Ultra-fast physics-based modeling of the elephant trunk

With more than 90,000 muscle fascicles, the elephant trunk is a complex biological structure and the largest known muscular hydrostat. It achieves unprecedented control through intricately orchestrated contractions of a wide variety of muscle architectures. Fascinated by the elephant trunk's unique performance, scientists of all disciplines are studying its anatomy, function, and mechanics, and use it as an inspiration for biomimetic soft robots. Yet, to date, there is no precise mapping between microstructural muscular activity and macrostructural trunk motion, and our understanding of the elephant trunk remains incomplete. Specifically, no model of the elephant trunk employs formal physics-based arguments that account for its complex muscular architecture, while preserving low computational cost to enable fast screening of its configuration space. Here we create a reduced-order model of the elephant trunk that can - within a fraction of a second - predict the trunk's motion as a result of its muscular activity. To ensure reliable results in the finite deformation regime, we integrate first principles of continuum mechanics and the theory of morphoelasticity for fibrillar activation. We employ dimensional reduction to represent the trunk as an active slender structure, which results in closed-form expressions for its curvatures and extension as functions of muscle activation and anatomy. We create a high-resolution digital representation of the trunk from magnetic resonance images to quantify the effects of different muscle groups. We propose a general solution method for the inverse motion problem and apply it to extract the muscular activations in three representative trunk motions: picking a fruit; lifting a log; and lifting a log asymmetrically. For each task, we identify key features in the muscle activation profiles. Our results suggest that the elephant trunk either autonomously reorganizes muscle activation upon reaching the maximum contraction or chooses the inverse problem branches that avoid reaching the contraction constraints throughout the motion. Our study provides a complete quantitative characterization of the fundamental science behind elephant trunk biomechanics, with potential applications in the material science of flexible structures, the design of soft robots, and the creation of flexible prosthesis and assist devices.