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MODE-III CRACK-TIP STRESS FIELDS IN GRADIENT ELASTICITY INCORPORATING SURFACE EFFECT

Alireza Ostadhossein (Pennsylvania State University)

SES Medal Symposium in honor of D.J. Steigmann

Mon 4:20 - 5:40

MacMillan 115

The surface effect is examined in the mode-III nano-crack problem under anti-plane traction in a linearly elastic solid based on strain gradient elasticity formulated by Aifantis. Since the surface to volume ratio increases at this scale, the usual continuum theory which neglects the surface effects, fails to provide reasonable results. The surface mechanics are incorporated resorting the continuum based surface/interface model of Gurtin and Murdoch. Neumann expansion and Filon’s method has been adopted to solve the integral equation for obtaining the stress and deformation fields, numerically. Due to surface elasticity incorporation, it is observed that, contrary to the LEFM and the strain gradient results, the stress at the crack-tip remains finite and depends on crack size. Moreover, as gradient elasticity theory predicts, the crack closes smoothly, not completely sharp as in LEFM, at its physical tip.