 
Summary: A Boundary Integral Method for Computing Elastic
Moment Tensors for Ellipses and Ellipsoids
Habib Ammari
Hyeonbae Kang
Hyundae Lee§
October 25, 2005
Abstract
We compute the elastic moment tensors for ellipses and ellipsoids using a systematic
method based on layer potentials. Our computations reveal an underlying relation
between the elastic moment tensors and the single layer potential.
1 Introduction
Let B be a bounded Lipschitz domain in Rd
, d = 2, 3. Suppose that the Lam´e parameters
of B are given by (, µ), while those of the background Rd
\ B are given by (, µ). Attached
to the inclusion B is a 4tensor mij
pq, i, j, p, q = 1, . . . , d, called the elastic moment tensor
(EMT), or the elastic polarization tensor. The notion of EMT can be most simply described
in the following manner. Denote by L,µ the Lam´e operator associated with the parameters
and µ and consider H to be a vectorvalued function satisfying L,µH = 0 in Rd
