Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers

Elastic waves are scattered by an elastic inclusion. The interface between the inclusion and the surrounding material is imperfect: the displacement and traction vectors on one side of the interface are assumed to be linearly related to both the displacement vector and the traction vector on the other side of the interface. The literature on such inclusion problems is reviewed, with special emphasis on the development of interface conditions modeling different types of interface layer. Inclusion problems are formulated mathematically, and uniqueness theorems are proved. Finally, various systems of boundary integral equations over the interface are derived.

[1]  D. S. Jones,et al.  LOW-FREQUENCY SCATTERING BY A BODY IN LUBRICATED CONTACT , 1983 .

[2]  Jan Drewes Achenbach,et al.  REFLECTION AND TRANSMISSION OF ELASTIC WAVES BY A PERIODIC ARRAY OF CRACKS. , 1985 .

[3]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[4]  A. Toledano,et al.  SHEAR-DEFORMABLE TWO-LAYER PLATE THEORY WITH INTERLAYER SLIP , 1988 .

[5]  G. Murty.  A theoretical model for the attenuation and dispersion of stoneley waves at the loosely bonded interface of elastic half spaces , 1975 .

[6]  A. H. Shah,et al.  Effect of Interface Layers on Scattering of Elastic Waves , 1988 .

[7]  Jacob Aboudi,et al.  Damage in composites—Modeling of imperfect bonding , 1987 .

[8]  S. Rokhlin,et al.  An elastic interface wave guided by a thin film between two solids , 1980 .

[9]  E. Sternberg,et al.  Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , 1980 .

[10]  S. Rokhlin,et al.  Analysis of boundary conditions for elastic wave interaction with an interface between two solids , 1991 .

[11]  M. Kitahara,et al.  On a Method to Analyze Scattering Problems of an Inclusion with Spring Contacts , 1988 .

[12]  F. Smithies,et al.  Singular Integral Equations , 1955, The Mathematical Gazette.

[13]  Z. L. Li,et al.  Reflection and Transmission of Rayleigh Surface Waves by a Material Interphase , 1991 .

[14]  Anders E Boström,et al.  Elastodynamic Scattering From Inclusions Surrounded by Thin Interface Layers , 1990 .

[15]  P. Olsson,et al.  2–D elastodynamic scattering from a semi–infinite cracklike flaw with interfacial forces , 1991 .

[16]  Z. Hashin.  Composite Materials with Interphase: Thermoelastic and Inelastic Effects , 1991 .

[17]  R. B. Thompson,et al.  Long wavelength elastic scattering from a planar distribution of inclusions , 1985 .

[18]  Fadil Santosa,et al.  A model for a composite with anisotropic dissipation by homogenization , 1989 .

[19]  Joseph L. Rose,et al.  A transverse‐wave ultrasonic oblique‐incidence technique for interfacial weakness detection in adhesive bonds , 1988 .

[20]  A. Mal.  Guided waves in layered solids with interface zones , 1988 .

[21]  M. Schoenberg.  Elastic wave behavior across linear slip interfaces , 1980 .

[22]  Paul A. Martin,et al.  ON THE SCATTERING OF ELASTIC WAVES BY AN ELASTIC INCLUSION IN TWO DIMENSIONS , 1990 .

[23]  A. Mal,et al.  Elastic Waves in Layered Media with Interface Features , 1989 .

[24]  A. Nayfeh,et al.  Simulation of the Influence of Bonding Materials on the Dynamic Behavior of Laminated Composites , 1978 .

[25]  A. H. Shah,et al.  Phase velocity and attenuation of plane elastic waves in a particle-reinforced composite medium , 1988 .

[26]  R. Kleinman,et al.  The resistive and conductive problems for the Exterior Helmholtz Equation , 1990 .

[27]  J. Aboudi.  Wave propagation in damaged composite materials , 1988 .

[28]  Anders E Boström,et al.  Elastodynamic scattering from inclusions with thin interface layers , 1988 .

[29]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .

[30]  J. Jones,et al.  Waves at a Flexibly Bonded Interface , 1967 .

[31]  Anders Klarbring,et al.  Derivation of a model of adhesively bonded joints by the asymptotic expansion method , 1991 .

[32]  G. Murty,et al.  On the parametric model of loose bonding of elastic half spaces , 1976 .

[33]  Dominique Leguillon,et al.  Homogenized constitutive law for a partially cohesive composite material , 1982 .

[34]  A. Mal,et al.  Dynamic elastic moduli of a suspension of imperfectly bonded spheres , 1974, Mathematical Proceedings of the Cambridge Philosophical Society.

[35]  H. Ledbetter,et al.  Effect of Interface Properties on Wave Propagation in a Medium With Inclusions , 1986 .

[36]  R. B. Thompson,et al.  Ultrasonic scattering from imperfect interfaces: A quasi-static model , 1984 .