{
 "title": "Tie patch test: two blocks with non-matching meshes tied together in uniaxial tension",
 "kind": "theory",
 "source": "The patch test for mesh tying: a tie across non-matching meshes must transmit a constant stress exactly; B. I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal. 38(3):989–1012, 2000; M. A. Puso, A 3D mortar method for solid mechanics, IJNME 59:315–336, 2004. Uniaxial stress between frictionless symmetry planes is uniform in both blocks",
 "quantities": [
  {
   "id": "szz_10",
   "quantity": "σ_zz of the lower block's corner element under the tie (element 10)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      10
     ]
    },
    "pointer": "/elements/0/stress/0/2"
   },
   "value": 10.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes"
  },
  {
   "id": "szz_14",
   "quantity": "σ_zz of the lower block's centre element under the tie (element 14)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      14
     ]
    },
    "pointer": "/elements/0/stress/0/2"
   },
   "value": 10.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes"
  },
  {
   "id": "szz_1",
   "quantity": "σ_zz of the lower block's bottom corner element (element 1)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      1
     ]
    },
    "pointer": "/elements/0/stress/0/2"
   },
   "value": 10.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes"
  },
  {
   "id": "szz_19",
   "quantity": "σ_zz of the upper block's corner element over the tie (element 19)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      19
     ]
    },
    "pointer": "/elements/0/stress/0/2"
   },
   "value": 10.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes"
  },
  {
   "id": "szz_26",
   "quantity": "σ_zz of the upper block's top far corner element (element 26)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      26
     ]
    },
    "pointer": "/elements/0/stress/0/2"
   },
   "value": 10.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "uniaxial stress E ε = 1000 × 0.01 is the exact discrete solution: the dual mortar conditions hold for the linear field on both meshes"
  },
  {
   "id": "sxx_14",
   "quantity": "σ_xx of element 14 (uniaxial stress: 0)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "elements": [
      14
     ]
    },
    "pointer": "/elements/0/stress/0/0"
   },
   "value": 0.0,
   "tolerance": {
    "absolute": 1e-09
   },
   "reason": "the tie must not hold the lateral contraction of either mesh"
  },
  {
   "id": "uz_interface",
   "quantity": "u_z at the tied secondary node (0.5, 0.5, 1)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Pull",
     "at": [
      [
       0.5,
       0.5,
       1.0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/2"
   },
   "value": 0.01,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "the tied node follows the uniform strain field"
  }
 ]
}