TY - JOUR

T1 - Strain gradient elasticity for antiplane shear cracks

T2 - A hypersingular integrodifferential equation approach

AU - Fannjiang, Albert C.

AU - Chan, Youn Sha

AU - Paulino, Glaucio H.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We consider Casal's strain gradient elasticity with two material lengths l, l′ associated with volumetric and surface energies, respectively. For a Mode III finite crack we formulate a hypersingular integrodifferential equation for the crack slope supplemented with the natural cracktip conditions. The full-field solution is then expressed in terms of the crack profile and the Green function, which is obtained explicitly. For l′ = 0, we obtain a closed form solution for the crack profile. The case of small l′ is shown to be a regular perturbation. The question of convergence, as l, l′ → 0, is studied in detail both analytically and numerically.

AB - We consider Casal's strain gradient elasticity with two material lengths l, l′ associated with volumetric and surface energies, respectively. For a Mode III finite crack we formulate a hypersingular integrodifferential equation for the crack slope supplemented with the natural cracktip conditions. The full-field solution is then expressed in terms of the crack profile and the Green function, which is obtained explicitly. For l′ = 0, we obtain a closed form solution for the crack profile. The case of small l′ is shown to be a regular perturbation. The question of convergence, as l, l′ → 0, is studied in detail both analytically and numerically.

KW - Hypersingular integral equation

KW - Strain-gradient elasticity

UR - http://www.scopus.com/inward/record.url?scp=0036302212&partnerID=8YFLogxK

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U2 - 10.1137/S0036139900380487

DO - 10.1137/S0036139900380487

M3 - Article

AN - SCOPUS:0036302212

VL - 62

SP - 1066

EP - 1091

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -