Geodesic
Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 935-948

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Within the framework of two-dimensional elasticity theory, a heterogeneous body with a narrow inclusion lying strictly inside the body is considered. It is assumed that the elastic properties of inclusion and its width depend on the small parameter $\delta>0$. Moreover, we assume that the inclusion has a curvilinear rough boundary. We show that there exist three type of limiting problem as $\delta\to0$: $p>1$ – body with crack without interaction of its faces; $p=1$ – body with crack with adhesive interaction of its faces; $p\in[0,1)$ – homogeneous body (no crack).
Keywords: asymptotic analysis, inhomogeneous elastic body, narrow inclusion, curvilinear crack
Mots-clés : interface conditions. 
@article{SEMR_2022_19_2_a39,
     author = {I. V. Fankina and A. I. Furtsev and E. M. Rudoy and S. A. Sazhenkov},
     title = {Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {935--948},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a39/}
}
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I. V. Fankina; A. I. Furtsev; E. M. Rudoy; S. A. Sazhenkov. Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 935-948. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a39/