On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion

2019 ◽  
Vol 237 (4) ◽  
pp. 530-545 ◽  
Author(s):  
A. I. Furtsev
Keyword(s):  
Thin Inclusion ◽  
Thin Obstacle

Thin inclusion approach for modelling of heterogeneous conducting materials

2006 ◽  
Vol 155 (2) ◽  
pp. 239-245 ◽  
Author(s):  
Nikolay Lavrov ◽  
Alevtina Smirnova ◽  
Haluk Gorgun ◽  
Nigel Sammes
Keyword(s):  
Thin Inclusion ◽  
Conducting Materials

scholarly journals Regularity for the fully nonlinear parabolic thin obstacle problem

2021 ◽  
pp. 2150011
Author(s):  
Georgiana Chatzigeorgiou
Keyword(s):  
Parabolic Equation ◽  
Viscosity Solution ◽  
Nonlinear Parabolic Equation ◽  
Obstacle Problem ◽  
Elliptic Case ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Nonlinear Parabolic ◽  
Parabolic Case ◽  
Thin Obstacle

We prove [Formula: see text] regularity (in the parabolic sense) for the viscosity solution of a boundary obstacle problem with a fully nonlinear parabolic equation in the interior. Following the method which was first introduced for the harmonic case by L. Caffarelli in 1979, we extend the results of I. Athanasopoulos (1982) who studied the linear parabolic case and the results of E. Milakis and L. Silvestre (2008) who treated the fully nonlinear elliptic case.

scholarly journals The problem of the partial delamination of the elastic interface thin inclusion in the conditions of longitudinal shear of the bimaterial

2021 ◽  
pp. 60-66
Author(s):  
Yosyf Piskozub
Keyword(s):  
Longitudinal Direction ◽  
Longitudinal Shear ◽  
Analytical Determination ◽  
Thin Inclusion ◽  
The Matrix ◽  
Elastic Interface ◽  
Modular Method ◽  
Inclusion Matrix ◽  
Mechanical Nature

The problem of longitudinal displacement of a bi -material with a thin inclusion of arbitrary physical and mechanical nature at the interface of the matrix materials is considered. The bulk is loaded by normal compression and various force factors in the longitudinal direction. The possibility of partial delamination of a part of the boundary between the inclusion and the matrix, where dry friction slip occurs, is assumed. A complete system of equations for the formulated problem is constructed. It is proposed to construct the solution using the structural modular method of jump functions, a description of which is given. A condition for the appearance of a slip zone on the inclusion-matrix boundary is founded. A convergent iterative algorithm for numerically analytical determination of the size of this zone is developed.

scholarly journals Antiplane Deformation of a Bimaterial with Thin Interfacial Nonlinear Elastic Inclusion

2018 ◽  
Vol 12 (3) ◽  
pp. 190-195
Author(s):  
Heorhiy Sulym ◽  
Yosyf Piskozub ◽  
Julian Polanski
Keyword(s):  
Elastic Inclusion ◽  
Singular Integral Equations ◽  
Longitudinal Shear ◽  
Variable Coefficients ◽  
Thin Inclusion ◽  
Shear Stresses ◽  
Antiplane Deformation ◽  
Characteristic Parameters ◽  
Analytical Functions ◽  
Nonlinear Elastic

Abstract The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.

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