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WYPIWYG hyperelasticity for isotropic, compressible materials

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Abstract

Nowadays the most common approach to model elastic behavior at large strains is through hyperelasticity. Hyperelastic models usually specify the shape of the stored energy function. This shape is modulated by some material parameters that are computed so the predicted stresses best fit the experimental data. Many stored energy functions have been proposed in the literature for isotropic and anisotropic materials, either compressible or incompressible. What-You-Prescribe-Is-What-You-Get (WYPIWYG) formulations present a different approach which may be considered an extension of the infinitesimal framework. The shape of the stored energy is not given beforehand but computed numerically from experimental data solving the equilibrium equations. The models exactly fit the experimental data without any material parameter. WYPIWYG procedures have comparable efficiency in finite element procedures as classical hyperelasticity. In this work we present a WYPIWYG numerical procedure for compressible isotropic materials and we motivate the formulation through an equivalent infinitesimal model.

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Acknowledgments

Partial financial support for this work has been given by Grants DPI2011-26635 and DPI2015-69801-R from the Dirección General de Proyectos de Investigación of the Ministerio de Economía y Competitividad of Spain. F. J. Montáns also acknowledges the support of the Department of Mechanical and Aerospace Engineering of University of Florida during the sabbatical period in which this paper was finished and that of the Ministerio de Educación, Cultura y Deporte of Spain for the financial support for that stay under Grant PRX15/00065.

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  1. Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Pza.Cardenal Cisneros, 28040, Madrid, Spain

    José Crespo, Marcos Latorre & Francisco Javier Montáns

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  1. José Crespo
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  2. Marcos Latorre
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  3. Francisco Javier Montáns
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Correspondence to Francisco Javier Montáns.

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Crespo, J., Latorre, M. & Montáns, F.J. WYPIWYG hyperelasticity for isotropic, compressible materials . Comput Mech 59, 73–92 (2017). https://doi.org/10.1007/s00466-016-1335-6

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