Geodesic
Asymptotic justification of the models of thin inclusions in an elastic body in the antiplane shear problem
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 103-119

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The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a power-law dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter vanishes and construct an asymptotic model of an elastic body containing a thin inclusion. We also show that, depending on the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion, ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strong convergence is established of the family of solutions of the original problem to the solution of the limiting one.
Keywords: asymptotic analysis, antiplane shear, inhomogeneous elastic body, thin rigid inclusion, thin elastic inclusion, crack. . 
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     author = {E. M. Rudoy and H. Itou and N. P. Lazarev},
     title = {Asymptotic justification of the models of thin inclusions in an elastic body in the  antiplane shear problem},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {103--119},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a7/}
}
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E. M. Rudoy; H. Itou; N. P. Lazarev. Asymptotic justification of the models of thin inclusions in an elastic body in the  antiplane shear problem. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 103-119. http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a7/