Geodesic
On modeling elastic bodies with defects
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 153-166

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The paper concerns a mathematical analysis of equilibrium problems for 2D elastic bodies with thin defects. The defects are characterized with a damage parameter. A presence of defects implies that the problems are formulated in a nonsmooth domain with a cut. Nonlinear boundary conditions at the cut faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are analyzed. The paper provides an asymptotic analysis with respect to the damage parameter. We obtain invariant integrals over curves surrounding the defect tip. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.
Keywords: defect, damage parameter, non-penetration boundary conditions, variational inequality, optimal control, derivative of energy functional. 
@article{SEMR_2018_15_a86,
     author = {A. M. Khludnev},
     title = {On modeling elastic bodies with defects},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {153--166},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a86/}
}
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A. M. Khludnev. On modeling elastic bodies with defects. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 153-166. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a86/