While soft robots have many attractive features compared to their hard counterparts, developing tractable models for these highly deformable, nonlinear, systems is challenging. In a recent paper, the authors published a non-classic, five-parameter constitutive relation for a rod-based model of a widely used, pneumatically actuated soft robot arm. It is natural to ask if the complexity of the relation can be eliminated by redesigning the actuator? To this end, finite element models and experimental results are used to further explore the five-parameter constitutive relation. For multiple designs of the pneumatically actuated soft robot arm, we are able to demonstrate how finite element models can be employed in place of experiments to specify the constitutive relations and how the relations are scalable by actuator length and applied pressure. Our primary result is the finding that the five-parameter constitutive relation is germane to pneumatically actuated soft robot arms and the parameters for this relation can be determined by three finite element simulations.

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.