  While isotropic in-plane swelling problems for thin elastic sheets have been
studied extensively in recent years, many shape-programmable materials,
including nematic solids and 3D-printed structures, are anisotropic, as are
most industrial sheet materials. In this theoretical work, we consider central
swelling and shrinkage of plates of aspect ratio and material properties
relevant to the manufacture of engineered wood composite panels in which both
in-plane swelling and material stiffness are highly orthotropic, leading to
multiple separations in energy scales. With transverse swelling in the soft
direction, and gradients in the stiff direction, the warped plates adopt two
distinct types of configurations, axisymmetric and twisted, which we illustrate
with toy models. We employ a two-parameter family of isometries to embed the
metric programmed by the swelling, thus reducing the problem to one of
minimizing bending energy alone. A simple argument is seen to closely predict
averaged axisymmetric curvatures. While purely cylindrical shapes are
unobtainable by pure in-plane swelling, they can be closely approximated in a
highly anisotropic system. However, anisotropy can favor twisting, and breaks a
degenerate soft deformation mode associated with minimal surfaces in isotropic
materials. Bifurcations from axisymmetric to twisted shapes can be induced by
anisotropy or by certain attributes of a central shrinkage profile. Finally, we
note how our findings indicate practical limitations on the diagnosis of
moisture inhomogeneities in manufactured panels by observation of warped
conformations, due to the sensitivity of the qualitative response to specifics
of the profile.
