ASME Journal of Applied Mechanics
Y.-S.
Chan
Computer Science and Mathematics Division, Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37831, U.S.A.
G.H. Paulino
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, IL 61801, U.S.A.
A.C. Fannjiang
Department of Mathematics, University of California,Davis, CA 95616, U.S.A.
Abstract
A mode III crack problem is a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths l and l', which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived assuming that the shear modulus G is a function of x, i.e. G=G(x)=G0ebx, where G0 and b are material constants. A hypersingular integrodifferential equation is derived and discretized by means of the collocation method and a Chebyshev polynomial expansion. Numerical results are given in terms of the crack opening displacements, strains, and stresses with various combinations of the parameters l, l', and b. Formulas for the stress intensity factors (SIFs), KIII, are derived and numerical results are provided.
Key words: mode III, crack,
functionally graded material, FGM, anisotropic, constitutive equations, strain
gradient elasticity, material gradation, integral equation method, hypersingular,
partial differential equations, high-order continuum theory