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Article

Using Voronoi Tessellation Diagrams to Visualize the Mechanical Response of Interacting Axisymmetric Simultaneous Propagating Waves

by
Zherui Martinez-Guo
School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN 47907, USA
Symmetry 2025, 17(4), 555; https://doi.org/10.3390/sym17040555 (registering DOI)
Submission received: 23 November 2024 / Revised: 2 April 2025 / Accepted: 3 April 2025 / Published: 5 April 2025
(This article belongs to the Section Mathematics)

Abstract

When two axisymmetric stress waves of the same strength propagate radially at the same velocity, the stress wave wavefronts collide and interact along a specific locus, which is the perpendicular bisector between the two sources. The maximum principal stress occurs along this perpendicular bisector, and the tensile stresses result in crack bridging between the two source points. This symmetric wave propagation behavior allows us to use the Voronoi tessellation diagram and its symmetric dual graph, the Delaunay triangulation, to gain first-order insight into complex wave propagation phenomena for an arbitrary distribution of wave propagation sources. The inherent symmetry of these simultaneous wave propagation mechanics allows us to rapidly visualize and predict the stress wave propagation and interactions, and the resultant crack bridging patterns that arise from random blast sources. The current work is focused on rock blast fracture mechanics, but the visualization scheme can be implemented for any application where waves propagate axisymmetrically and interact.
Keywords: Voronoi tessellation; Delaunay triangulation; wave propagation; principal stress; axisymmetric source Voronoi tessellation; Delaunay triangulation; wave propagation; principal stress; axisymmetric source

Share and Cite

MDPI and ACS Style

Martinez-Guo, Z. Using Voronoi Tessellation Diagrams to Visualize the Mechanical Response of Interacting Axisymmetric Simultaneous Propagating Waves. Symmetry 2025, 17, 555. https://doi.org/10.3390/sym17040555

AMA Style

Martinez-Guo Z. Using Voronoi Tessellation Diagrams to Visualize the Mechanical Response of Interacting Axisymmetric Simultaneous Propagating Waves. Symmetry. 2025; 17(4):555. https://doi.org/10.3390/sym17040555

Chicago/Turabian Style

Martinez-Guo, Zherui. 2025. "Using Voronoi Tessellation Diagrams to Visualize the Mechanical Response of Interacting Axisymmetric Simultaneous Propagating Waves" Symmetry 17, no. 4: 555. https://doi.org/10.3390/sym17040555

APA Style

Martinez-Guo, Z. (2025). Using Voronoi Tessellation Diagrams to Visualize the Mechanical Response of Interacting Axisymmetric Simultaneous Propagating Waves. Symmetry, 17(4), 555. https://doi.org/10.3390/sym17040555

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