Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.