verification: nonlinear oracle cases and the nonlinear solver's documentation

Theory cases for the nonlinear solver, each frozen as a fixture: uniaxial
stretch of a neo-Hookean block to twice its length (closed form), the
nonlinear patch test on a distorted hex8 mesh, a quarter turn of the same
mesh (objectivity: zero stress), the elastica of a hex20 cantilever at
P L²/(E I) = 1, 2, 5, 10 against Bisshopp–Drucker (0.2–0.5 %), and the
inflation of a thick neo-Hookean tube by a follower pressure against
Rivlin's closed form (0.08 % at the bore). A finite-strain Cook's membrane
is pending its transcribed reference. docs/fem.md describes the
formulation, the material point interface, the follower-pressure choice and
what nonlinear steps refuse; the literature, parity and roadmap pages
follow.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 04:00:21 -04:00
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# Uniaxial stretch of a neo-Hookean block
A unit cube of 2 × 2 × 2 hex20 elements, symmetry planes x = 0, y = 0, z = 0, the face x = 1
pulled to x = 2 (λ = 2) in a nonlinear static step; E = 10, ν = 0.3 with the neo-Hookean
option (μ = 3.84615, κ = 8.33333). The lateral stretch l = 0.813143719 solves σ_yy = 0 (bisection
on the closed form), and σ_xx = 8.060135422. The deformation is homogeneous, so every element
reproduces it exactly.