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Smooth hyperelastic potentials for 1D problems of bimodular materials

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Abstract

A family of one parametric infinitely differentiable hyperelastic potentials for three-dimensional infinitesimal problems of bimodular isotropic materials is constructed, yielding a set of uniform approximations to the discontinuous stepwise elastic modulus adopted in the original one-dimensional bimodular formulation. The introduced potentials enable either analytical solutions or construction of the explicit governing equations for a number of static and dynamic problems. Theorem of convergence to the discontinuous bimodular modulus is proved.

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Funding

The work was funded by the Ministry of Science and Higher Education of RF, grant FSWG-2023-0004.

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  1. Moscow State University of Civil Engineering, Moscow, Russia

    Sergey V. Kuznetsov

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Kuznetsov, S.V. Smooth hyperelastic potentials for 1D problems of bimodular materials. Acta Mech 235, 1911–1920 (2024). https://doi.org/10.1007/s00707-023-03827-5

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