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<p>While physics-informed neural networks (PINNs) have been widely recognized as a powerful tool for constitutive modeling, many existing PINN-based hyperelastic models are trained on data generated from traditional constitutive models, limiting their capability to describe the intrinsic mechanical behavior of real materials. To address this issue, we propose a PINN-based hyperelastic constitutive model that is directly trained with experimental data. The proposed framework ensures a priori satisfaction of fundamental constitutive principles. Thermodynamic consistency is automatically achieved by formulating the network to output the hyperelastic potential, while objectivity and material symmetry are guaranteed by utilizing the invariants as inputs. Furthermore, polyconvexity is strictly enforced through a modified architecture based on input convex neural networks (ICNNs). The model is directly trained against stress–strain data by minimizing a loss function based on the mean squared error of the stress tensor—a variant of Sobolev training adapted for experimental data in which the potential is not directly accessible. The model’s extrapolation capability and broad applicability are demonstrated through comprehensive validation against experimental datasets for various soft materials under complex biaxial loading conditions. Finally, the model is verified through finite element simulations implemented as a UHYPER subroutine, accurately predicting the response of components with complex geometries and heterogeneous strain fields. The results indicate that this data-driven, physics-informed approach offers a robust and applicable tool for engineering applications.</p>

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A PINN-Based Hyperelastic Constitutive Model Trained with Experimental Data

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Yibo Wang,
  • Zefeng Yu,
  • Shan Tang,
  • Rui Xiao

摘要

While physics-informed neural networks (PINNs) have been widely recognized as a powerful tool for constitutive modeling, many existing PINN-based hyperelastic models are trained on data generated from traditional constitutive models, limiting their capability to describe the intrinsic mechanical behavior of real materials. To address this issue, we propose a PINN-based hyperelastic constitutive model that is directly trained with experimental data. The proposed framework ensures a priori satisfaction of fundamental constitutive principles. Thermodynamic consistency is automatically achieved by formulating the network to output the hyperelastic potential, while objectivity and material symmetry are guaranteed by utilizing the invariants as inputs. Furthermore, polyconvexity is strictly enforced through a modified architecture based on input convex neural networks (ICNNs). The model is directly trained against stress–strain data by minimizing a loss function based on the mean squared error of the stress tensor—a variant of Sobolev training adapted for experimental data in which the potential is not directly accessible. The model’s extrapolation capability and broad applicability are demonstrated through comprehensive validation against experimental datasets for various soft materials under complex biaxial loading conditions. Finally, the model is verified through finite element simulations implemented as a UHYPER subroutine, accurately predicting the response of components with complex geometries and heterogeneous strain fields. The results indicate that this data-driven, physics-informed approach offers a robust and applicable tool for engineering applications.