Dilatationally Nonlinear Elastic Materials: (1) Some Theory

Abstract

This paper, which is the first in a two part study, addresses certain issues concerning the small strain theory of nonlinear elasticity. It considers isotropic materials which possess a linear response in shear and a nonlinear response in dilatation, and (i) establishes an explicit necessary and sufficient condition for the existence of piecewise homogeneous deformations, (ii) obtains a characterization of the set of all such deformations, (iii) derives an expression for the driving traction on a surface of discontinuity in the strain, and finally (iv) discusses the notion of a kinetic law. While the analysis is carried out within a three-dimensional setting, the results are shown to have a particularly simple form when expressed in terms of a certain constitutive function sigma. In Part II of this study we examine a specific boundary value problem.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1988
Accession Number
ADA202824

Entities

People

  • Guo-hua Jiang
  • Rohan Abeyaratne

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Ceramic Matrix Composites
  • Continuum Mechanics
  • Differential Equations
  • Discontinuities
  • Elastic Materials
  • Elastic Properties
  • Equations
  • Materials
  • Mechanical Engineering
  • Mechanics
  • Phase Transformations
  • Stress Strain Relations
  • Stresses
  • Three Dimensional
  • Traction

Fields of Study

  • Mathematics

Readers

  • Business Analytics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.