{
 "title": "MacNeal–Harder patch test for solids (hex8 with incompatible modes)",
 "kind": "benchmark",
 "source": "MacNeal and Harder, 'A proposed standard set of problems to test finite element accuracy', Finite Elements in Analysis and Design 1 (1985) 3–20: Fig. 3 (p. 6) geometry and inner node locations, Table 2(c) (p. 10) boundary displacements and theoretical solution",
 "quantities": [
  {
   "id": "sxx",
   "quantity": "σ_xx at inner node 7 (0.788, 0.693, 0.644)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/0"
   },
   "value": 2000.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "syy",
   "quantity": "σ_yy at inner node 7 (0.788, 0.693, 0.644)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/1"
   },
   "value": 2000.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "szz",
   "quantity": "σ_zz at inner node 7 (0.788, 0.693, 0.644)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/2"
   },
   "value": 2000.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "txy",
   "quantity": "τ_xy at inner node 7",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/3"
   },
   "value": 400.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "txz",
   "quantity": "τ_xz at inner node 7",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/4"
   },
   "value": 400.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "tyz",
   "quantity": "τ_yz at inner node 7",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/stress/5"
   },
   "value": 400.0,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  },
  {
   "id": "u7",
   "quantity": "u_x at inner node 7",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Patch",
     "at": [
      [
       0.788,
       0.693,
       0.644
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 0.0014565000000000001,
   "tolerance": {
    "relative": 1e-09
   },
   "reason": "a patch test is passed exactly: the tolerance only admits rounding"
  }
 ]
}