Flexel ecosystem: simulating mechanical systems from entities with arbitrarily complex mechanical responses

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior, such as large shape changes, effect of pre-tension, negative stiffness and instabilities. While traditional finite element analysis is capable of simulating a specific nonlinear structure quantitatively, it can be costly and cumbersome to use due to the high number of degrees of freedom involved. We propose a framework to facilitate the exploration of highly nonlinear structures under quasistatic conditions. In our framework, models are simplified by introducing `flexels', elements capable of intrinsically representing the complex mechanical responses of compound structures. By extending the concept of nonlinear springs, flexels can be characterized by multi-valued response curves, and model various mechanical deformations, interactions and stimuli, e.g., stretching, bending, contact, pneumatic actuation, and cable-driven actuation. We demonstrate that the versatility of the formulation allows to model and simulate, with just a few elements, complex mechanical systems such as pre-stressed tensegrities, tape spring mechanisms, interaction of buckled beams and pneumatic soft gripper actuated using a metafluid. With the implementation of the framework in an easy-to-use Python library, we believe that the flexel formulation will provide a useful modeling approach for understanding and designing nonlinear mechanical structures.