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
Y1 - 2002
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
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U2 - 10.1137/S0036139900380487
DO - 10.1137/S0036139900380487
M3 - Article
AN - SCOPUS:0036302212
SN - 0036-1399
VL - 62
SP - 1066
EP - 1091
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 3
ER -