Steady Waves in a Nonlinear Theory of Viscoelasticity.
Abstract
This work considers the propagation of steady waves in viscoelastic material for which the nonlinear strain measure is not necessarily convex. The shape of such a wave is governed by an ordinary nonlinear integro-differential equation having a possibly singular difference kernel. The existence and structure of a solution depends upon the relation of the wavespeed, a parameter in the problem, to two speeds based upon the state of the material ahead of the wave. Solutions are constructed by a monotone iterative scheme which is proven to converge to a unique solution within restricted classes of functions depending upon the wavespeed. A simple numerical approximation to the iterative scheme is used to produce graphs of solutions. An algebraic quasielastic approximation produces upper bounds on discontinuous ( shock and acceleration wave) solutions. For a material such as polymethyl methacrylate (pmma) having a small power in a power-law model of its compliance, this approximation is found to be useful for accurately predicting the structure of shock solutions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1987
- Accession Number
- ADA185548
Entities
People
- Gregory T. Warhola
Organizations
- Air Force Institute of Technology