Structure-preserving simulation of Cosserat rod dynamics in a mixed, port-Hamiltonian framework
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Although the Cosserat rod model is well established, mixed formulations and corresponding finite element methods for its dynamic behavior remain relatively scarce. Likewise, only few works have explored Cosserat rods within the port-Hamiltonian (PH) framework, despite the framework’s natural suitability for modeling complex interconnected systems. To this end, we present an energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large deformations and rotations. The mixed formulation employs independent configuration, velocity, and stress variables, ensuring objectivity and eliminating locking effects. Finite rotations are handled using a director-based parametrization that avoids singularities and results in a constant mass matrix. This leads to an infinite-dimensional nonlinear PH system governed by partial differential–algebraic equations with a quadratic energy functional. A time-differentiated compliance representation of the stress–displacement relations enables the straightforward inclusion of kinematic constraints, such as inextensibility or shear rigidity. Dissipative material behavior (via generalized Maxwell models) and nonstandard actuation mechanisms (such as pneumatic chambers or tendons) integrate naturally into the same framework. Finally, a structure-preserving finite element discretization leads to a finite dimensional PH system. Combined with a midpoint-based time integrator, the approach yields exact energy and momentum balance laws in discrete time, thus enhancing robustness for long-term simulations. As illustrated by numerical examples, the present framework establishes a new approach to energy-momentum consistent formulations in computational mechanics involving finite rotations. More details can be found in the related manuscript.
