Geodesic
Problem of equilibrium for hyperelastic body with rigid inclusion and non-penetrating crack
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 17-40.

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The paper deals with a solid body containing a rigid inclusion with a crack on its boundary. This body is assumed to be hyperelastic; therefore, we describe it within the framework of finite-strain theory. Moreover, we implement a non-interpenetration condition, which does not allow the opposite crack faces to penetrate each other. The main object of our research is energy minimization corresponding to the problem of equilibrium for the described body. By the use of variational methods, it is shown that this problem has a solution. Then we discuss a boundary value problem that is satisfied by the equilibrium solution.
Keywords: crack, rigid inclusion, non-interpenetration condition, contact, hyperelastic material, finite-strain elasticity, energy minimization. 
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     author = {A. I. Furtsev},
     title = {Problem of equilibrium for hyperelastic body with rigid inclusion and non-penetrating crack},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {17--40},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a22/}
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A. I. Furtsev. Problem of equilibrium for hyperelastic body with rigid inclusion and non-penetrating crack. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 17-40. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a22/