CMN 2026

Learning the Behavior of Isotropic and Anisotropic Elastomers from a Mnimum Set of Experimental Data

  • Benitez, José María (Universidad Politécnica de Madrid)
  • Sanz, Miguel Ángel (Universidad Politécnica de Madrid)
  • Ben-Yelun, Ismael (Universidad Politécnica de Madrid)
  • Montáns, Francisco Javier (Universidad Politécnica de Madrid)

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Elastomers have a complex nonlinear entropic behavior characterized by its long polymeric chains and inner structure, leading to configurations with different statistical probabilities. For more than a century, two approaches and thousands of models have been developed to capture the complex behavior under general loading [1]. The first approach is the physical approach, based on statistical mechanics, where minimal data is needed. An initial success was the ability to describe with just one parameter the nonlinear behavior of rubber under a tensile test. However, that approach is not general enough to model the wide variety of polymers and soft tissues. The second approach is the mathematical or phenomenological one where a series of experiments adjust some material parameters on a proposed form of the stored energy function. Here, the needed data is substantially larger, including several types of experiments. Today, machine learning (ML) procedures can learn the behavior of any polymer if sufficient data is available; in the end ML represents nonlinear multivariable data of complex systems by generating a best approximate support function (explicit or implicit). However, despite claims that data is ubiquitous, available data for polymers come typically from a tensile test, a pure shear test, and sometimes an equibiaxial test. In the case of orthotropic polymers, similar data are obtained for tests in principal orthotropy directions. The purpose of this presentation is to address the minimal number of tests (experimental curves) needed to characterize an elastomer for isotropic, transversely isotropic and orthotropic materials. We demonstrate that the behavior learned from those minimal tests is capable of representing the material behavior with good accuracy under any general loading pattern [2].