K_stretch was the Gauss-Newton Hessian of the stretch force, not its Jacobian.
With elongation e_a = L_a^2 - L0_a^2 and force f = -sum_ab M_ab e_a grad(e_b)/2,
K = 2 sum_ab M_ab (s_a d_a)(s_b d_b)^T + sum_a Me_a (Laplacian_a (x) I3)
and only the first term was there. The second is proportional to the edge
tension Me_a = sum_b M_ab e_b, so it vanishes at rest and grows with strain:
the operator was first-order correct and no more. Finite-differencing it
against -d(qfrc_passive)/dq on a mesh dilated by 5% gives 7.8% of the force
scale; with the term it is exact to roundoff.
Add only the tensile part. The geometric block is Me_a*[[I,-I],[-I,I]] over the
edge's two vertices, which is positive semi-definite exactly when Me_a >= 0; a
compressed edge would make K indefinite, and both consumers -- the CG
constraint solver and the PCG in mjd_effSolve -- require SPD. The clamp is
structural, so no eigendecomposition is needed, and it is confined to the
operator: mj_flexPassiveStretch keeps the full Me_a, so no force changes.
Both the matrix-free operator and the CSR assembly the effective metric builds
from are updated, since they must agree.
This changes how flexes with elastic2d="stretch" integrate under the implicit
integrators and the effective metric -- bag.xml moves, poncho.xml is
bit-identical because bending energy is quadratic and has no geometric term.
The interpolated-flex path still uses its Gauss-Newton approximation, which
FlexInterpDerivativesDeformed asserts.
Alessio
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