Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies

2016 ◽  
Vol 172 (1) ◽  
pp. 281-297 ◽  
Author(s):  
Alexander Khludnev
Keyword(s):  
Parameter Identification ◽  
Elastic Bodies ◽  
Rigidity Parameter

Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies

2015 ◽  
Vol 22 (4) ◽  
pp. 737-750 ◽  
Author(s):  
AM Khludnev ◽  
L Faella ◽  
TS Popova
Keyword(s):  
Rigid Inclusion ◽  
Existence Of Solutions ◽  
Elastic Inclusion ◽  
Joint Point ◽  
Elastic Bodies ◽  
Rigidity Parameter ◽  
Elastic Inclusions ◽  
Type Boundary ◽  
Crack Faces ◽  
Inequality Type

This paper concerns an equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin rigid inclusion. It is assumed that the inclusions have a joint point and we analyze a junction problem for these inclusions. The existence of solutions is proved and the different equivalent formulations of the problem are discussed. In particular, the junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, the inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. We investigate the convergence to infinity and zero of a rigidity parameter of the elastic inclusion. It is proved that in the limit, we obtain a rigid inclusion and a zero rigidity inclusion (a crack).

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