An Asymptotic Finite-Deformation Analysis of the Elastostatic Field near the Tip of a Crack.
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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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