solver, model: arc-length control with critical points from the inertia

NonlinearStatic.arc_length {constraint, max_load_factor, displacement_limit}: Riks–Crisfield
arc-length increments (cylindrical or spherical arc, tangent predictor signed by the angle
criterion, the constraint's quadratic root chosen by the angle with the last iterate), arcs
grown, shrunk and cut back as increments are. The converged state's tangent is factored for the
next predictor (LDLᵀ when indefinite); its negative eigenvalues are recorded per increment and
changes in their count are reported as limit or bifurcation points. Ends at the maximum load
factor, a displacement limit or the increment cap. Abaqus *STATIC, RIKS; LS-DYNA refuses it by
name; forms gain the arc-length group. A shallow arch of hex20 snaps through on the closed-form
path (1.9 %), both limit points found, inertia 0 → 1 → 0 between them.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/solvers/literature.md

@@ -1244,6 +1244,14 @@ update are written from (cited again in the module docs):
   indefinite sparse symmetric linear equations*, ACM TOMS 9(3):302–325, 1983; J. W. H. Liu, *The
   multifrontal method for sparse matrix solution: theory and practice*, SIAM Review
   34(1):82–109, 1992.
+- Arc-length: E. Riks, *An incremental approach to the solution of snapping and buckling
+  problems*, Int. J. Solids Struct. 15(7):529–551, 1979; M. A. Crisfield, *A fast
+  incremental/iterative solution procedure that handles "snap-through"*, Computers & Structures
+  13:55–62, 1981; E. Ramm, *Strategies for tracing the nonlinear response near limit points*, in
+  *Nonlinear Finite Element Analysis in Structural Mechanics*, Springer 1981, 63–89; the
+  predictor's sign, M. Feng, D. Perić, D. R. J. Owen, Computers & Structures 58(3):479–485, 1996.
+  Snap-through of a shallow sinusoidal arch: Y. C. Fung, A. Kaplan, NACA TN 2840, 1952;
+  Timoshenko & Gere 1961, §7.6.
 - Iterative refinement: N. J. Higham, *Accuracy and Stability of Numerical Algorithms*, 2nd ed.,
   SIAM 2002, §12.2.
 - Linear buckling and the initial-stress stiffness: K.-J. Bathe, *Finite Element Procedures*,