{
 "title": "A quarter turn strains and stresses nothing (objectivity)",
 "kind": "theory",
 "source": "Objectivity of the total Lagrangian formulation and of the hyperelastic stress: a rigid motion x = R X + c gives C = I and σ = 0 whatever the rotation (Bonet & Wood 2008, §3.4 and §5.2; T. Belytschko, W. K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, 2nd ed., Wiley 2014, §5.5)",
 "quantities": [
  {
   "id": "ux",
   "quantity": "u_x at inner node 22: the rotation's",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Turn",
     "nodes": [
      22
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": -0.011149180525904245,
   "tolerance": {
    "absolute": 1e-09
   },
   "reason": "the inner nodes follow the rigid rotation exactly"
  },
  {
   "id": "uy",
   "quantity": "u_y at inner node 22: the rotation's",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Turn",
     "nodes": [
      22
     ]
    },
    "pointer": "/nodes/0/displacement/1"
   },
   "value": 0.07859051161172886,
   "tolerance": {
    "absolute": 1e-09
   },
   "reason": "the inner nodes follow the rigid rotation exactly"
  },
  {
   "id": "uz",
   "quantity": "u_z at inner node 22: the rotation's",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Turn",
     "nodes": [
      22
     ]
    },
    "pointer": "/nodes/0/displacement/2"
   },
   "value": -0.06744133108582467,
   "tolerance": {
    "absolute": 1e-09
   },
   "reason": "the inner nodes follow the rigid rotation exactly"
  },
  {
   "id": "von_mises",
   "quantity": "von Mises stress at inner node 22",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Turn",
     "nodes": [
      22
     ]
    },
    "pointer": "/nodes/0/von_mises"
   },
   "value": 0.0,
   "tolerance": {
    "absolute": 1e-08
   },
   "reason": "zero up to rounding of stresses of order E = 1000: a 90° turn leaves no strain"
  }
 ]
}