verification: implicit plasticity oracle cases and documentation

Four cases, each against its closed form: uniaxial tension of a J2 cube to a
logarithmic strain of 0.2 (Kirchhoff stress exact; 0.13 % from the explicit
solver's hypoelastic Cauchy stress, the elastic volume change between the two
laws), the Bauschinger effect of linear kinematic hardening on a load path
back to zero strain (exact), Hill's elastic-perfectly plastic thick cylinder
(bore displacement at a plastic radius of 1.5a within 0.009 %, collapse
pressure within 2e-8; the pending case is now active) and a cantilever's
plastic collapse, converged 3.1 % above beam theory's hinge, the bound a
continuum exceeds. docs/fem.md, the literature, ROADMAP (M15), parity and the
oracle page follow.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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@@ -1186,3 +1186,28 @@ update are written from (cited again in the module docs):
transcribed finite-strain values), R. D. Cook, J. Struct. Div. ASCE 100(ST9):1851–1863, 1974,
and J. C. Simo, F. Armero, IJNME 33:1413–1449, 1992; tube inflation, R. S. Rivlin, Phil. Trans. R. Soc. A
242:173–195, 1949, and R. W. Ogden, *Non-Linear Elastic Deformations*, Dover 1997.
## Part N: Implicit plasticity (finite and small strain), as implemented
- Multiplicative J2 plasticity with a Hencky elastic energy and the exponential return map in
the principal logarithmic strains, which keeps the classical radial return of the
infinitesimal theory: J. C. Simo, *Algorithms for static and dynamic multiplicative plasticity
that preserve the classical return mapping schemes of the infinitesimal theory*, CMAME
99(1):61–112, 1992, DOI [10.1016/0045-7825(92)90123-2](https://doi.org/10.1016/0045-7825(92)90123-2);
J. C. Simo, T. J. R. Hughes, *Computational Inelasticity*, Springer 1998, ch. 9.
- The radial return (shared with explicit dynamics) and its consistent tangent
K I⊗I + 2Gθ ℙ − 2Gθ̄ n⊗n: Simo & Hughes 1998, §3.3, Box 3.2 (A4.1); J. C. Simo, R. L. Taylor,
*Consistent tangent operators for rate-independent elastoplasticity*, CMAME 48(1):101–118,
1985, DOI [10.1016/0045-7825(85)90070-2](https://doi.org/10.1016/0045-7825(85)90070-2).
- The derivative of the matrix logarithm by divided differences (Daleckii–Krein), smooth through
equal stretches: R. Bhatia, *Matrix Analysis*, Springer 1997, §V.3.
- Kinematic hardening at finite strain (refused for now; the route when it comes): additive
plasticity in the Lagrangian logarithmic strain space, C. Miehe, N. Apel, M. Lambrecht, CMAME
191(47–48):5383–5425, 2002, DOI [10.1016/S0045-7825(02)00438-3](https://doi.org/10.1016/S0045-7825(02)00438-3).
- Prager's linear kinematic hardening: W. Prager, *The theory of plasticity: a survey of recent
achievements*, Proc. Inst. Mech. Eng. 169:41–57, 1955.
- Verification references: the thick cylinder's plastic zone and collapse pressure, R. Hill,
*The Mathematical Theory of Plasticity*, Oxford 1950, ch. V; the cantilever's plastic hinge,
B. G. Neal, *The Plastic Methods of Structural Analysis*, 3rd ed., Chapman & Hall 1977, and the
continuum's velocity fields, W. Prager, P. G. Hodge, *Theory of Perfectly Plastic Solids*,
Wiley 1951.