{
  "annotation_id": "3298c80a-fecb-4204-b647-8451a10b7ccd",
  "date_created": "2026-03-02T18:00:42.158000Z",
  "date_modified": "2026-03-02T18:00:42.158000Z",
  "file_hash": "3731aba541199832f1a830d761842e81b06b78301ffdde0e85f8087caf6ba6a4",
  "private": false,
  "record": {
    "abstract": "A coordinate independent derivation of the Eulerian and Lagrangian strain\ntensors of finite deformation theory is given based on the parallel propagator,\nthe world function, and the displacement vector field as a three-point tensor.\nThe derivation explicitly shows that the Eulerian and Lagrangian strain tensors\nare two-point tensors, each a function of both the spatial and material\ncoordinates. The Eulerian strain is a two-point tensor that transforms as a\nsecond rank tensor under transformation of spatial coordinates and transforms\nas a scalar under transformation of the material coordinates. The Lagrangian\nstrain is a two-point tensor that transforms as scalar under transformation of\nspatial coordinates and transforms as a second rank tensor under transformation\nof the material coordinates. These transformation properties are needed when\ntransforming the strain tensors from one frame of reference to another moving\nframe.",
    "arxiv_id": "physics/0211003",
    "authors": [
      "Thomas B. Bahder"
    ],
    "categories": [
      "physics.class-ph",
      "physics.gen-ph"
    ],
    "title": "Transformation Properties of the Lagrangian and Eulerian Strain Tensors",
    "url": "https://arxiv.org/abs/physics/0211003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e2a2659d-3473-4526-9194-fcb9603803ee",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}