On constitutive relations for a rod-based model of a pneu-net bending actuator

The recent surge of interest in soft robotics has led to interesting designs and fabrication of flexible actuators composed of soft matter. Modeling these actuators to obtain quantitative estimates of their dynamics is challenging. In the present paper, a rod-based model for a popular pneumatically activated soft robot arm is developed. The model is based on Euler's theory of the elastica and is arguably the simplest possible model. Through a synthesis of experiment and theory, we find that the constitutive relations needed to accurately capture the deformation of the arm differ considerably from the simple classical relation that the bending moment is linearly proportional to a change in curvature. The present paper also provides a framework to evaluate whether future soft robot actuator designs can be captured using simple models.