Nuclei of strain at three-dimensional bimaterial interfaces

Markenscoff, X.; Ye, W.

doi:10.1090/qam/1604833

Authors: X. Markenscoff and W. Ye
Journal: Quart. Appl. Math. 56 (1998), 191-200
MSC: Primary 73C02
DOI: https://doi.org/10.1090/qam/1604833
MathSciNet review: MR1604833
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Abstract: When nuclei of strain approach the interface of two materials, the displacement fields may not be unique and may depend on the direction from which the interface is approached. For example, the displacement fields of a center of dilatation at the interface of two materials are not unique and depend on the direction of approach to the interface. To avoid misunderstanding, it can be stressed that each of the two fields is continuous at the interface. In this paper, we show that there are 12 independent displacement functions of second-order singularities uniquely defined at an interface. The limits of all other nuclei of strain at the interface are linear combinations of these 12 independent displacement functions.

J. L. Carvalho and J. H. Curran, Two-dimensional Green’s functions for elastic bi-materials, Trans. ASME J. Appl. Mech. 59 (1992), no. 2, 321–327. MR 1176292, DOI https://doi.org/10.1115/1.2899523
J. Dundurs and M. Hetényi, Transmission of force between two semi-infinite solids, Trans. ASME Ser. E. J. Appl. Mech. 32 (1965), 671–674. MR 187471
John Dundurs and Xanthippi Markenscoff, The Sternberg-Koiter conclusion and other anomalies of the concentrated couple, Trans. ASME J. Appl. Mech. 56 (1989), no. 2, 240–245. MR 1001747, DOI https://doi.org/10.1115/1.3176074

X. Markenscoff, J. Dundurs, and W. Ye, Elastic singularities at bimaterial interfaces, AMD, Vol. 148, Defects and Anelasticity in the Characterization of Crystalline Solids, ASME, 1992, pp. 93–96

Raymond D. Mindlin and David H. Cheng, Nuclei of strain in the semi-infinite solid, J. Appl. Phys. 21 (1950), 926–930. MR 37715

L. Rongved, Force interior to one of two joined semi-infinite solids, In Proc. First Midwestern Conf. on Solid Mech., University of Illinois, Urbana, Illinois, 1955, pp. 55–59

Sinnathurai Vijayakumar and Donald E. Cormack, Green’s functions for the biharmonic equation: bonded elastic media, SIAM J. Appl. Math. 47 (1987), no. 5, 982–997. MR 908460, DOI https://doi.org/10.1137/0147065

S. Vijayakumar and D. E. Cormack, Nuclei of strain for bi-material elastic media with sliding interface, Journal of Elasticity 17, 285–290 (1987)

W. Ye, Nuclei of strain at bimaterial interfaces, Master’s thesis, University of California, San Diego, 1992

H. Y. Yu and S. C. Sanday, Elastic fields in joined half-spaces due to nuclei of strain, Proc. Roy. Soc. London Ser. A 434 (1991), no. 1892, 503–519. MR 1126866, DOI https://doi.org/10.1098/rspa.1991.0110