9505342 Tzavaras We propose to study various topics related to the formation, propagation and resolution of singularities during the dynamic deformation of continuous media. The topics are: (i) Effect of viscosity on shock propagation for hyperbolic conservation laws. (ii) Fluid-mechanic limits for discrete velocity models for Riemann data. (iii) Formation of shear bands at high strain rates. The proposed techniques are from the domain of qualitative theory of partial differential equations, with the use of computational tools when necessary to guide the theory. The proposed problems vary from concrete models for specific phenomena, to general theory hyperbolic systems of conservation laws, to developing techniques for studying the transition from discrete to continuum theories. The theoretical understanding of structures such as shock waves and shear bands is critical for designing improved algorithms in technological applications where such phenomena are dominant. Shear bands are regions of intensely localized strain that appear during high speed deformations of metals and often precede rupture. Shear bands play a major role in ballistic penetration of metals and in various manufacturing processes involving metals.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9505342
Program Officer
Deborah Lockhart
Project Start
Project End
Budget Start
1995-07-01
Budget End
1999-06-30
Support Year
Fiscal Year
1995
Total Cost
$60,000
Indirect Cost
Name
University of Wisconsin Madison
Department
Type
DUNS #
City
Madison
State
WI
Country
United States
Zip Code
53715