  We investigate the stability and geometrically non-linear dynamics of slender
rods made of a linear isotropic poroelastic material. Dimensional reduction
leads to the evolution equation for the shape of the poroelastica where, in
addition to the usual terms for the bending of an elastic rod, we find a term
that arises from fluid-solid interaction. Using the poroelastica equation as a
starting point, we consider the load controlled and displacement controlled
planar buckling of a slender rod, as well as the closely related instabilities
of a rod subject to twisting moments and compression when embedded in an
elastic medium. This work has applications to the active and passive mechanics
of thin filaments and sheets made from gels, plant organs such as stems, roots
and leaves, sponges, cartilage layers and bones.
