A physics-guided smoothing method for material modeling with digital image correlation (DIC) measurements

TL;DR

This paper tackles errors in DIC-derived displacement and strain fields during biaxial testing by introducing physics-guided smoothing (PGS), which uses a reproducing kernel basis subject to partial physics constraints to ensure physically admissible fields. The approach couples RK-based displacement reconstruction with a positive-strain loss, and provides an analytic solution for the data-only case, enabling scalable, parallelizable processing. The smoothed fields feed into a nonlocal constitutive learning framework (peridynamic neural operator), yielding improved predictive accuracy and revealing fiber orientation fields in heterogeneous tissues. Across two real datasets (isotropic nitrile gloves and anisotropic porcine TVAL tissue), PGS improves downstream modeling performance, eliminates non-physical strains, and enhances interpretability and generalization, supporting its practical utility in material modeling from DIC data.

Abstract

In this work, we present a novel approach to process the DIC measurements of multiple biaxial stretching protocols. In particular, we develop a optimization-based approach, which calculates the smoothed nodal displacements using a moving least-squares algorithm subject to positive strain constraints. As such, physically consistent displacement and strain fields are obtained. Then, we further deploy a data-driven workflow to heterogeneous material modeling from these physically consistent DIC measurements, by estimating a nonlocal constitutive law together with the material microstructure. To demonstrate the applicability of our approach, we apply it in learning a material model and fiber orientation field from DIC measurements of a porcine tricuspid valve anterior leaflet. Our results demonstrate that the proposed DIC data processing approach can significantly improve the accuracy of modeling biological materials.

Figures (8)

• Figure 1: Dataset 1: Comparison of reconstructed strain fields.
• Figure 2: Dataset 1: Comparison of displacements and strains from three types of datasets. Circles highlight a non-physical region where the negative strain needs to be eliminated.
• Figure 3: Dataset 1: Learnt kernel function showing the isotropic feature in this specimen (left); and the predicted displacement field $\mathbf{u}$ when given a substantially different body loading $\mathbf{b}$ (right), showing generalizability.
• Figure 4: Dataset 2: Comparison of the minimum strain from three datasets.
• Figure 5: Dataset 2: Learnt kernel function and fiber orientation, showing the anisotropic and heterogeneous nature of this material.