dorsal/arxiv
View SchemaTransformation Properties of the Lagrangian and Eulerian Strain Tensors
| Authors | Thomas B. Bahder |
|---|---|
| Categories | |
| ArXiv ID | physics/0211003 |
| URL | https://arxiv.org/abs/physics/0211003 |
Abstract
A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates. The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates. The Lagrangian strain is a two-point tensor that transforms as scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates. These transformation properties are needed when transforming the strain tensors from one frame of reference to another moving frame.
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"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"
],
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"physics.class-ph",
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"title": "Transformation Properties of the Lagrangian and Eulerian Strain Tensors",
"url": "https://arxiv.org/abs/physics/0211003"
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