QF Solver 0.2.5a0 formula inventory

This inventory defines formulas to audit and verify. It does not select a new constitutive model or authorize implementation.

ID	Capability	Governing relation	Existing basis	Required decision/proof
F-01	Global equilibrium	R(u, q, lambda) = Fint - lambda Fext + Fc = 0	separate nonlinear/contact residuals	sign convention and one common residual contract
F-02	Full Newton	K_T delta_u = -R, u_{i+1}=u_i+delta_u	small-strain and geometric loops	one convergence policy and tangent composition
F-03	Small strain	epsilon = sym(grad u)	common J2 element contract	preserve 0.2.4 behavior
F-04	J2 yield	f = sigma_eq - (sigma_y + H alpha)	VonMisesElastoplasticMaterial	re-derive convention and cyclic limitations
F-05	J2 flow/return	associative deviatoric radial return	existing material	analytical path and state verification
F-06	J2 tangent	C_alg = d sigma_{n+1}/d epsilon_{n+1}	existing algorithmic tangent	FD sensitivity near elastic/plastic transition
F-07	Finite kinematics	F = I + Grad_X u	TET4 TL kernel	approve reference/current configuration conventions
F-08	Green-Lagrange strain	E = 0.5 (F^T F - I)	TET4 TL kernel	objectivity and element FD proof
F-09	TL stress/work conjugacy	S conjugate to E, P = F S	StVK TET4	approve material measure for each model
F-10	Internal virtual work	delta Wint = integral(delta E : S dV0)	TL assembly	internal force and energy derivative FD
F-11	Tangent decomposition	K_T = K_material + K_geometric + K_contact	separate paths exist	sparse common assembly and FD consistency
F-12	Linear buckling	(K + lambda K_G) phi = 0 or sign-equivalent form	bounded sparse TET4/HEX8 route	preload/sign/normalization convention
F-13	Arc length	g(delta u, delta lambda, ds) = 0	sparse augmented correction helper	choose one Crisfield/Riks constraint and sign rule
F-14	Normal gap	g_n = (x_s - x_m) dot n_m	contact package	orientation, projection and finite-sliding update
F-15	Normal contact	complementarity or approved regularization	active-set contact exists	choose multiplier/penalty/augmented formulation
F-16	Coulomb friction	||t_t|| <= mu t_n, stick/slip complementarity	regularized experimental path	optional objective frame/state formulation
F-17	External work	incrementally consistent Wext	partial nonlinear work diagnostics	load-path integration convention
F-18	Energy balance	Wext - Ue - Dp - residual_terms = 0	not fully qualified	define treatment of contact/friction work
F-19	Plastic dissipation	Dp >= 0 for the retained associative J2 model	material states	per-increment and accumulated proof
F-20	Transaction	state_committed unchanged until accepted increment	MaterialStateSession	extend to contact/continuation and adversarial proof

Formula review checklist

For each formula before coding:

1. cite the reference or existing controlled derivation;
2. declare tensor ordering, signs, configuration and units;
3. identify work-conjugate measures;
4. derive residual and consistent tangent together;
5. define analytical and finite-difference checks;
6. record singular/degenerate cases;
7. obtain Owner approval for any scope-changing constitutive assumption.