An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is further objective and locking-free. Finite rotations are represented using a director formulation that avoids singularities and yields a constant mass matrix. This results in an infinite-dimensional nonlinear port-Hamiltonian (PH) system governed by partial differential-algebraic equations with a quadratic energy functional. Using a time-differentiated compliance form of the stress-strain relations allows for the imposition of kinematic constraints, such as inextensibility or shear-rigidity. A structure-preserving finite element discretization leads to a finite-dimensional system with PH structure, thus facilitating the design of an energy-momentum consistent integration scheme. Dissipative material behavior (via the generalized-Maxwell model) and non-standard actuation approaches (via pneumatic chambers or tendons) integrate naturally into the framework. As illustrated by selected numerical examples, the present framework establishes a new approach to energy-momentum consistent formulations in computational mechanics involving finite rotations.

翻译：本文提出了一种基于能量的建模框架，用于描述经历大位移和大转动的空间Cosserat杆的非线性动力学。该混合公式具有独立的位移、速度和应力变量，并进一步具备客观性和无闭锁性。有限转动采用导向矢量公式表示，避免了奇异性并得到恒定质量矩阵。由此得到一个由具有二次能量泛函的偏微分-代数方程控制的无限维非线性端口哈密顿系统。利用应力-应变关系的时域微分柔度形式，可以施加运动学约束，如不可延伸性或抗剪刚性。通过结构保持有限元离散化，得到一个具有端口哈密顿结构的有限维系统，从而便于设计能量-动量一致的积分格式。耗散材料行为（通过广义麦克斯韦模型）和非标准驱动方法（通过气动腔或肌腱）可自然地融入该框架。如所选数值算例所示，本框架为涉及有限转动的计算力学中的能量-动量一致公式建立了一种新方法。