Adaptive Material Fingerprinting for the fast discovery of polyconvex feature combinations in isotropic and anisotropic hyperelasticity

2026-04-07

AI Summary

This work addresses the challenge of efficiently discovering complex constitutive relationships for both isotropic and anisotropic hyperelastic materials, a task traditionally hindered by reliance on continuous optimization within fixed model forms. The authors propose an adaptive material fingerprinting technique that constructs a scalable library of strain energy density basis functions and integrates an iterative pattern recognition algorithm to automatically assemble optimal models directly from experimental data in real time. By enabling arbitrary linear combinations of basis functions and optionally embedding multiplicative convexity-based physical constraints, the method transcends the limitations of predefined model libraries while ensuring thermodynamic consistency. Validated on datasets from rubber and animal skin tissues, the approach successfully identifies high-fidelity constitutive models—including multi-parameter forms such as Ogden and Holzapfel–Gasser–Ogden—with remarkable accuracy and computational efficiency.

Abstract

We recently proposed a method called Material Fingerprinting for the rapid discovery of mechanical material models that avoids solving continuous optimization problems. Material Fingerprinting assumes that each material exhibits a unique response when subjected to a standardized experimental setup, which is interpreted as the material's mechanical fingerprint. If a database of fingerprints is generated in an offline phase, a model for an unseen experimental measurement can be discovered in real time by comparing the experimentally measured fingerprint to the fingerprints in the database. In our original contributions, the database comprised a fixed number of material models, each with a fixed number of parameters. To increase the fitting flexibility of Material Fingerprinting, we propose an adaptive model database coupled with an iterative pattern recognition algorithm that refines the material model in each step. This strategy enables Material Fingerprinting to discover arbitrary linear combinations of material models from the database, rather than being restricted to selecting a single model from a predefined set. In comparison to previous works on Material Fingerprinting, this enables the discovery of more complex models, such as multi-term Ogden models or the anisotropic Holzapfel-Gasser-Ogden model. To design the adaptive database, we leverage sums of strain energy density feature functions that depend on isotropic and anisotropic invariants. All modeling features satisfy fundamental physical constraints, and polyconvexity can be optionally enforced via a simple user-controlled switch. We test the method on experimental data stemming from mechanical tests of isotropic rubber materials and anisotropic animal skin tissue.

Problem

• hyperelasticity
• material modeling
• polyconvexity
• anisotropy
• constitutive discovery

Innovation

• Adaptive Material Fingerprinting
• polyconvexity
• hyperelasticity
• model discovery
• anisotropic invariants