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R. Heuer et al.:
"On the stiffness of spring model for closed crack";
International Journal of Engineering Science, 44 (2006), 13; 874 - 888.

Implications of the spring model used for a closed crack are discussed in terms of the resulting asymptotic crack-tip singularity as well as the field solutions for specific examples of an anti-plane crack. The spring stiffness distribution on the crack surfaces is assumed to be represented by the sum of a constant term and a singular term that is inversely proportional to the distance from the crack tip. Exact expressions for the eigenfunction around the crack tip are obtained and the stress singularity is discussed in some details. The stress singularity at the crack tip is found to be governed by the parameter of the singular stiffness term but not by the constant stiffness term. When the singular stiffness vanishes, the stress singularity reduces to the well-known inverse square-root singularity of an open (traction-free) crack, irrespective of the constant stiffness. In order to delineate the influence of the stiffness distribution on the stress intensity factor (SIF), the crack opening displacement (COD) and the stress distribution on the crack plane, analytical descriptions as well as numerical solutions are also demonstrated for an anti-plane crack under static and dynamic shear loading by the aid of the singular integral equation technique.