Using the complex variable formulation developed by Suo (1990), we
derive an explicit closed-form expression for the compressibility of a
quasihypotrochoidal pore in an infinite degenerate orthotropic elastic
material. The shape of the pore boundary is hypotrochoidal in the
-plane
where
is the single complex variable appearing in Suo’s formulation. The pore
compressibility is defined as the fractional decrease in the area of the
pore due to a remote hydrostatic pressure of unit magnitude. The
compressibility is independent of the rotation of the pore boundary in the
-plane
for all cases except pores of fourfold symmetry in the
-plane.
The compressibilities of pores having fourfold symmetry in the
-plane vary
with
,
where
is the rotation angle of the pore boundary in the
-plane.
We also derive a closed-form expression for the compressibility of a pore having an
()-fold axis of
quasisymmetry with
in an infinite degenerate orthotropic elastic material. The pore,
which is described by a three-term mapping function, has an
()-fold axis of
symmetry in the
-plane.
