forked from 1b-agent/fieldcraft-upstream
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
13 lines
1000 B
Markdown
13 lines
1000 B
Markdown
# Hertz line contact in plane strain (implicit mortar contact of 2D edges)
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The 2D form of `nl-hertz-cylinder`: the same steel cylinder of radius R = 10 mm on a steel block
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(E = 210 GPa, ν = 0.3; mm, N, MPa), now a plane strain model of unit thickness meshed with quad4:
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the cylinder's lower part a 2.5 mm wide block whose bottom edge is the circular arc (20 × 10,
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graded towards the contact), on a 5 × 5 mm foundation (24 × 14), symmetric about x = 0. A
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pressure on the indenter's top edge carries the load P = 2265.57 N/mm (per length of the whole
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cylinder) for Hertz's half-width b = 0.5 mm and peak pressure p₀ = 2884.6 MPa. Soft springs hold
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the indenter's top until the contact closes. One nonlinear static step without nonlinear
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geometry: small sliding, edge-to-edge mortar contact of the round edge (secondary) on the flat
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(main) by an augmented Lagrangian. The references and tolerances are the 3D case's, so the two
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discretisations of one problem are checked against one closed form.
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