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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 9/2016

02-04-2016 | Original

Junction problem for rigid and semirigid inclusions in elastic bodies

Authors: Alexander Khludnev, Tatiana Popova

Published in: Archive of Applied Mechanics | Issue 9/2016

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Abstract

The paper is concerned with equilibrium problems for 2D elastic bodies having thin inclusions with different properties. In particular, rigid and semirigid inclusions are considered. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved for each equilibrium problem, and different equivalent formulations of these problems are discussed. In particular, junction conditions at the joint point are found. A delamination of the inclusions is also assumed. This means that we have a crack, and inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We discuss a convergence to zero and infinity of a rigidity parameter of the semirigid inclusion and analyze limit problems.
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Literature
1.
Ciarlet, P.G., Le Dret, H., Nzengwa, R.: Junctions between three dimensional and two dimensional linearly elastic structures. J. Math. Pures Appl. 6, 261–295 (1989)MathSciNetMATH
2.
3.
Gao, Y., Ricoeur, A., Zhang, L.-L., Yang, L.-Z.: Crack solutions and weight functions for plane problems in three-dimensional quasicrystals. Arch. Appl. Mech. 84(8), 1103–1115 (2014)CrossRef
4.
Gaudiello, A., Zappale, E.: Junction in a thin multidomain for a forth order problem. Math. Models Methods Appl. Sci. 16(12), 1887–1918 (2006)MathSciNetCrossRefMATH
5.
6.
7.
8.
Khludnev, A.M., Kovtunenko, V.A.: Analysis of Cracks in Solids. WIT Press, Southampton (2000)
9.
Khludnev, A.M.: Elasticity Problems in Non-smooth Domains. Fizmatlit, Moscow (2010)
10.
Khludnev, A.M.: Problem of a crack on the boundary of a rigid inclusion in an elastic plate. Mech. Solids 45(5), 733–742 (2010)CrossRef
11.
Khludnev, A.M., Leugering, G.: On elastic bodies with thin rigid inclusions and cracks. Math. Methods Appl. Sci. 33(6), 1955–1967 (2010)MathSciNetMATH
12.
Khludnev, A.M., Negri, M.: Crack on the boundary of a thin elastic inclusion inside an elastic body. Z. Angew. Math. Mech. 92(5), 341–354 (2012)CrossRefMATH
13.
Khludnev, A.M., Leugering, G.R.: Delaminated thin elastic inclusion inside elastic bodies. Math. Mech. Complex Syst. 2(1), 1–21 (2014)MathSciNetCrossRefMATH
14.
Khludnev, A.M., Leugering, G.R.: On Timoshenko thin elastic inclusions inside elastic bodies. Math. Mech. Solids 20(5), 495–511 (2015)MathSciNetCrossRefMATH
15.
Khludnev, A.M.: Shape control of thin rigid inclusions and cracks in elastic bodies. Arch. Appl. Mech. 83(10), 1493–1509 (2013)CrossRefMATH
16.
Kovtunenko, V.A.: Sensitivity of interfacial cracks to non-linear crack front perturbations. Z. Angew. Math. Mech. 82(6), 387–398 (2002)MathSciNetCrossRefMATH
17.
Kovtunenko, V.A.: Shape sensitivity of curvilinear cracks on interface to non-linear perturbations. Z. Angew. Math. Phys. 54(3), 410–423 (2003)MathSciNetCrossRefMATH
18.
Kozlov, V.A., Ma’zya, V.G., Movchan, A.B.: Asymptotic Analysis of Fields in a Multi-structure, Oxford Math. Monogr. Oxford University Press, New York (1999)
19.
Lazarev, N.P., Rudoy, E.M.: Shape sensitivity analysis of Timoshenko plate with a crack under the nonpenetration condition. Z. Angew. Math. Mech. 94(9), 730–739 (2014)MathSciNetCrossRefMATH
20.
Lazarev, N.P.: Problem of equilibrium of the Timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity. J. Appl. Mech. Tech. Phys. 54(2), 322–330 (2013)MathSciNetCrossRefMATH
21.
Lazarev, N.P.: Shape sensitivity analysis of the energy integrals for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion. Z. Angew. Math. Phys. 66(4), 2025–2040 (2015)MathSciNetCrossRefMATH
22.
23.
24.
Morozov, N.F.: Mathematical Problems of the Theory of Cracks. Nauka, Moscow (1984)MATH
25.
Nazarov, S.A., Plamenevsky, B.A.: Elliptic Problems in Domains with Piecewise Smooth Boundaries. Walter de Gruyter, Berlin (1994)CrossRefMATH
26.
Neustroeva, N.V.: A rigid inclusion in the contact problem for elastic plates. J. Appl. Ind. Math. 4(4), 526–538 (2010)MathSciNetCrossRef
27.
Panasenko, G.: Multi-scale Modelling for Structures and Composites. Springer, New York (2005)MATH
28.
Rotanova, T.A.: Unilateral contact problem for two plates with a rigid inclusion in the lower plate. J. Math. Sci. 188(4), 452–462 (2013)MathSciNetCrossRefMATH
29.
Rudoi, E.M.: Differentiation of energy functionals in the problem on a curvilinear crack with possible contact between the shores. Mech. Solids 42(6), 935–946 (2007)CrossRef
30.
Rudoy, E.M.: Asymptotic behavior of the energy functional for a three-dimensional body with a rigid inclusion and a crack. J. Appl. Mech. Tech. Phys. 52(2), 252–263 (2011)MathSciNetCrossRef
31.
32.
33.
Shcherbakov, V.V.: Optimal control of rigidity parameter of thin inclusions in elastic bodies with curvilinear cracks. J. Math. Sci. 203(4), 591–604 (2014)MathSciNetCrossRef
34.
Shcherbakov, V.V.: On an optimal control problem for the shape of thin inclusions in elastic bodies. J. Appl. Ind. Math. 7(3), 435–443 (2013)MathSciNetCrossRefMATH
35.
Shcherbakov, V.V.: Existence of an optimal shape of the thin rigid inclusions in the Kirchhoff–Love plate. J. Appl. Ind. Math. 8(1), 97–105 (2014)MathSciNetCrossRef
36.
37.
Yao, J.: Instability of a composite reinforced with coated inclusions due to interface debonding. Arch. Appl. Mech. 85(4), 415–432 (2015)CrossRef
Metadata
Title
Junction problem for rigid and semirigid inclusions in elastic bodies
Authors
Alexander Khludnev
Tatiana Popova
Publication date
02-04-2016
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 9/2016
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-016-1135-7

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