elasticity, 45, 33-44, 1996.
- 25. S. D. Boccara, An investigation of micropolar moduli and characteristic lengths of heterogeneous materials and a reduction of constants in plane elasticity with eigenstrains, M.Sc. Thesis, Georgia Institute of Technology, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0002-0074
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