jyvikoandClaude Opus 5.5
227c4544ed
Plane strain, plane stress and axisymmetric models take contact pairs and general (self) contact on the linear edges of tri3 and quad4 elements: edges oriented out of their elements, the edge mortar of fem with the thickness or 2 pi r in the weights, the element's area over the edge's length as the thickness under it, and the in-plane rows of the tangent blocks. Verified by the contact patch test in plane strain and axisymmetric (to 1e-9 small sliding, 1e-4 finite), Hertz's line contact on quad4 edges (Johnson 1985, 4.3; equal to the hex8 model's to 1e-5), and a hybrid rubber C-ring closing on itself that moves node for node as the one-layer solid ring. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
Hertz line contact in plane strain (implicit mortar contact of 2D edges)
The 2D form of nl-hertz-cylinder: the same steel cylinder of radius R = 10 mm on a steel block
(E = 210 GPa, ν = 0.3; mm, N, MPa), now a plane strain model of unit thickness meshed with quad4:
the cylinder's lower part a 2.5 mm wide block whose bottom edge is the circular arc (20 × 10,
graded towards the contact), on a 5 × 5 mm foundation (24 × 14), symmetric about x = 0. A
pressure on the indenter's top edge carries the load P = 2265.57 N/mm (per length of the whole
cylinder) for Hertz's half-width b = 0.5 mm and peak pressure p₀ = 2884.6 MPa. Soft springs hold
the indenter's top until the contact closes. One nonlinear static step without nonlinear
geometry: small sliding, edge-to-edge mortar contact of the round edge (secondary) on the flat
(main) by an augmented Lagrangian. The references and tolerances are the 3D case's, so the two
discretisations of one problem are checked against one closed form.