Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
Eulerian and Lagrangian measures for Laplace stretch are established, along with a strategy to ensure that these measures are indifferent to observer. At issue is a need to accommodate two invariant properties that arise as a byproduct of the Gram–Schmidt factorization procedure, which is used in th...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Elsevier
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/94073c3e044b48de872d7a33340491af |
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| Sumario: | Eulerian and Lagrangian measures for Laplace stretch are established, along with a strategy to ensure that these measures are indifferent to observer. At issue is a need to accommodate two invariant properties that arise as a byproduct of the Gram–Schmidt factorization procedure, which is used in the construction of these stretch tensors. Specifically, a Gram–Schmidt factorization of the deformation gradient implies that the 1 coordinate direction and the normal to the 12 coordinate plane remain invariant under transformations of Laplace stretch. The strategy proposed, which addresses these mathematical consequences, is that the selected 1 coordinate direction has minimal transverse shear, and that its adjoining 12 coordinate plane has minimal in-plane shear. From this foundation, a framework is built for the construction of constitutive equations that can use either the Eulerian or Lagrangian Laplace stretch as its primary kinematic variable. |
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