Add 2D membrane elasticity for interpolated flex shell mode

When elastic2d="stretch" is set on an interpolated flexcomp, treat the bounding box boundary as membrane elements rather than volumetric cells. This computes plane-stress stiffness over the boundary faces and updates the runtime force/derivative kernels accordingly.

Interior vertex tracking (moving vertices that follow the deforming shell) is not yet implemented so all mesh vertices need to be on the bounding box surface or the background grid should have no interior nodes (i.e. cellcount should be 1 on at least one axis).

PiperOrigin-RevId: 907654080
Change-Id: I51b90e2f6a1d1b036f9604e42de20e377dc5d3f9

test/engine/engine_passive_test.cc

@@ -847,5 +847,41 @@ TEST_F(PassiveTest, PolynomialDampingTendon) {
   mj_deleteModel(m);
 }
 
+// shell-mode (elastic2d=stretch) flexcomp must have zero passive spring forces
+// at rest (initial configuration); any nonzero force indicates a rotation
+// mismatch between compile-time reference positions and runtime corotation.
+TEST_F(ElasticityTest, ShellModeZeroForceAtRest) {
+  static constexpr char xml[] = R"(
+  <mujoco>
+    <option gravity="0 0 0"/>
+    <worldbody>
+      <flexcomp type="grid" count="8 8 8" spacing=".07 .07 .07" pos="0 0 1"
+                dim="3" cellcount="1 1 1" radius=".001" rgba="0 .7 .7 1"
+                mass="5" name="softbody" dof="trilinear">
+        <elasticity young="1e4" poisson="0.1" damping="0.01"
+                    elastic2d="stretch" thickness="0.02"/>
+        <contact selfcollide="none" internal="false"/>
+      </flexcomp>
+    </worldbody>
+  </mujoco>
+  )";
+
+  char error[1024] = {0};
+  mjModel* m = LoadModelFromString(xml, error, sizeof(error));
+  ASSERT_THAT(m, testing::NotNull()) << error;
+  mjData* d = mj_makeData(m);
+
+  mj_forward(m, d);
+
+  // all spring forces should be zero at rest
+  for (int i = 0; i < m->nv; i++) {
+    EXPECT_NEAR(d->qfrc_spring[i], 0, 1e-10)
+        << "nonzero spring force at DOF " << i;
+  }
+
+  mj_deleteData(d);
+  mj_deleteModel(m);
+}
+
 }  // namespace
 }  // namespace mujoco