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