Using the radon transform to solve inclusion problems in elasticity

International Journal of Solids and Structures

Volumn 41, Issue 3-4, 2004, Pages 585-606

  Franciosi, P ^a   Lormand, G ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

Elasticity; Eshelby inclusion problem; Green operator integral; Radon transform

Indexed keywords

APPROXIMATION THEORY; ELASTIC MODULI; GEOMETRY; INCLUSIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; MICROSTRUCTURE; MORPHOLOGY; PROBLEM SOLVING;

RADON TRANSFORMS;

ELASTICITY;

ELASTICITY; INCLUSION;

EID: 0346670147     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2003.10.011     Document Type: Article

References (30)

1. Berveiller M. Fassi-Fehri O. Hihi A. The problem of two plastic and heterogeneous inclusions in an anisotropic medium International Journal of Engineering Sciences 25 6 1987 691-709
2. Bornert M. Stolz C. Zaoui A. Morphologically representative pattern-based bounding in elasticity Journal of the Mechanics and Physics of Solids 44 3 1996 307-331
3. Canova G.R. Wenk H.R. Molinari A. Deformation modelling of multiphase polycrystals: case of a quartz-mica aggregate Acta Metallurgica et Materialia 40 7 1992 1519-1530
4. Chiu Y.P. On the stress field due to initial strains in a cuboid surrounded by an infinite elastic space Journal of Applied Mechanics 12 1977 587-590
5. Christensen R.M. Mechanics of composite materials 1979 Wiley Interscience New York
6. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion and related problems Proceedings of the Royal Society London A 421 1957 379-396
7. ′ superalloy single crystals. Part II: numerical analysis of heterogeneity effects Acta Metallurgica et Materialia 45 4 1995 1567-1584
8. Gel'fand, I.M., Graev, M.I., Vilenkin, N.Ya., 1966. Generalised Functions, Integral Geometry and Representation Theory, Vol. 5, Academic Press, New York and London
9. Hill R. The elastic behaviour of crystalline aggregates Proceedings of the Physical Society A 65 1952 349-354
10. Jiang L.Z. Integral representation and Green's functions for 3D time-dependent thermo-piezoelectricity International Journal of Solids and Structures 37 2000 6155-6171
11. Kinoshita N. Mura T. Elastic fields of inclusions in anisotropic media Physica Status Solidi A 5 1971 759-768
12. Kneer G. Calculation of elastic moduli of polycrystalline aggregates with textures Physica Status Solidi A 9 1965 825-838
13. Kröner E. Berechnung der elastischen constanten des vielkristalls aus den konstanten des einkristalls Zeitschrift fur Physik 1958 151-504
14. Lykotrakis G. Georgiadis H.G. The three dimensional steady-state thermo-elastodynamic problem of moving sources over a half space International Journal of Solids and Structures 40 2003 899-940
15. Mura T. Micro-mechanics of defects in solids 1982 Martinus Nijhoff La Hague
16. Mura T. The determination of the elastic field of a polygonal star shaped inclusions Mechanics Research Communications 24 5 1997 473-482
17. Nemat-Nasser S. Hori M. Micro-mechanics: overall properties of heterogeneous materials 1999 North-Holland Amsterdam
18. Ponte Castaneda P. Willis J.R. The effect of spatial distribution on the effective behaviour of composite materials and cracked media Journal of the Mechanics and Physics of Solids 43 12 1995 1919-1951
19. Riccardi A. Montheillet F. Translation et expansion des potentiels harmoniques spheroidaux: application à deux problmes délasticité linéaire Comptes Rendus de l'Académie des Sciences Paris 325 1998 241-248
20. Riccardi A. Montheillet F. A generalised self-consistent model for solids containing randomly oriented spheroidal inclusions Acta Mechanica 133 1999 39-56
21. Rodin G.J. Eshelby's inclusion problem for polygons and polyhedra Journal of the Mechanics and Physics of Solids 44 1996 1977-1995
22. Sabar H. Buisson M. Berveiller M. The inhomogeneous and plastic inclusion problem with moving boundary International Journal of Plasticity 7 1991 759-772
23. Santalo A. Integral geometry and geometric probability Encyclopedia of mathematics and its applications 1976 Addision-Wesley Reading MA
24. Walpole L.J. The elastic field of an inclusion in an anisotropic medium Proceedings of the Royal Society London A 300 1967 270-289
25. Walpole L.J. Elastic behaviour of composites materials Advances in Applied Mechanics 21 1981 169-242
26. Willis J.R. Variational and related methods for the overall properties of composites Advances in Applied Mechanics 21 1981 1-78
27. Withers P.J. The determination of the elastic field of an ellipsoidal inclusion in a transversally isotropic medium Philosophical Magazine A 59 4 1989 759-781
28. Wu L. Du S.Y. The elastic field caused by a circular cylindrical inclusion--Part I Journal of Applied Mechanics 62 1995 579-584
29. Wu L. Du S.Y. The elastic field caused by a circular cylindrical inclusion--Part II Journal of Applied Mechanics 62 1995 585-589
30. Zeller R. Dederich P.H. Elastic constants of polycrystals Physic State Solids (b) 55 1973 831-842