{
  "id": "1705.11121",
  "version": "v1",
  "published": "2017-05-31T14:56:42.000Z",
  "updated": "2017-05-31T14:56:42.000Z",
  "title": "Collisions in shape memory alloys",
  "authors": [
    "Michel Frémond",
    "Michele Marino",
    "Elisabetta Rocca"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by an hammer stroke.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-31T14:56:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shape memory alloys",
      "collisions",
      "sma 2d solid subject",
      "austenite-martensites phase changes",
      "hammer stroke"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}