TY - JOUR

T1 - Asymptotics of anisotropic weakly curved inclusions in an elastic body

AU - Khludnev, A. M.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Under study are the boundary value problems describing the equilibrium of twodimensional elastic bodies with thin anisotropic weakly curved inclusions in presence of separations. The latter implies the existence of a crack between the inclusion and the matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces that exclude mutual penetration of the crack faces. This leads to the formulation of the problems with unknown contact area. The passage to limits with respect to the rigidity parameters of the thin inclusions is inspected. In particular, we construct the models as the rigidity parameters go to infinity and analyze their properties.

AB - Under study are the boundary value problems describing the equilibrium of twodimensional elastic bodies with thin anisotropic weakly curved inclusions in presence of separations. The latter implies the existence of a crack between the inclusion and the matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces that exclude mutual penetration of the crack faces. This leads to the formulation of the problems with unknown contact area. The passage to limits with respect to the rigidity parameters of the thin inclusions is inspected. In particular, we construct the models as the rigidity parameters go to infinity and analyze their properties.

KW - crack

KW - elastic body

KW - limit model

KW - nonlinear boundary condition

KW - thin inclusion

UR - http://www.scopus.com/inward/record.url?scp=85013917401&partnerID=8YFLogxK

U2 - 10.1134/S1990478917010100

DO - 10.1134/S1990478917010100

M3 - Article

AN - SCOPUS:85013917401

VL - 11

SP - 88

EP - 98

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -