An approximate analytical 3-D solution for the stresses and strains in eigenstrained cubic materials

International Journal of Solids and Structures

Volumn 35, Issue 22, 1998, Pages 2931-2958

  Muller W H ^a   Neumann, S ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FOURIER TRANSFORMS; INCLUSIONS; STRAIN; STRESSES;

DISCRETE FOURIER TRANSFORMS; EIGENSTRAINED CUBIC MATERIAL;

APPROXIMATION THEORY;

EID: 0032132208     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00350-8     Document Type: Article

References (20)

1. Auld, B. A. (1990) Acoustics Fields and Waves in Solids, Vol. I, 2nd edn. Krieger, Malabar, Florida.
2. Dreyer, W. (1995) Development of microstructure based viscoplastic models for an advanced design of single crystal hot section components. In : Periodic Progress Report, Development of Microstructural Based Viscoplastic Models for an Advanced Design of Single Crystal Hot Section Components, ed. J. Olschewski. Brite/Euram Programme, A.1-17-A.1-29.
3. Dreyer, W. and Olschewski, J. (1994) Order-disorder transitions under load in single crystal superalloys : theory. In Solid → Solid Phase Transformations, ed. W. C. Johnson, J. M. Howe, D. E. Laughlin and W. A. Soffa, pp. 419-424. The Minerals, Metals and Materials Society.
4. Dreyer, W., Müller, W. H. and Olschewski, J. (1997) An approximate analytical 2-D solution for the stresses and strains in eigenstrained cubic materials. Acta Mechanica, submitted.
5. Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series, and Products. Academic Press, New York.
6. Hazotte, A. and Lacaze, J. (1994) Caractérisation quantitative de la microstructure des superalliages à base de nickel. La Revue de Métallurgie-CIT/Science et Génie des Matériaux, Février 1994, pp. 277-294.
7. Ignat, M., Buffiere, J.-Y. and Chaix, J. M. (1993) Microstructures induced by a stress gradient in a nickel-base superalloy. Acta metall. mater. 41(3), 855-862.
8. Khachaturyan, A. G. and Shatalov, G. A. (1969) Elastic-interaction potential of defects in a crystal. Soviet Physics - Solid State 11 (1), 118-123.
9. Mader, W. (1987) On the electron diffraction contrast caused by large inclusions. Philosophical Magazine A 55(1), 59-83.
10. McCormack, M., Khachaturyan, A. G. and Morris, Jr, J. W. (1992) A two-dimensional analysis of the evolution of coherent precipitates in elastic media. Acta Metall. Mater. 40(2), 325-336.
11. Mura, T. (1987) Micromechanics of Defects in Solids. Second revised edn. Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
12. Moulinec, H. and Suquet, P. (1994) A fast numerical method for computing the linear and non-linear mechanical properties of composites. C.R. Acad. Sci. Paris 318(II), 1417-1423.
13. Moulinec, H. and Suquet, P. (1996) A numerical method for computing the overall response of composites from images of their microstructures. In Microstructure - Property Interactions in Composite Materials, ed. R. Pyrz, pp. 235-246.
14. Moulinec, H. and Suquet, P. (1997) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comp. Meth. Appl. Mech. Engng, in print.
15. Müller, W. H. (1996) Mathematical vs experimental stress analysis of inhomogeneities in solids. Journal de Physique IV. Colloque C1, supplément au Journal de Physique III 6, C1-139-C1-148.
16. Pineau, A. (1975) Influence of uniaxial stress on the morphology of coherent precipitates during coarsening -elastic energy considerations. Acta Metallurgica 24, 559-564.
17. Socrate, S. and Parks, D. M. (1993) Numerical determination of the elastic driving force for directional coarsening in Ni-superalloys. Acta metall. mater. 41(7), 2185-2209.
18. Tien, K. and Copley, S. M. (1970) The effect of orientation and sense of applied uniaxial stress on the morphology of coherent gamma prime precipitates in stress annealed nickel-base superalloy crystals. Metallurgical Transactions 2, 543-553.
19. Wang, Y., Chen, L.-Q. and Khachaturyan, A. G. (1992) Particle translational motion and reverse coarsening phenomena in multiparticle systems induced by a long-range elastic interaction. Physical Review B 46(17), 11,194-11,197.
20. Wolfram, S. (1992) Mathematica® Ein System für Mathematik auf dem Computer. Zweite Auflage. Addison-Wesley Publishing Company, Bonn.