Material Fingerprinting: A shortcut to material model discovery without solving optimization problems

TL;DR

The paper introduces Material Fingerprinting, a database-driven framework to rapidly identify material models from data without solving non-convex optimization problems. It defines fingerprints from standardized experiments, builds a diverse fingerprint database across candidate hyperelastic models, and uses cosine similarity to match unseen data to the closest fingerprint, yielding both model form and parameters. Numerical benchmarks with supervised (homogeneous) and unsupervised (heterogeneous) data demonstrate high accuracy and robustness to noise, including cases where the ground-truth model is absent from the database. The approach ensures physically admissible, interpretable models and offers a scalable offline-online workflow applicable to a wide range of material behaviors and experimental designs.

Abstract

We propose Material Fingerprinting, a new method for the rapid discovery of mechanical material models from direct or indirect data that avoids solving potentially non-convex optimization problems. The core assumption of Material Fingerprinting is that each material exhibits a unique response when subjected to a standardized experimental setup. We can interpret this response as the material's fingerprint, essentially a unique identifier that encodes all pertinent information about the material's mechanical characteristics. Consequently, once we have established a database containing fingerprints and their corresponding mechanical models during an offline phase, we can rapidly characterize an unseen material in an online phase. This is accomplished by measuring its fingerprint and employing a pattern recognition algorithm to identify the best matching fingerprint in the database. In our study, we explore this concept in the context of hyperelastic materials, demonstrating the applicability of Material Fingerprinting across different experimental setups. Initially, we examine Material Fingerprinting through experiments involving homogeneous deformation fields, which provide direct strain-stress data pairs. We then extend this concept to experiments involving complexly shaped specimens with heterogeneous deformation fields, which provide indirect displacement and reaction force measurements. We show that, in both cases, Material Fingerprinting is an efficient tool for model discovery, bypassing the challenges of potentially non-convex optimization. We believe that Material Fingerprinting provides a powerful and generalizable framework for rapid material model identification across a wide range of experimental designs and material behaviors, paving the way for numerous future developments.

Figures (8)

• Figure 1: Schematic overview of the Material Fingerprinting workflow. The top row depicts the supervised approach using tests with homogeneous deformation fields, while the bottom row illustrates the unsupervised case based on heterogeneous deformations. In the offline phase, a database of material fingerprints is generated synthetically. During the online phase, the fingerprint of an unseen material is measured and matched to the closest entry in the database using a pattern recognition algorithm, enabling fast material model discovery.
• Figure 2: Illustration of supervised Material Fingerprinting. The measurement is compared to all fingerprints in the database. Each row in the database represents a fingerprint computed using a specific set of model parameters, with the color qualitatively indicating differences in the magnitude of the fingerprint components. While the full database contains a large number of fingerprints derived from various models, the figure illustrates a subset only. The fingerprints are grouped and displayed by model type, excluding simple models that have a single parameter only.
• Figure 3: Illustration of supervised Material Fingerprinting. The measurement, illustrated by a black curve, is compared to all entries in the database, illustrated by colored regions. The database entries are grouped and visualized separately for each model, excluding simple models that have a single parameter only.
• Figure 4: Specimen geometry and loading conditions for unsupervised Material Fingerprinting. During the experiment, the reaction forces $R_1$ and $R_2$, along with displacements at selected points near the central hole, are measured for all load steps.
• Figure 5: Stress response of the discovered models in comparison to the uniaxial tension (left) and simple shear (right) data with the highest noise level.