The pre-strained elastica

Most biological solids are residually strained. Thus, even in the absence of external loads, there are globally equilibrated internal stresses. This is likely crucial for stability and the control of growth and movement. We use experiments and theory to investigate a variant of a classical problem in the stability of structures, the Euler elastica. We show that the usual buckling instability of a pre-strained elastica differs significantly from that of the classical case: the beam is considerably more stable against buckling, but suffers from a sub-critical instability. We then experimentally validate these theoretical predictions using a 3D printed model. We conclude with some thoughts on how to extend our framework to more complex geometries and structures.