HOMOGENEOUS CONSTITUTIVE EQUATIONS FOR MATERIALS WITH PERMANENT MEMORY

Abstract

Nonlinear homogeneous constitutive equations are developed in this thesis for highly filled polymeric materials such as solid propellants. In the range of strains below vacuole dilatation these materials obey the homogeneity rule of linearity but do not obey the superposition rule. Such materials typically exhibit an irreversible 'stress softening' called the 'Mullins' Effect.' The development in this dissertation stems from attempting to mathematically describe the failing microstructure of these composite materials in terms of a linear cumulative damage model. It is demonstrated that pth order Lebesgue norms of the strain history can be used to describe the state of damage in these materials and can also be used in the constitutive equation to characterize their time dependent mechanical response to strain disturbances. Stress analysis procedures for materials having nonlinear homogeneous constitutive equations are developed for two and three dimensional proportional boundary value problems. A series of correspondence principles are derived wherein half of the solution, either the stresses or the strains, can be obtained by solving an equivalent linear elastic problem. The remaining half of the solution can be obtained by substituting the linear elastic solution into the nonlinear homogeneous constitutive equation.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1970
Accession Number
AD0711657

Entities

People

  • Richard J. Farris

Organizations

  • University of Utah

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Composite Materials
  • Composite Propellants
  • Constitutive Equations
  • Continuum Mechanics
  • Differential Equations
  • Elastic Properties
  • Experimental Data
  • Materials
  • Materials Laboratories
  • Materials Science
  • Materials Testing
  • Mechanics
  • Regression Analysis
  • Strain Rate
  • Stress Analysis
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mechanical Engineering/Mechanics of Materials.