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A moment–curvature-based constitutive model for interactive simulation of visco-plastic rods

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Abstract

A moment–curvature constitutive model is proposed for the dynamic simulation of visco-plastic rods subject to time-varying loads and constraints at interactive rates. Smooth spline functions are used to discretize the geometry of the rod and its kinematics with the centerline coordinates as degrees of freedom (DOF) and scalar twist as degrees of freedom (DOF). The plastic curvature is defined as a uniformly varying field in contrast to localized lumped plasticity models, suitable for simulation of spatial rods that undergo uniform plastic deformation such as a cable or surgical suture thread. The yield criterion and plastic/visco-plastic flow rule are developed for spatial rods taking advantage of the availability of smooth moment–curvature fields using the spline-based formulation. With the Bishop frame field as a reference, the material curvatures are quantified using the twist degree of freedom, enabling tracking the plastic fields with scalar twist, thereby eliminating slopes as DOF. Taking advantage of the invariant sub-blocks and the sparsity of the dynamic system matrix arising from the numerical discretization, an hierarchical (H-matrix) solution approach is utilized for efficient computation. Uniform curvature bending tests and moment relaxation tests are performed to study the convergence behavior of the model. Several real-world tests involving contact are performed to demonstrate the applicability of the model in interactive simulations.

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Data availability statement

No new data were created or analyzed in this study and data sharing is not applicable to this article.

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Acknowledgements

The authors gratefully acknowledge the support of this study by the following NIH/NIBIB grant number: 1R01EB014305. Discussions with Rahul are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Karthikeyan Panneerselvam & Suvranu De

  2. Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA

    Karthikeyan Panneerselvam & Suvranu De

  3. FAMU-FSU College of Engineering, Tallahassee, USA

    Suvranu De

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  1. Karthikeyan Panneerselvam
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Correspondence to Suvranu De.

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Panneerselvam, K., De, S. A moment–curvature-based constitutive model for interactive simulation of visco-plastic rods. Engineering with Computers 40, 2971–2983 (2024). https://doi.org/10.1007/s00366-023-01938-0

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