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Description
Large deformations cannot be neglected in many engineering dynamics applications due to their significant contribution to the overall system dynamics. For instance, human gait analysis often employs multibody models that conventionally represent body segments as rigid bodies. However, bones are covered with muscles and other soft tissues that are not rigidly connected with the bones but act as a wobbling mass. While the dynamics of bones can be adequately modeled under the assumption of small deformations, accurately capturing the dynamics of wobbling masses requires accounting for nonlinear elastic forces due to large deformations and nonlinear material behavior. The nodal-based floating frame of reference formulation offers an efficient computational framework for modeling linearly elastic flexible multibody systems. However, incorporating nonlinear elastic forces within the modally-reduced nodal-based floating frame of reference formulation remains challenging, particularly in a computationally efficient and non-intrusive manner. State-of-the-art approaches, such as projection-based reduction combined with hyper-reduction techniques, allow the inclusion of fully nonlinear force expressions. Despite their accuracy, these methods are computationally demanding and require low-level access to a finite element code, making them less practical for many applications. This work explores different approaches for considering nonlinear elastic forces in the modally reduced nodal-based floating frame of reference formulation, which does not require low-level access to a finite element code. Three methods are explored in this work. The first method involves using multiple floating frames to account for nonlinear effects. The second method involves the successive linearization of the nonlinear elastic forces. In the third method, we aim to derive an expression for the nonlinear elastic forces by integrating the components of the tangent stiffness matrix. To achieve this, multiple tangent stiffness matrices corresponding to different nonlinear static finite element solutions are exported for both methods two and three. We then apply matrix interpolation techniques from parametric model order reduction to obtain a computable and integrable representation of the tangent stiffness matrix, ultimately enabling a closed-form expression for the nonlinear elastic forces. Numerical experiments demonstrate the computational efficiency and accuracy of the methods considered.
