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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Sandipan Paul, Alan D. Freed, John D. Clayton
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	74A20 15A23 Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/94073c3e044b48de872d7a33340491af
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:94073c3e044b48de872d7a33340491af
record_format	dspace
spelling	oai:doaj.org-article:94073c3e044b48de872d7a33340491af2021-12-01T05:05:49ZCoordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches2666-496810.1016/j.apples.2020.100029https://doaj.org/article/94073c3e044b48de872d7a33340491af2021-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300297https://doaj.org/toc/2666-4968Eulerian 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.Sandipan PaulAlan D. FreedJohn D. ClaytonElsevierarticle74A2015A23Engineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 5, Iss , Pp 100029- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	74A20 15A23 Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	74A20 15A23 Engineering (General). Civil engineering (General) TA1-2040 Sandipan Paul Alan D. Freed John D. Clayton Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
description	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.
format	article
author	Sandipan Paul Alan D. Freed John D. Clayton
author_facet	Sandipan Paul Alan D. Freed John D. Clayton
author_sort	Sandipan Paul
title	Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
title_short	Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
title_full	Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
title_fullStr	Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
title_full_unstemmed	Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches
title_sort	coordinate indexing: on the use of eulerian and lagrangian laplace stretches
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/94073c3e044b48de872d7a33340491af
work_keys_str_mv	AT sandipanpaul coordinateindexingontheuseofeulerianandlagrangianlaplacestretches AT alandfreed coordinateindexingontheuseofeulerianandlagrangianlaplacestretches AT johndclayton coordinateindexingontheuseofeulerianandlagrangianlaplacestretches
_version_	1718405556981465088

Coordinate indexing: On the use of Eulerian and Lagrangian Laplace stretches

Ejemplares similares