Integrable Generalized Wave Equations Exhibiting a Hypoelastic Compressible Rate-Sensitive Material Flow

[+] Author and Article Information
M. Ziv

Department of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa, Israel

J. Appl. Mech 44(3), 419-423 (Sep 01, 1977) (5 pages) doi:10.1115/1.3424094 History: Received October 01, 1976; Revised February 01, 1977; Online July 12, 2010


Numerically integrable wave (characteristic) equations governing quasi-linear material motion are derived in generalized spatial curvilinear coordinates. The material under consideration is assigned an isentropic hypoelastic/compressible visco-perfectly plastic flow behavior where geometrical nonlinearities prevail throughout, while finite strains correspond only to the anelastic component of the constitutive equation. The characteristics formulation for the flow is derived under a tensor approach, based on those discontinuity relations that are compatible with the geometric description of hyperbolic partial differential equations. Results for spatial multidimensional integration schemes are presented in the form of nonlinear characteristic equations along their orthogonal path of integration (bicharacteristic curves) varying according to wave speed.

Copyright © 1977 by ASME
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