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Fracture Network Mathematics
Independent Researcher, Vancouver, Canada
- 1 Independent Researcher, Vancouver, Canada
Journal of Modern Physics·Volume 17 (2026)·Pages 111–123·Published 6 February 2026·DOI10.4236/jmp.2026.172007
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Abstract
Analytic solutions for elastostatic displacement due to vertical/shear traction applied to the faces of a single crack in a 2D plane are reviewed in Section 2. The purpose of this review is to introduce mathematics relevant to specifying multi-crack elastostatic displacements. In Section 3, the relation between multi- crack elastostatic displacement fields and Riemann surface geometry is discussed. Section 4 explains why 2D multi-crack solutions appear limited to describe idealized cracks in 2 spatial dimensions, and conjectures how 3D fracture networks in the lithosphere can be described in terms of singular spectrum analysis of crack phase fields.
KeywordsMode IMode IIMulti-CrackStatisticsSingular Spectrum Analysis
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