Elastic as Limit of Viscoelastic Response, in a Context of Self-Similar Viscous Limits

Abstract

We study the equations of one-dimensional isothermal elastic response as the small viscosity limit of the equations of viscoelasticity, in a context of self-similar viscous limits for Riemann data. The limiting procedure is justified and a solution of the Riemann problem for the equations of elasticity is obtained. The emerging solution is composed of two wave fans, each consisting of rarefactions, shocks and contact discontinuities, separated by constant states. At shocks the self-similar viscous solution has the internal structure of traveling waves, and an admissibility criterion identified by Wendroff is fulfilled.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1994
Accession Number
ADA277043

Entities

People

  • Anthanasios E. Tzavaras

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Computational Science
  • Construction
  • Differential Equations
  • Discontinuities
  • Elastic Properties
  • Equations
  • Equations Of State
  • Formulas (Mathematics)
  • Inequalities
  • Materials
  • Navier Stokes Equations
  • Sequences
  • Theorems
  • Traveling Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Mechanical Engineering/Mechanics of Materials.
  • Systems Analysis and Design