An Asymptotic Finite-Deformation Analysis of the Elastostatic Field near the Tip of a Crack.

Abstract

The paper contains an asymptotic treatment, consistent with the fully nonlinear equilibrium theory of compressible elastic solids, of the stresses and deformations near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. The loading applied at infinity is taken to be one of uniform uni-axial tension at right angles to the faces of the crack. For the particular class of elastic materials considered the tensile stress in large homogeneous uni-axial extension is asymptotic to a continuously adjustable power of the corresponding principal stretch. The asymptotic analysis of the foregoing crack problem is reduced to a nonlinear eigenvalue problem, the solution of which is established in closed form, in terms of elementary functions and certain transcendental integrals of such functions. (Author Modified Abstract)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1973
Accession Number
AD0757777

Entities

People

  • Eli Sternberg
  • James K. Knowles

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Eigenvalues
  • Elastic Materials
  • Integrals
  • Materials
  • Mathematics
  • Right Angles
  • Stresses
  • Tensile Stress
  • Traction

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Materials Science (Mechanical Engineering).
  • Structural Dynamics.