Mimosa: A model for a self-actuating structural system

The pulvinus of the Mimosa pudica allows the plant curl up its leaves and drop its stems over a very short time span. This high strain, high strain-rate, but low energy movement is made possible through a series of hydraulic-type actuators - the cells. As the cells on one side of the pulvinus lose water and deflate, it bends over, moving whatever is attached to it. We have examined the action of the pulvinus with a computational model to investigate possible scaling effects and to determine what material properties might be required to build a larger artificial "pulvinus". The pulvinus is modeled as cantilever beam composed of layered axial water-filled balloons (or cells). The water is assumed to have no tensile strength, and the balloon material is assumed linear-elastic. The stresses and strains in the pulvinus are determined using a moment-curvature analysis. Our analyses indicate that the balloon material requirements needed to achieve the full range of motion while sustaining a load of 10 times its self-weight are an elastic modulus of 12.5 MPa, an ultimate tensile strength of 25 MPa and a failure strain of at least 200%, for which a set of readily available candidate materials does not currently exist.