Nonlinear Stress-Strain and Inelastic Rebound with Exponential Stiffness

Abstract

Bilinear or power-law presentations are often used to describe the application and release of tension or compression. Here a new nonlinear equation of motion with exact solutions is developed which can describe not only a tension or compression half-cycle, but the entire hysteretic loop. Solutions of the same equation can be used to describe impact phenomena which are important in a number of areas from package cushioning to stopping a fragment or bullet. Oscillatory solutions can also be applied to a variety of mechanical and electrical phenomena. Specific examples are given to some two-segment limit cycles which are special cases of more general solutions. Methods of generalizing the approach used to many other cases are also indicated. Keywords: Mechanics, Stress, Strain, Hysteresis, Nonlinear equations.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1988
Accession Number
ADA195667

Entities

People

  • James T. Dehn

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Army
  • Complex Variables
  • Compression
  • Continuity
  • Cushioning
  • Differential Equations
  • Engineering
  • Equations
  • Frequency
  • Mechanical Engineering
  • Mechanics
  • Nonlinear Differential Equations
  • Numbers
  • Oscillation
  • Oscillators
  • Real Variables
  • Square Roots

Readers

  • Explosive Engineering.
  • Mechanical Engineering/Mechanics of Materials.
  • Operations Research