CDEM-derived cumulative maximum tensor shear: Mechanics, derivation, and generation of the attribute

Fault zones were treated as finite-width deformation structures rather than discontinuous lines. A cumulative maximum tensor shear attribute, γp,max, was defined from incremental plastic strain and accumulated as a non-decreasing shear-path-length measure. In two dimensions, instantaneous maximum tensor shear corresponded to the radius of the in-plane strain Mohr circle. The component and principal-strain forms were derived, and their factor-of-two relation to engineering shear was made explicit. A monotonic simple-shear example showed that the thickness-averaged cumulative attribute satisfied s=2γ¯p,maxt, whereas nonuniform or rotating deformation required integration across the band. Continuum-Discrete Element Method (CDEM) examples showed high cumulative shear along modeled fault cores and tips and lower values across distributed deformation zones. The workflow produced registered mechanical targets and structural models suitable for subsequent synthetic-seismic and machine-learning experiments, while remaining subject to small-strain, constitutive, and spatial-resolution limitations.