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Reiterated homogenization of a laminate with imperfect contact:gain-enhancement of effective properties

Applied Mathematics and Mechanics(English Edition) 2018年第8期39卷 1119-1146页

作者： F.E.ALVAREZ-BORGES J.BRAVO-CASTILLERO M.E.CRUZ R.GUINOVART-DIAZ L.D.PEREZ-FERNANDEZ R.RODRIGUEZ-RAMOS F.J.SABINA Facultad de Matematica y Computacion Departamento de MatematicaUniversidad de La HabanaSan Lazaro y LHabana 4La HabanaCP 10400Cuba Departamento de Matematicas y Mecanica Universidad Nacional Autonoma de MexicoInstituto de Investigaciones en Matematicas Aplicadas y en Sistemas01000 CDMXAP 20-126M′exico Departamento de Engenharia Mecanica Universidade Federal do Rio de JaneiroPolitecnica/COPPECaixa Postal 68503Rio de JaneiroRJCEP 21941-972Brasil Departamento de Matematica e Estatistica Universidade Federal de PelotasCaixa Postal 354PelotasRio Grande do SulCEP 96010-900Brasil

A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

关键词： reiterated homogenization method(RHM) imperfect contact variational formulation effective coefficient gain

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A FINITE DIFFERENCE METHOD FOR TWO DIMENSIONAL ELLIPTIC INTERFACE PROBLEMS WITH imperfect contact

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Journal of Computational Mathematics 2024年第5期42卷 1328-1355页

作者： Fujun Cao Dongfang Yuan Dongxu Jia Guangwei Yuan School of Science Inner Mongolia University of Science and TechnologyBaotou 014010Inner MongoliaChina School of Science Tianjin University of TechnologyTianjin 300384China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009Beijing 100088China

In this paper two dimensional elliptic interface problem with imperfect contact is considered,which is featured by the implicit jump condition imposed on the imperfect contact interface,and the jumping quantity of the unknown is related to the flux across the interface.A finite difference method is constructed for the 2D elliptic interface problems with straight and curve interface ***,the stability and convergence analysis are given for the constructed ***,in particular case,it is proved to be *** examples for elliptic interface problems with straight and curve interface shapes are tested to verify the performance of the *** numerical results demonstrate that it obtains approximately second-order accuracy for elliptic interface equations with implicit jump condition.

关键词： Finite difference method Elliptic interface problem imperfect contact

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