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On crack propagations in elastic bodies with thin inclusions. / Khludnev, A. M.; Popova, T. S.
In: Сибирские электронные математические известия, Vol. 14, 01.01.2017, p. 586-599.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On crack propagations in elastic bodies with thin inclusions
AU - Khludnev, A. M.
AU - Popova, T. S.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.
AB - The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.
KW - Crack
KW - Delamination
KW - Nonpenetration boundary condition
KW - Optimal control
KW - Semirigid inclusion
KW - Thin elastic inclusion
KW - Timoshenko beam
UR - http://www.scopus.com/inward/record.url?scp=85042740604&partnerID=8YFLogxK
U2 - 10.17377/semi.2017.14.050
DO - 10.17377/semi.2017.14.050
M3 - Article
AN - SCOPUS:85042740604
VL - 14
SP - 586
EP - 599
JO - Сибирские электронные математические известия
JF - Сибирские электронные математические известия
SN - 1813-3304
ER -
ID: 10220974