Table 1. Nomenclature.

xi	spatial coordinates (x 1, x 2, x 3) = (x,y,z)
ui	displacement vector components (u 1, u 2, u 3) = (u,v,w)
εij	strain tensor components
eij	elastic strain tensor components
βij	transformation strain tensor components
	eigenstrain tensor components
σij	stress tensor components
δij	Kronecker delta components
δijkl	4th-order identity tensor components
ti	traction vector components
ni	unit normal vector components
si	unit tangent vector components
V I, V M	inclusion, matrix subregions
ai	ellipsoid principal axes (a 1, a 2, a 3) = (a,b,c)
V e	ellipsoid volume
S	inclusion-matrix interface surface
μ,κ	shear modulus, bulk modulus
Cijkl	elasticity modulus tensor components
E ,v	Young’s modulus, Poisson’s ratio
φ, ψ	potential functions
Bijk, Dijkl	displacement, strain tensor operators
	Eshelby tensor components
λ	Eshelby parameter
I, Ii, Iij	Eshelby integrals
F, E	elliptic integrals of 1st & 2nd kind
θ, k	elliptic integral arguments
Mij, Nij	defined intermediate integrals
Q, ω	defined constants
αk, A, h, G, J, Λ, Γ, P	defined intermediate functions
η	matrix/inclusion modulus ratio
U	mechanical strain energy