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Title: Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

Abstract

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to the complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.

Authors:
 [1]; ORCiD logo [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1399566
Report Number(s):
SAND-2017-8749J
Journal ID: ISSN 0374-3535; 656283
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Elasticity
Additional Journal Information:
Journal Volume: 131; Journal Issue: 2; Journal ID: ISSN 0374-3535
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Interface; Dislocation; Anisotropic; Stroh formalism; Green’s function

Citation Formats

Juan, Pierre -Alexandre, and Dingreville, Remi. Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity. United States: N. p., 2017. Web. doi:10.1007/s10659-017-9655-0.
Juan, Pierre -Alexandre, & Dingreville, Remi. Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity. United States. doi:10.1007/s10659-017-9655-0.
Juan, Pierre -Alexandre, and Dingreville, Remi. Wed . "Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity". United States. doi:10.1007/s10659-017-9655-0. https://www.osti.gov/servlets/purl/1399566.
@article{osti_1399566,
title = {Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity},
author = {Juan, Pierre -Alexandre and Dingreville, Remi},
abstractNote = {Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to the complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.},
doi = {10.1007/s10659-017-9655-0},
journal = {Journal of Elasticity},
number = 2,
volume = 131,
place = {United States},
year = {2017},
month = {9}
}

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Works referenced in this record:

Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media
journal, February 1990

  • Suo, Z.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 427, Issue 1873
  • DOI: 10.1098/rspa.1990.0016

A continuum theory of elastic material surfaces
journal, December 1975

  • Gurtin, Morton E.; Ian Murdoch, A.
  • Archive for Rational Mechanics and Analysis, Vol. 57, Issue 4
  • DOI: 10.1007/BF00261375

Explicit solution and invariance of the singularities at an interface crack in anisotropic composites
journal, January 1986


Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces
journal, March 2003


Atomistic modeling of the interaction of glide dislocations with “weak” interfaces
journal, November 2008


Plane boundaries and straight dislocations in elastically anisotropic materials
journal, June 1969


Explicit solutions for collinear interface crack problems
journal, January 1993


Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N
journal, January 1988


Transmission of Force Between Two Semi-Infinite Solids
journal, September 1965

  • Dundurs, J.; Hete´nyi, M.
  • Journal of Applied Mechanics, Vol. 32, Issue 3
  • DOI: 10.1115/1.3627277

Surface stress and the chemical equilibrium of small crystals—II. Solid particles embedded in a solid matrix
journal, January 1982


A semi-analytical method to estimate interface elastic properties
journal, July 2009


From coherent to incoherent mismatched interfaces: A generalized continuum formulation of surface stresses
journal, December 2014

  • Dingreville, Rémi; Hallil, Abdelmalek; Berbenni, Stéphane
  • Journal of the Mechanics and Physics of Solids, Vol. 72
  • DOI: 10.1016/j.jmps.2014.08.003

Use of analytical relations in evaluation of exponential integral functions
journal, August 2005


A simplified algorithm for the second-order sound fields
journal, December 2000

  • Ding, Desheng
  • The Journal of the Acoustical Society of America, Vol. 108, Issue 6
  • DOI: 10.1121/1.1320471

Screw dislocation interacting with imperfect interface
journal, October 2003


A new dislocation-like model for imperfect interfaces and their effect on load transfer
journal, January 1998


Recent developments in anisotropic elasticity
journal, January 2000


The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth
journal, January 1931


Interfacial excess energy, excess stress and excess strain in elastic solids: Planar interfaces
journal, May 2008

  • Dingreville, Rémi; Qu, Jianmin
  • Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 5
  • DOI: 10.1016/j.jmps.2007.11.003

Neutron Transport in a Nonuniform Slab with Generalized Boundary Conditions
journal, May 1970

  • Belleni‐Morante, A.
  • Journal of Mathematical Physics, Vol. 11, Issue 5
  • DOI: 10.1063/1.1665293

Displacements and tractions along interfaces
journal, November 1987


The Elastic Inclusion With a Sliding Interface
journal, June 1984

  • Mura, T.; Furuhashi, R.
  • Journal of Applied Mechanics, Vol. 51, Issue 2
  • DOI: 10.1115/1.3167617

Anisotropic elasticity with applications to dislocation theory
journal, May 1953


Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials
journal, September 1991

  • Qu, Jianmin; Li, Qianqian
  • Journal of Elasticity, Vol. 26, Issue 2
  • DOI: 10.1007/BF00041220

Elastic analysis of finite stiffness bimaterial interfaces: application to dislocation–interface interactions
journal, May 1998


Existence of an extraordinary degenerate matrix N for anisotropic elastic materials
journal, August 1996

  • Ting, T.
  • The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 49, Issue 3
  • DOI: 10.1093/qjmam/49.3.405

Elastic Green's function for a composite solid with a planar interface
journal, February 1989

  • Tewary, V. K.; Wagoner, R. H.; Hirth, J. P.
  • Journal of Materials Research, Vol. 4, Issue 1
  • DOI: 10.1557/JMR.1989.0113

Green's function in plane anisotropic bimaterials with imperfect interface
journal, October 2006


Dislocations and Cracks in Anisotropic Elasticity
journal, June 1958


Atomistic simulations of dislocation–interface interactions in the Cu-Ni multilayer system
journal, September 2000


Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity
journal, February 2017

  • Juan, Pierre-Alexandre; Dingreville, Rémi
  • Journal of the Mechanics and Physics of Solids, Vol. 99
  • DOI: 10.1016/j.jmps.2016.10.009