TY - JOUR

T1 - Equilibrium problem for elastic body with delaminated T-shape inclusion

AU - Khludnev, Alexander

AU - Popova, Tatyana

PY - 2020/10/1

Y1 - 2020/10/1

N2 - We analyze an equilibrium problem for 2D elastic body with a T-shape thin inclusion in presence of damage. A part of the inclusion is elastic, and the other part is a rigid one. A delamination of the inclusion from the elastic body is assumed, thus forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The damage is characterized by a positive parameter. The paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero. A passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed. Junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion. An existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known.

AB - We analyze an equilibrium problem for 2D elastic body with a T-shape thin inclusion in presence of damage. A part of the inclusion is elastic, and the other part is a rigid one. A delamination of the inclusion from the elastic body is assumed, thus forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The damage is characterized by a positive parameter. The paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero. A passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed. Junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion. An existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known.

KW - Crack

KW - Damage parameter

KW - Elastic body

KW - Inverse problem

KW - Junction condition

KW - Thin inclusion

KW - SEMIRIGID INCLUSIONS

KW - MECHANICAL INTERPLAY

KW - TIMOSHENKO

KW - EULER-BERNOULLI

KW - THIN MULTIDOMAIN

KW - RIGID INCLUSIONS

KW - JUNCTION PROBLEM

KW - SENSITIVITY-ANALYSIS

KW - ENERGY INTEGRALS

KW - BOUNDARY

UR - http://www.scopus.com/inward/record.url?scp=85082129077&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2020.112870

DO - 10.1016/j.cam.2020.112870

M3 - Article

AN - SCOPUS:85082129077

VL - 376

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 112870

ER -