EQUATION REGISTRY

Curl, rotation and shear

Curl is not the full symmetric shear strain; independent nonlinear orientation requires its own definition.

Theory · FOUNDATIONEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-004
ΩT=∇×uT,ω=12ΩT,eijdev=12(∂iuj+∂jui)−13δij∇⋅u\boldsymbol\Omega_T=\nabla\times\mathbf u_T,\quad\boldsymbol\omega=\tfrac12\boldsymbol\Omega_T,\quad e^{\rm dev}_{ij}=\tfrac12(\partial_i u_j+\partial_j u_i)-\tfrac13\delta_{ij}\nabla\cdot\mathbf u

Curl is not the full symmetric shear strain; independent nonlinear orientation requires its own definition.
Chapter reference: Ch. 5 (5.4.19), (5.6.1)–(5.6.2), (5.6.22); kinematic expansion · ASD-BOOK-ddbade997b45

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Ch. 5 (5.4.19), (5.6.1)–(5.6.2), (5.6.22); kinematic expansion

Registered formula checked individually against the final manuscript; The mathematical content agrees; the existing expression and its derivation conditions are retained.

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  • Curl is not the full symmetric shear strain; independent nonlinear orientation requires its own definition.

Source locators: p1318 · p1467 · p2064 · p2216 · p2273

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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SD-51779505a476 · Ch. 5 (5.4.19), (5.6.1)–(5.6.2), (5.6.22); kinematic expansion

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