The emergence of “soft” robots, whose bodies are made from stretchable materials, has fundamentally changed the way we design and construct robotic systems. Demonstrations and research show that soft robotic systems can be useful in rehabilitation, medical devices, agriculture, manufacturing and home assistance. Increasing need for collaborative, safe robotic devices have combined with technological advances to create a compelling development landscape for soft robots.

However, soft robots are not yet present in medical and rehabilitative devices, agriculture, our homes, and many other human-collaborative and human-interactive applications. This gap between promise and practical implementation exists because foundational theories and techniques that exist in rigid robotics have not yet been developed for soft robots. Theories in traditional robotics rely on rigid body displacements via discrete joints and discrete actuators, while in soft robots, kinematic and actuation functions are blended, leading to nonlinear, continuous deformations rather than rigid body motion.

This dissertation addresses the need for foundational techniques using continuum mechanics. Three core questions regarding the use of continuum mechanical models in soft robotics are explored:​ (1) whether or not continuum mechanical models can describe existing soft actuators, (2) which physical phenomena need to be incorporated into continuum mechanical models for their use in a soft robotics context, and (3) how understanding on continuum mechanical phenomena may form bases for novel soft robot architectures. Theoretical modeling, experimentation, and design prototyping tools are used to explore Fiber-Reinforced Elastomeric Enclosures (FREEs), an often-used soft actuator, and to develop novel soft robot architectures based on auxetic behavior.

This dissertation develops a continuum mechanical model for end loading on FREEs. This model connects a FREE’s actuation pressure and kinematic configuration to its end loads by considering stiffness of its elastomer and fiber reinforcement. The model is validated against a large experimental data set and compared to other FREE models used by roboticists. It is shown that the model can describe the FREE’s loading in a generalizable manner, but that it is bounded in its peak performance. Such a model can provide the novel function of evaluating the performance of FREE designs under high loading without the costs of building and testing prototypes. This dissertation further explores the influence viscoelasticity, an inherent property of soft polymers, on end loading of FREEs. The viscoelastic model developed can inform soft roboticists wishing to exploit or avoid hysteresis and force reversal. The final section of the dissertations explores two contrasting styles of auxetic metamaterials for their uses in soft robotic actuation. The first metamaterial architecture is composed of beams with distributed compliance, which are placed antagonistic configurations on a variety of surfaces, giving ride to shape morphing behavior. The second metamaterial architecture studied is a “kirigami” sheet with an orthogonal cut pattern, utilizing lumped compliance and strain hardening to permanently deploy from a compact shape to a functional one. This dissertation lays the foundation for design of soft robots by robust physical models, reducing the need for physical prototypes and trial-and-error approaches. The work presented provides tools for systematic exploration of FREEs under loading in a wide range of configurations. The work further develops new concepts for soft actuators based on continuum mechanical modeling of auxetic metamaterials. The work presented expands the available tools for design and development of soft robotic systems, and the available architectures for soft robot actuation.