verification: Coulomb friction between sliding blocks

An oracle case of a block pressed on another and slid with static and kinetic coefficients (mu_k N carried once slipping), and the docs of the friction formulation; ROADMAP M7 and parity updated. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
2026-10-14 15:14:14 -04:00
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+# Coulomb friction: a block slid on another (implicit mortar contact)
+
+A unit cube (2 × 2 × 2 hex8) on a 2 × 1 × 1 block (6 × 3 × 2 hex8), meshes not matching, E = 1000,
+ν = 0.3. The base of the lower block is held; the top of the upper block is pressed down by 0.02
+and moved 0.1 sideways in proportion over one nonlinear static step without nonlinear geometry.
+The contact pair has μ_s = 0.3 and μ_k = 0.2: the sideways demand far exceeds the friction, so
+the interface slips, with the kinetic coefficient once the nodes slip, and carries μ_k N.
@@ -0,0 +1,61 @@
+{
+ "title": "Coulomb friction: a block pressed on another and slid (implicit mortar contact)",
+ "kind": "theory",
+ "source": "Coulomb's law of dry friction: a sliding interface carries μ_k times the normal force against the slip (C. A. Coulomb, Théorie des machines simples, Mém. Math. Phys. Acad. Sci. 10:161–332, 1785; P. Wriggers, Computational Contact Mechanics, 2nd ed., Springer 2006, §5.2)",
+ "quantities": [
+  {
+   "id": "kinetic",
+   "quantity": "the tangential over the normal force across the sliding interface",
+   "measure": {
+    "from": "slide",
+    "pointer": "/contacts/0/force/0",
+    "over": {
+     "from": "slide",
+     "pointer": "/contacts/0/force/2",
+     "scale": -1.0
+    }
+   },
+   "value": 0.2,
+   "tolerance": {
+    "relative": 0.001
+   },
+   "reason": "once the interface slips its friction is μ_k N exactly (the return map puts every slipping node's traction on the cone); the force opposes the upper block's motion"
+  },
+  {
+   "id": "balance",
+   "quantity": "the tangential contact force on the upper block over the sideways reaction at its top (they balance)",
+   "measure": {
+    "from": "slide",
+    "pointer": "/contacts/0/force/0",
+    "over": {
+     "command": "results.reactions",
+     "params": {
+      "step": "Slide",
+      "sets": [
+       "top"
+      ]
+     },
+     "pointer": "/sets/0/force/0"
+    }
+   },
+   "value": -1.0,
+   "tolerance": {
+    "relative": 1e-06
+   },
+   "reason": "the friction carries the whole sideways load"
+  },
+  {
+   "id": "slipping",
+   "quantity": "the secondary nodes that slip (all 9)",
+   "measure": {
+    "from": "slide",
+    "pointer": "/contacts/0/slipping_nodes"
+   },
+   "value": 9.0,
+   "tolerance": {
+    "exact": true
+   },
+   "reason": "a sideways demand far beyond μ N slips the whole interface"
+  }
+ ]
+}
@@ -0,0 +1,17 @@
+{
+  "note": "FieldCraft's accepted results for this case, written by `cargo xtask oracle --bless`. A result outside its band fails CI.",
+  "values": {
+    "balance": {
+      "band": 1e-9,
+      "value": -0.999999977621409
+    },
+    "kinetic": {
+      "band": 2.0000000000000003e-10,
+      "value": 0.199999793528717
+    },
+    "slipping": {
+      "band": 9.000000000000001e-9,
+      "value": 9.0
+    }
+  }
+}
@@ -0,0 +1,16 @@
+[
+ {"command": "mesh.block", "params": {"body": "Lower", "kind": "hex8", "corners": [[0, 0, 0], [2, 0, 0], [2, 1, 0], [0, 1, 0], [0, 0, 1], [2, 0, 1], [2, 1, 1], [0, 1, 1]], "divisions": [6, 3, 2], "faces": {"1": "bottom", "2": "top"}}},
+ {"command": "mesh.block", "params": {"body": "Upper", "kind": "hex8", "corners": [[0.5, 0, 1], [1.5, 0, 1], [1.5, 1, 1], [0.5, 1, 1], [0.5, 0, 2], [1.5, 0, 2], [1.5, 1, 2], [0.5, 1, 2]], "divisions": [2, 2, 2], "faces": {"1": "bottom", "2": "top"}, "merge": 0}},
+ {"command": "model.set.create", "params": {"name": "all", "geometry": [{"body": "Lower"}, {"body": "Upper"}]}},
+ {"command": "model.set.create", "params": {"name": "lower_top", "geometry": [{"body": "Lower", "face": "top"}]}},
+ {"command": "model.set.create", "params": {"name": "upper_bottom", "geometry": [{"body": "Upper", "face": "bottom"}]}},
+ {"command": "model.set.create", "params": {"name": "base", "geometry": [{"body": "Lower", "face": "bottom"}]}},
+ {"command": "model.set.create", "params": {"name": "top", "geometry": [{"body": "Upper", "face": "top"}]}},
+ {"command": "model.material.create", "params": {"name": "Mat", "elastic": {"type": "isotropic", "young": 1000.0, "poisson": 0.3}}},
+ {"command": "model.section.create", "params": {"name": "all", "set": "all", "material": "Mat", "kind": {"type": "solid"}}},
+ {"command": "interaction.contact.pair", "params": {"name": "interface", "main": "lower_top", "secondary": "upper_bottom", "friction": {"static": 0.3, "kinetic": 0.2, "decay": 1.0}}},
+ {"command": "model.boundary_condition.create", "params": {"name": "base", "type": "fixed", "target": {"set": "base"}}},
+ {"command": "model.boundary_condition.create", "params": {"name": "slide", "type": "displacement", "target": {"set": "top"}, "values": [0.1, 0, -0.02, null, null, null]}},
+ {"command": "model.step.create", "params": {"name": "Slide", "procedure": {"type": "nonlinear_static", "nonlinear_geometry": false, "initial_increment": 0.25}, "boundary_conditions": ["base", "slide"], "loads": []}},
+ {"command": "solve.nonlinear", "params": {"step": "Slide"}, "id": "slide"}
+]