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

arXiv: https://arxiv.org/abs/2505.18784 · HTML: https://mlsanity.com/paper/2505.18784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 8 of 8)

- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Physical Inertial Poser (PIP): Physics-aware Real-time Human Motion Tracking from Sparse Inertial Sensors](https://mlsanity.com/paper/2203.08528/) (2022)
- [Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling](https://mlsanity.com/paper/2203.08205/) (2022)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [A Review Paper: Noise Models in Digital Image Processing](https://mlsanity.com/paper/1505.03489/) (2015)
- [Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses](https://mlsanity.com/paper/2401.06070/) (2024)
- [Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements](https://mlsanity.com/paper/2403.18597/) (2024)
- [Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions](https://mlsanity.com/paper/2505.01060/) (2025)

## Abstract (arXiv)

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.