A Multiscale Fracture Model Combining Peridynamics and Partition of Unity Method: Experimental Validation

Core Concepts

A combined peridynamic and partition of unity method is used to efficiently model multiscale fracture behavior, and the approach is validated against experimental data.

Abstract

The paper presents a combined peridynamic (PD) and partition of unity method (PUM) approach for modeling multiscale fracture behavior. The key aspects are:

The PUM is used to solve the global linear elasticity problem, while the PD model is employed locally to capture fracture growth.
The PD subdomain is chosen adaptively to include the current crack tip and nearby features that influence crack growth, and this subdomain moves with the crack.
The elastic fields from the undamaged PUM region provide boundary conditions for the local PD simulations to grow the crack path.
Once the updated crack path is found, the elastic field in the body is updated using PUM basis functions with appropriate enrichment near the crack.
The combined PUM/PD approach is validated against three experimental three-point bending tests, and the results show good agreement between the simulated and experimental crack paths.
Compared to using a fixed, larger PD subdomain, the adaptive moving PD subdomain provides better accuracy while reducing computational cost.
The authors identify remaining challenges for fully automating the interaction between the PUM and PD components, such as automatic identification of the PD region, automated crack path extraction, and optimal frequency of information exchange between the global and local models.

Stats

The force applied in the experiments is 9×10^5 N.
The final simulation time is 0.001 s.
The node spacing for the PD model is 0.00049609375 m, and for the PUM it is 0.00396875 m.
The PD horizon size is 8 times the node spacing, i.e., 0.00396875 m.

Quotes

"The subdomain needed for the PD simulation is chosen to include the current crack tip together with nearby features that will influence crack growth."
"Once the current crack geometry is established via the local PD approximation we construct respective enrichment basis functions and use the PUM to efficiently determine the elastic displacement outside the crack and in the complete body."

Key Insights Distilled From

A Multiscale Fracture Model using Peridynamic Enrichment of Finite Elements within an Adaptive Partition of Unity: Experimental Validation

by Matthias Bir... at arxiv.org 05-02-2024

https://arxiv.org/pdf/2405.00011.pdf

Deeper Inquiries

How can the automatic identification of the PD region be improved, especially in cases without an initial crack

Automatic identification of the PD region, especially in cases without an initial crack, can be improved by implementing stress-based or strain-based damage models. These models can monitor stress or strain levels and trigger the placement of the PD region when certain thresholds are exceeded. Another approach could involve utilizing machine learning algorithms to detect the interface region for coupling local and nonlocal models. By training the algorithm on various scenarios and patterns, it can learn to identify the optimal placement of the PD region based on the material response and structural characteristics.

What are the potential drawbacks of the global-local enrichment approach compared to a fully coupled PD-PUM method, and how can they be addressed

The global-local enrichment approach, while efficient and effective in capturing multiscale behavior, may have some drawbacks compared to a fully coupled PD-PUM method. One potential drawback is the need for manual intervention in determining the frequency of information exchange between the global and local problems. This manual adjustment can lead to suboptimal results and may require additional computational resources. To address this, an automated algorithm can be developed to dynamically adjust the information exchange frequency based on the crack propagation behavior and structural response, ensuring optimal synchronization between the two models.

Can the combined PUM/PD framework be extended to dynamic fracture problems, and what challenges would need to be overcome

The combined PUM/PD framework can be extended to dynamic fracture problems by running both methods concurrently and exchanging information at regular intervals. However, dynamic fracture simulations introduce challenges such as the need for smaller time steps in the local PD problem, ensuring synchronization between the global and local models, and updating the crack path in real-time. To overcome these challenges, the framework can be enhanced with adaptive time-stepping algorithms, real-time data exchange protocols, and automated crack path extraction techniques. Additionally, implementing robust error estimation methods and adaptive mesh refinement strategies can help improve the accuracy and efficiency of dynamic fracture simulations within the combined framework.