The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

Authors

Dawn A. Lott, New Jersey Institute of Technology
Stuart S. Antman, College of Computer, Mathematical, & Natural Sciences
William G. Szymczak, U.S. Naval Research Laboratory

Document Type

Article

Publication Date

7-20-2001

Abstract

We formulate an efficient numerical algorithm based on finite-difference approximations and inspired by algorithms from gas dynamics to treat the quasilinear wave equation wtt = [α(w²x + w²y)wx]x + [α(w²x + w²y)wy]y governing antiplane motions of incompressible, isotropic nonlinearly elastic bodies in two-dimensions. In particular, we are concerned with the treatment of focusing and shocks for bodies whose material response differs markedly from that of linear elasticity. We carefully validate our method by comparing our results with those of the axisymmetric version of this equation in polar coordinates. © 2001 Academic Press.

Identifier

0347078340 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1006/jcph.2001.6783

ISSN

00219991

First Page

201

Last Page

226

Issue

1

Volume

171

Grant

DMS 99 71823

Fund Ref

National Science Foundation

Recommended Citation

Lott, Dawn A.; Antman, Stuart S.; and Szymczak, William G., "The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies" (2001). Faculty Publications. 15138.
https://digitalcommons.njit.edu/fac_pubs/15138