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A mixed-order interpolation solid element for efficient arterial wall simulations

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Abstract

A numerical strategy tailored to model the mechanical equilibrium in vascular vessels is presented. The formulation, based on a specific arrangement of finite elements, exploits the shell-like structure of the vessel wall by proposing a mixed-order approximation of the displacement field. The fields across the thickness are represented by a single element with high order polynomial approximation while the in-plane components are described through low-order 2D polynomials. The formulation is versatile to accommodate any kind of hyperelastic constitutive material model undergoing large strains. A series of numerical examples is presented to validate the effectiveness of the proposed approach. These examples range from benchmark problems reported in the literature to applications in the domain of cardiovascular modeling. The proposed approach proved to be effective and efficient in simulating the mechanics of vascular vessels.

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Acknowledgements

LAMA is supported in part by Brazilian agency CNPq (Grant Number 302210/2020-2). PJB and RAF are supported in part by Brazilian agencies CNPq (Grant Numbers 301224/2016-1, 407751/2018-1 and 301636/2019-2), and FAPESP (Grant Number 2014/50889-7).

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Authors and Affiliations

  1. National Laboratory for Scientific Computing, Av. Getulio Vargas 333, Petrópolis, 25651-075, Brazil

    L. A. Mansilla Alvarez, R. A. Feijóo & P. J. Blanco

  2. National Institute of Science and Technology in Medicine Assisted by Scientific Computing, INCT-MACC, Petrópolis, Brazil

    L. A. Mansilla Alvarez, G. D. Ares, R. A. Feijóo & P. J. Blanco

  3. National University of Mar del Plata, UNMdP, Mar del Plata, Argentina

    G. D. Ares

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  1. L. A. Mansilla Alvarez
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Correspondence to L. A. Mansilla Alvarez.

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Mansilla Alvarez, L.A., Ares, G.D., Feijóo, R.A. et al. A mixed-order interpolation solid element for efficient arterial wall simulations. Comput Mech 73, 67–87 (2024). https://doi.org/10.1007/s00466-023-02356-1

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