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1

Influence of imperfect interface of anisotropic thermomagnetoelectroelastic bimaterial solids on interaction of thin deformable inclusions

Sulym Heorhiy, Vasylyshyn Andrii, Pasternak Iaroslav

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 3

242--249

EN

This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.

2

Thin inclusion in elastic body: identiﬁcation of damage parameter

Khludnev Alexander

Control and Cybernetics

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2019

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Vol. 48, No. 1

13--29

EN

In the paper, we consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion crossing an external boundary. The elastic body has a defect which is characterized by a positive damage parameter. The presence of a defect means that the problem is formulated in a non-smooth domain. Non-linear boundary conditions at the defect faces are imposed to prevent the mutual penetration between the faces. Both variational and diﬀerential problem formulations are proposed, and existence of solutions is established. We study an asymptotics of solutions with respect to the damage parameter as well as with respect to a rigidity parameter of the inclusion. Identiﬁcation problems for ﬁnding the damage parameter are investigated. To this end, existence of solutions of optimal control problems is proven.

3

Mixed boundary value problem for an anisotropic thermoelastic half-space containing thin inhomogeneities

Sulym Heorhiy, Pasternak Iaroslav, Smal Mariia, Vasylyshyn Andrii

Acta Mechanica et Automatica

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2019

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Vol. 13, no. 4

238--244

EN

The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

4

Antiplane deformation of a bimaterial with thin interfacial nonlinear elastic inclusion

Sulym H., Piskozub Y., Polanski J.

Acta Mechanica et Automatica

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2018

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Vol. 12, no. 3

190--195

EN

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.

5

Boundary element analysis of anisotropic thermomagnetoelectroelastic solids with 3D shell-like inclusions

Pasternak I., Sulym H.

Acta Mechanica et Automatica

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2017

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Vol. 11, no. 4

308--312

EN

The paper presents novel boundary element technique for analysis of anisotropic thermomagnetoelectroelastic solids containing cracks and thin shell-like soft inclusions. Dual boundary integral equations of heat conduction and thermomagnetoelectroelasticity are derived, which do not contain volume integrals in the absence of distributed body heat and extended body forces. Models of 3D soft thermomagnetoelectroelastic thin inclusions are adopted. The issues on the boundary element solution of obtained equations are discussed. The efficient techniques for numerical evaluation of kernels and singular and hypersingular integrals are discussed. Nonlinear polynomial mappings are adopted for smoothing the integrand at the inclusion’s front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the inclusion’s front. Numerical example is presented.

6

Boundary integral equations for an anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities

Sulym H., Pasternak I., Tomashivskyy M.

Acta Mechanica et Automatica

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2016

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Vol. 10, no. 1

66--74

EN

This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant interfacial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

7

Modelling of stress state of elastic medium containing perfectly and imperfectly bonded thin inclusions and overlays

Sulym H., Pasternak I.

Mechanics and Control

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2011

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Vol. 30, no. 3

176-181

EN

This study considers modelling of two-dimensional stress state of solids containing thin elastic inclusions. In modeling the coupling principle for continua of different dimension is utilized. Basing on the model of inclusion under the perfect contact three other models of imperfect contact are developed. The simplest one is a model of thin inclusion, which is completely delaminated at certain segments. Two other models take into account a smooth contact between inclusion and a solid, and also a contact with friction. The developed models are easy to introduce into the used boundary element approach. The model of inclusion, completely debonded at one face, is also used in modeling of solids with thin elastic overlays or stringers.

PL

W pracy przy użyciu zasady sprzężenia kontinuów różnowymiarowych rozważane są sposoby matematycznego modelowania zagadnienia płaskiego dla ośrodków sprężystych zawierających cienkie inkluzje. Zasadniczy model matematyczny dla cienkiej inkluzji połączonej w doskonały sposób z tarczą uwzględnia możliwość sprężystego odkształcenia w kierunkach: poprzecznym i wzdłużnym względem osi inkluzji oraz efekty jej zginania. Zostały sprecyzowane trzy szczególne modele niedoskonałego kontaktu inkluzji. Najprostszym z nich jest model cienkiego wtrącenia, które wzdłuż pewnych segmentów jest odseparowane od macierzy. Dwa inne modele uwzględniają gładki kontakt inkluzji z ciałem oraz kontakt z tarciem. Opracowane modele łatwo łączy się ze schematem metody elementów brzegowych. Model cienkiej inkluzji zupełnie odseparowanej wzdłuż jednej strony nadaje się również do badania ośrodków z cienkim wzmocnieniem powierzchniowym (nakładką).

8

Plastic interfacial slip of periodic systems of rigid thin inclusions undergoing longitudinal shear

Kryven V. A., Sulym G. T., Yavorska M. I.

Journal of Theoretical and Applied Mechanics

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2006

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Vol. 44 nr 4

837-848

EN

Plastic interfacial slip at the longitudinal shear of double periodic systems of thin rigid inclusions in elasto-plastic solids is investigated. Plastic deformations are considered to be localized in the thin layers on the inclusion-matrix boundary at the inclusion tips. The length of plastic layers and the rupture displacement value at the inclusions tips caused by plastic interfacial slip are determined. Particular cases of uniperiodical parallel or collinear inclusion systems are analyzed in detail.

PL

W ramach antypłaskiego stanu odkształcenia przeanalizowano plastyczny poślizg na granice kontaktu dwuokresowego układu cienkich sztywnych inkluzji z ośrodkiem sprężysto-plastycznym podczas ścinania. Założono, że odkształcenia plastyczne znajdują się w cienkich warstwach na granicy inkluzji w otoczeniu ich końców. Wyznaczono długość warstw plastycznych oraz wartość skoku przemieszczenia spowodowanego plastycznym prześlizganiem. Dokładnie rozpatrzono również szczególne przypadki jednookresowych zagadnień dla inkluzji w jednej i w równoległych płaszczyznach.