{
 "title": "Elastic bar striking a rigid wall (explicit)",
 "kind": "theory",
 "source": "One-dimensional elastic impact on a rigid wall: contact time 2L/c, rebound at the impact speed, contact stress ρcv₀; Graff, Wave Motion in Elastic Solids, Dover 1991, §2.3; Johnson, Impact Strength of Materials, Arnold 1972, §1.6",
 "quantities": [
  {
   "id": "u_front",
   "quantity": "displacement of the struck end at t = 0.3 (in contact until 2L/c = 0.2, then leaving at v₀)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Impact",
     "at": [
      [
       0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 0.009999999999999998,
   "tolerance": {
    "relative": 0.03
   },
   "reason": "the contact ends at 2L/c in the elastic theory; the discrete release front is spread over a few elements, a few tenths of a percent of the time, and the rebound speed is v₀ to about 1%"
  },
  {
   "id": "u_back",
   "quantity": "displacement of the far end at t = 0.3 (−v₀L/c, then +v₀ after the reflection)",
   "measure": {
    "command": "solve.probe",
    "params": {
     "step": "Impact",
     "at": [
      [
       10.0,
       0,
       0
      ]
     ]
    },
    "pointer": "/nodes/0/displacement/0"
   },
   "value": 0.01,
   "tolerance": {
    "relative": 0.03
   },
   "reason": "as for the struck end"
  },
  {
   "id": "ke",
   "quantity": "kinetic energy after the rebound over the initial ½mv₀²",
   "measure": {
    "from": "solve",
    "pointer": "/energy/kinetic",
    "scale": 1999.9999999999995
   },
   "value": 1.0,
   "tolerance": {
    "relative": 0.02
   },
   "reason": "an elastic impact keeps the kinetic energy; quadratic bulk viscosity in the compression front and the vibration left in the bar take about 1%"
  }
 ]
}