TITLE:
Fracture Network Mathematics
AUTHORS:
Daniel S. Brox
KEYWORDS:
Mode I, Mode II, Multi-Crack, Statistics, Singular Spectrum Analysis
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.2,
February
6,
2026
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.