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

TL;DR

This work tackles efficient multiscale fracture modeling by coupling a local peridynamic (PD) region with a global partition of unity method (PUM). The main approach uses a moving, adaptive PD subdomain around the crack tip to drive boundary data for the global PUM and to enrich the PUM solution with the PD-determined crack path. Validation against three-point bending experiments shows good agreement between experiments and simulations, with the moving PD region offering substantial computational savings while preserving accuracy, driven by parameters such as horizon $\delta$, energy release rate $G_c$, Young's modulus $E$, and Poisson ratio $\nu$. The work demonstrates a practical, scalable framework for fracture simulations and highlights avenues for automation and extension to three dimensions.

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.

Figures (7)

• Figure 1: The combined PUM/PD simulator. Adapted from BIRNER2023103360.
• Figure 2: Parametrized geometry of the 3-point bending experiment. With Parameters $a$ for the length and $b$ for the position in $x$-direction of the initial crack. The values for the three cases are shown in Table \ref{['tab:geometry:3p:bending']}. Adapted from ingraffea1990probabilistic.
• Figure 3: Example for the discretization of the two models: The black mesh is used for the partition of unity method simulation of the global problem for Case 2. The blue dots are the discrete peridynamics nodes within the PD region. For simplicity, we showed one PD region at a later stage of the simulation from Figure \ref{['fig:3bending:crack:path:case2:boxes']}.
• Figure 4: \ref{['fig:3bending:crack:path:case1:path']} Experimentally obtained crack path for the Case 1 extracted from Figure 4.8 in ingraffea1990probabilistic in black. The red crack path shows the crack path obtained by our approach. The gray box is the PD domain used in NI2019126. \ref{['fig:3bending:crack:path:case1:box']} Simulated crack path with our approach in red and the moving PD region with the crack tip position. The light blue region at the crack tip is the initial square region. After that, the box color moves from light blue at the beginning to dark blue for the region used in the last simulation step.
• Figure 5: In the background is shown the PUM displacement field for the global problem for Case 2 for the second to last load step. The black box is the current box of the sequence of moving PD boxes, see Figure \ref{['fig:3bending:crack:path:case1:box']}. In the foreground the final step of the local problem. Here, we show in white the current crack path and in color the PD damage advancing the initial crack path. This path is extracted and fed into the next load step of the global problem as the current crack. Note that the crack path is shown for the reference configuration, not for the deformed configuration.