# 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:

- 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:
- Journal Article: 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 = {Wed Sep 13 00:00:00 EDT 2017},

month = {Wed Sep 13 00:00:00 EDT 2017}

}