solver: mortar contact in 2D models

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

crates/model/src/check.rs

@@ -388,13 +388,16 @@ impl Model {
             }
         }
 
-        // Contacts: their surfaces are element faces of solids.
+        // Contacts: their surfaces are element faces of solids, or edges of 2D elements.
         for (name, c) in &self.contacts {
             for set in c.surfaces.sets() {
                 let faces = &set_of(set).faces;
                 let solid = |f: &crate::ElementFace| self.elements.get(&f.element).is_some_and(|e| e.kind.dimension() == 3);
-                if faces.is_empty() {
-                    d.error(format!("contact `{name}`"), format!("set `{set}` has no element faces (a contact surface is a set of faces)"));
+                if faces.is_empty() && resolved.planar_edges(set).is_empty() {
+                    d.error(
+                        format!("contact `{name}`"),
+                        format!("set `{set}` has no element faces (a contact surface is a set of faces, or of 2D element edges)"),
+                    );
                 } else if !faces.iter().all(solid) {
                     d.error(
                         format!("contact `{name}`"),

crates/model/src/contact.rs

@@ -3,12 +3,12 @@
 //! A contact is a model definition, active in every step that can take it (explicit dynamics,
 //! and nonlinear static steps; the linear analyses refuse contact by name). Its
 //! surfaces are sets with element
-//! faces, so they survive remeshing like a pressure load does:
+//! faces (in a 2D model, element edges), so they survive remeshing like a pressure load does:
 //! - a **pair**: the faces of `main` against those of `secondary`, both ways (each surface's
 //!   nodes are kept out of the other's faces, so neither surface is privileged);
 //! - **general** contact: every face against every other face of one surface (single-surface or
 //!   self contact, for folding and buckling), or of every exterior face of the model's solid
-//!   elements when no surface is named.
+//!   elements (in a 2D model every exterior edge of its 2D elements) when no surface is named.
 //!
 //! **Friction** is Coulomb's law with a coefficient that falls from its static to its kinetic
 //! value with the slip rate γ̇: μ = μ_k + (μ_s − μ_k) e^{−d γ̇} (the exponential decay of