Sofia G. Mogilevskaya
University of Minnesota
Elasticity (economics)GeologyCluster (physics)Mathematical analysisMatrix (mathematics)Composite materialPlane (geometry)IsotropyViscoelasticityMaterials scienceFourier seriesGeometryIntegral equationSurface (mathematics)MathematicsNumerical analysisBoundary (topology)Boundary element methodClassical mechanicsSurface tensionLaplace transform
90Publications
25H-index
1,727Citations
Publications 91
Newest
Abstract null null This paper describes a boundary-element-based approach for the modeling and solution of potential problems that involve thin layers of varying curvature. On the modeling side, we consider two types of imperfect interface models that replace a perfectly bonded thin layer by a zero-thickness imperfect interface across which the field variables undergo jumps. The corresponding jump conditions are expressed via second-order surface differential operators. To quantify their accurac...
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#1Volodymyr I. Kushch (NASU: National Academy of Sciences of Ukraine)H-Index: 22
#2Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
The model of an anisotropic interface in an elastic particulate composite with initial stress is developed as the first-order approximation of a transversely isotropic interphase between an isotrop...
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#1Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
#2Anna Y. Zemlyanova (KSU: Kansas State University)H-Index: 10
Last. Volodymyr I. Kushch (NASU: National Academy of Sciences of Ukraine)H-Index: 22
view all 3 authors...
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#1Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
#2Anna Y. Zemlyanova (KSU: Kansas State University)H-Index: 10
Last. Vladislav Mantic (University of Seville)H-Index: 28
view all 3 authors...
Abstract This paper explores the possibility of using the Gurtin-Murdoch theory of material surface for modeling mechanical processes in nanomaterials reinforced by two-dimensional flexible and extensible nanoplatelets. In accordance with the theory, reinforcement is modeled by a vanishing thickness prestressed membrane embedded in an isotropic elastic matrix material. The governing equations for the model are reviewed with detailed discussion of the conditions at the membrane tips. Plane strain...
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#1Zhilin Han (Donghua University)H-Index: 3
#2Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
Last. Zhongrong Niu (Hefei University of Technology)H-Index: 12
view all 5 authors...
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Abstract We present a new methodology to derive imperfect interface models for the problems with interphase layers. The test case is potential problems, e.g., thermal conductivity, antiplane elasticity, etc. The methodology combines classical asymptotic analysis with concepts from the theory of complex-valued functions. Its major advantage over existing asymptotic approaches is the straightforward derivation of jump conditions that involve surface differential operators of arbitrary order, resul...
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#1S. Baranova (UMN: University of Minnesota)H-Index: 2
#2Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
Last. S. Jiménez-Alfaro (University of Seville)H-Index: 1
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The antiplane problem of an infinite isotropic elastic medium subjected to a far-field load and containing a zero thickness layer of arbitrary shape described by the Gurtin-Murdoch model is considered. It is shown that, under the antiplane assumptions, the governing equations of the complete Gurtin-Murdoch model are inconsistent for non-zero surface tension. For the case of vanishing surface tension, the analytical integral representations for the elastic fields and the dimensionless parameter t...
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#1Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
#2Volodymyr I. Kushch (NASU: National Academy of Sciences of Ukraine)H-Index: 22
Last. Anna Y. Zemlyanova (KSU: Kansas State University)H-Index: 10
view all 3 authors...
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#1Igor Sevostianov (NMSU: New Mexico State University)H-Index: 36
#2Sofia G. Mogilevskaya (UMN: University of Minnesota)H-Index: 25
Last. Volodymyr I. Kushch (NAS: National Academy of Sciences)H-Index: 22
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Abstract This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective ...
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#1Zhilin Han (Hefei University of Technology)H-Index: 3
#2Stein K.F. Stoter (UMN: University of Minnesota)H-Index: 5
Last. Dominik Schillinger (UMN: University of Minnesota)H-Index: 25
view all 7 authors...
Abstract Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formula...
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