A Cartesian parametrization for the numerical analysis of material instability

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; Ostien, Jakob T.; Lai, Zhengshou

doi:10.1002/nme.5228

Title: A Cartesian parametrization for the numerical analysis of material instability

Journal Article · Thu Feb 25 00:00:00 EST 2016 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5228· OSTI ID:1262242

Mota, Alejandro ^[1]; Chen, Qiushi ^[2]; Foulk, III, James W. ^[1]; Ostien, Jakob T. ^[1]; Lai, Zhengshou ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Clemson Univ., Clemson, SC (United States)

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, the performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.

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Research Organization:: Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1262242

Report Number(s):: SAND-2015-9106J; 643723

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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