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- W2004256283 abstract "Abstract The conservation laws in a nonlinear elastic dislocation continuum are studied by combining Noether's theorem with the Nonriemannian geometric theory. The distortion tensors are newly defined in the Lagrangian description and in the Eulerian description in terms of vielbein theory, which results in some simplifications in the theoretical derivation of these laws. The first step of the derivation is to build up two basic equations of variational invariance by applying simultaneously Noether's theorem to the integral actions of a dislocation continuum system, which are expressed both in the Lagrangian and in the Eulerian descriptions, respectively. Then, based on these two equations, as the second step, we use six infinitesimal transformations of both independent and dependent variables to obtain two sets of six specific conservation laws. These transformations are: time translation; material and spatial coordinate translations; material and spatial coordinate rotation as well as rotation of distortion tensors in the natural state. Finally, the duality principle is discussed in some detail between these two sets of conservation equations. In particular, a conservation law called the gauge angular momentum conservation law due to free rotation of anholonomic coordinate frame of a material body in the natural state is believed not to have been revealed before." @default.
- W2004256283 created "2016-06-24" @default.
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- W2004256283 date "1985-01-01" @default.
- W2004256283 modified "2023-09-27" @default.
- W2004256283 title "Duality principle of conservation laws in dislocation continuum" @default.
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- W2004256283 doi "https://doi.org/10.1016/0020-7683(85)90072-1" @default.
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