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Heterogeneous deformations of inflated hyperelastic membranes for data-driven constitutive modelling

  • Artur Ovsepyan EMAIL logo , Victoria Salamatova and Alexey Liogky
Published/Copyright: November 6, 2025

Abstract

This work introduces a data-driven approach for modelling the hyperelastic deformation of membranes using inflation tests. To ensure data sufficiency, we employ membranes with a non-homogeneous thickness profile, which expands significantly the experimental data range. An explicit interpolation method is used to define the data-driven constitutive relation, leveraging the Laplace stretch as a strain measure and its corresponding stress response function. The model recovers accurately inflated membrane profiles, with displacement field predictions exhibiting a relative error less than 1%. For stress fields, the error is below 5–6% across most of the membrane.

MSC 2010: 74S05; 74B20; 65N22

Funding statement: The work was supported by the Russian Science Foundation through the grant No. 24-21-20075.

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Received: 2025-09-02
Accepted: 2025-09-05
Published Online: 2025-11-06
Published in Print: 2025-11-25

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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