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Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies

Author

Listed:
  • Claudio Canales

    (Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, Chile)

  • Claudio García-Herrera

    (Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, Chile)

  • Eugenio Rivera

    (Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago 9170020, Chile)

  • Demetrio Macías

    (Laboratory Light, Nanomaterials & Nanotechnologies—L2n, University of Technology of Troyes & CNRS EMR 7004, 12 Rue Marie Curie, CS 42060, 10004 Troyes, France)

  • Diego Celentano

    (Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago 7820436, Chile)

Abstract

In this work, we propose a reliable and stable procedure to characterize anisotropic hyperelastic materials. For this purpose, a metaheuristic optimization method known as evolutionary strategies is used. The advantage of this technique with respect to traditional methods used for non-linear optimization, such as the Levenberg–Marquardt Method, is that this metaheuristic algorithm is oriented to the global optimization of a problem, is independent of gradients and allows to solve problems with constraints. These features are essential when characterizing hyperelastic materials that have non-linearities and are conditioned to regions of stability. To characterize the mechanical behavior of the arteries analyzed in this work, the anisotropic hyperelastic models of Holzapfel–Gasser–Ogden and Gasser–Holzapfel–Ogden are used. An important point of the analysis is that these models may present a non-physical behavior: this drawback is overcome by defining a new criterion of stabilization in conjunction with the evolutionary strategies. Finally, the finite element simulations are used in conjunction with the evolutionary strategies to characterize experimental data of the artery pressurization test, ensuring that the parameters obtained are stable and representative of the material response.

Suggested Citation

  • Claudio Canales & Claudio García-Herrera & Eugenio Rivera & Demetrio Macías & Diego Celentano, 2023. "Anisotropic Hyperelastic Material Characterization: Stability Criterion and Inverse Calibration with Evolutionary Strategies," Mathematics, MDPI, vol. 11(4), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:922-:d:1065664
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    References listed on IDEAS

    as
    1. Claudio M. García-Herrera & Diego J. Celentano & Marcela A. Cruchaga, 2013. "Bending and pressurisation test of the human aortic arch: experiments, modelling and simulation of a patient-specific case," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 16(8), pages 830-839, August.
    2. Claudio García-Herrera & Diego Celentano & Marcela Cruchaga & Francisco Rojo & José Atienza & Gustavo Guinea & José Goicolea, 2012. "Mechanical characterisation of the human thoracic descending aorta: experiments and modelling," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 15(2), pages 185-193.
    3. Fernández, J.R. & López-Campos, J.A. & Segade, A. & Vilán, J.A., 2018. "A genetic algorithm for the characterization of hyperelastic materials," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 239-250.
    4. J. A. López-Campos & J. P. S. Ferreira & A. Segade & J. R. Fernández & R. M. Natal, 2020. "Characterization of hyperelastic and damage behavior of tendons," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 23(6), pages 213-223, April.
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