Development of Numerical Solutions Using Matlab for the Eshelby Equations for an Ellipsoidal Inhomogeneity and
Inclusion in Elastic Materials
Personnel: J.O. Kaven, D.D. Pollard, Kurt Sternlof
Collaborators: Pradeep Sharma

Sponsor: Stanford Rock Fracture Project
Description: This project aims to make a computer code available that calculates stresses and displacements around an ellipsoidal inhomogeneity and inclusion. The solutions derived first by Eshelby in 1957 are implemented in MatLab, a programming language, and are applied in the research on deformation bands. The numerical solutions help understand the mechanics and development of such features. Eshelby's solutions have been widely applied in Engineering and build the foundation to many problems in micro-mechanics. In the realm of micro-mechanics stresses very near the perimeter of the ellipsoid are of interest, whereas in geologic applications stress and displacements fields in the vicinity of the inhomogeneity are important as well. Our goal is to supply a computer code that is capable of calculating these fields, and which helps to benchmark numerical approximations of BEM computer codes.

Selected Publications:

Eshelby, J.D., 1957, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, A241, pp.376-396