A Multiscale Fracture Model using Peridynamic Enrichment of Finite Elements within an Adaptive Partition of Unity: Experimental Validation (2405.00011v1)

Abstract: Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Within the PUM global-local enrichment scheme [1, 2] different physical models can exist to capture multiscale behavior. For instance, we consider classical linear elasticity globally and local zones where fractures occur. The elastic fields of the undamaged media provide appropriate boundary data for local PD simulations on a subdomain containing the crack tip to grow the crack path. Once the updated crack path is found, the elastic field in the body and surrounding the crack is updated using PUM basis with appropriate enrichment near the crack. The subdomain for the PD simulation is chosen to include the current crack tip as well as nearby features that will influence crack growth. This paper is part II of this series and validates the combined PD/PUM simulator against the experimental results presented in [3]. The presented results show that we can attain good agreement between experimental and simulation data with a local PD subdomain that is moving with the crack tip and adaptively chosen size.

• The paper introduces a coupled peridynamic and partition-of-unity framework that accurately simulates fracture growth using localized PD enrichment.
• The adaptive model efficiently integrates global linear elastic analysis with targeted PD simulations at crack tips to reduce computational costs.
• Experimental validation with three-point bending tests confirms the model's precision in predicting crack paths across varied material geometries.

Overview of Multiscale Fracture Modeling and Peridynamic Enrichment

This paper presents a multifaceted approach for modeling fractures in materials through the integration of the peridynamic (PD) method with the partition of unity method (PUM). This integration is implemented within an adaptive partition-of-unity framework, providing an efficient and precise way of simulating multiscale fracture mechanics problems. Specifically, the work focuses on the experimental validation of this combined PD/PUM simulator, supporting its accuracy and practicality through comparisons with established experimental data.

Approach and Mechanism

The method takes advantage of the PUM's adaptive enrichment capabilities that allow for diverse physical models, with classical linear elasticity applied globally, while specific areas, where fracture develops, employ local PD simulations. This adaptive partition-of-unity enrichment integrates both classical and PD models seamlessly, managing boundary conditions and simulating crack growth when fractures occur. A notable aspect of this methodology is its localized simulation of fracture growth by focusing the computationally expensive PD calculations on regions immediately surrounding the crack tip, thus conserving computational resources while enhancing simulation fidelity.

The process begins with a global linear elastic analysis done using PUM, which informs and constrains local PD models at micro scales. As cracks develop, this local information updates the global model, hence employing a feedback loop that fine-tunes the response of the entire system to local fracture events.

Validation and Numerical Results

The paper validates the proposed modeling approach using three-point bending experiments conducted by Ingraffea et al. (1990). The experimental setup involves variations in initial crack lengths and geometries with standard geometric parameters. The authors provided robust quantitative evidence supporting the model's accuracy by comparing simulated crack paths with experimentally observed ones. Results indicate a general trend wherein smaller, adaptive PD subdomains that accompany the crack tip tend to deliver more accurate predictions than larger, fixed PD regions. The adaptive methodology shows a strong correlation with experimental data, particularly illustrating the effectiveness of the model's predictive capabilities in simulating crack trajectories through heterogeneous material fields.

Implications and Future Developments

The blend of PD's capacity to handle discontinuities in material displacement fields with PUM's efficient handling of large-scale domains opens a promising avenue in fracture mechanics modeling. The method efficiently addresses the computational overhead typically associated with peridynamics by minimizing its domain size dynamically. While the current paper effectively addresses the need for high-fidelity simulations of crack growth in two dimensions, extensions to three-dimensional problems would enrich the potential applications of this work.

Future work should focus on automation, particularly concerning the identification and tracking of the PD subdomain location relative to areas of potential fracture, and refining the crack path extraction process. Additionally, investigating the methodology within dynamic simulation contexts could further illustrate its adaptability and efficacy under varying material deformation rates.

Overall, the combination of local PD modeling with global PUM constructs a comprehensive and adaptable framework capable of accurate, computationally efficient multiscale fracture analysis. As this method matures, it has the potential to inform novel design principles and material innovations in engineering contexts that prioritize structural reliability under stress-induced damage and failure scenarios.