The Development of a Robust Rigid–Flexible Interface and Continuum Model for an Elephant’s Trunk Using Hybrid Coordinate Formulations

The goal of this study was to construct a mathematical and computational model that accurately represents the complex, flexible movements and mechanics of an elephant’s trunk. Rather than serving as a biological study, the elephant trunk model was used as an application to demonstrate the effectiveness of a proposed rigid–flexible coupling framework. This model has broader applications beyond understanding the mechanics of an elephant trunk, including its potential use in designing flexible robotic systems and prosthetics, as well as contributions to the fields of biomechanics and animal locomotion. An elephant’s trunk, a highly flexible and muscular organ without bones, is best modeled using continuum mechanics to capture the dynamic behavior of its motion. Given the rigid body nature of an elephant’s head movement and the highly flexible nature of the trunk, a robust geometric framework for the rigid–flexible interface is crucial to accurately capture the complex interactions, force transmission, and dynamic behavior arising from their distinct motion characteristics and differing coordinate representations. Under the umbrella of flexible multibody dynamics, this study introduced a hybrid coordinate system, integrating the Natural Coordinates Formulation (NCF) and the Absolute Nodal Coordinates Formulation (ANCF), to establish the geometric constraints governing the interaction between the rigid body (the head) and the highly flexible body (the trunk). Moreover, the model illustrates how forces and moments are transmitted between these components in both direct and inverse scenarios. Various finite elements were evaluated to identify suitable elements for modeling the elephant’s trunk. The model’s accuracy was validated through simulations of bending, twisting, compression, and other characteristic trunk movements. The solution method is presented alongside the simulation analysis for various motion scenarios, providing a comprehensive framework for understanding and replicating the trunk’s complex dynamics.