Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data (Communications in Computational Physics, 2023)
Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures. We propose a multiscale data-driven approach with a hierarchical learning strategy for the discovery of a genericphysics-constrained anisotropic constitutive model for the heterogeneous hyperelasticmaterials. Based on the sparse multiscale experimental data, the constitutive artificialneural networks for hyperelastic component phases containing composite interfacesare established by the particle swarm optimization algorithm. A microscopic finiteelement coupled constitutive artificial neural networks solver is introduced to obtainthe homogenized stress-stretch relation of heterogeneous materials with different microstructures. And a dense stress-stretch relation dataset is generated by training aneural network through the FE results. Further, a generic invariant representationof strain energy function (SEF) is proposed with a parameter set being implicitly expressed by artificial neural networks (SANN), which describes the hyperelastic properties of heterogeneous materials with different microstructures. A convexity constraintis imposed on the SEF to ensure that the multiscale constitutive model is physically relevant, and the $ℓ_1$ regularization combined with thresholding is introduced to the lossfunction of SANN to improve the interpretability of this model. Finally, the multiscalemodel is hierarchically trained, cross-validated and tested using the experimental dataof cord-rubber composite materials with different microstructures. The proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials.