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

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 

作者机构：Facultad de Matematica y ComputacionDepartamento de MatematicaUniversidad de La HabanaSan Lazaro y LHabana 4La HabanaCP 10400Cuba Departamento de Matematicas y MecanicaUniversidad Nacional Autonoma de MexicoInstituto de Investigaciones en Matematicas Aplicadas y en Sistemas01000 CDMXAP 20-126M′exico Departamento de Engenharia MecanicaUniversidade Federal do Rio de JaneiroPolitecnica/COPPECaixa Postal 68503Rio de JaneiroRJCEP 21941-972Brasil Departamento de Matematica e EstatisticaUniversidade Federal de PelotasCaixa Postal 354PelotasRio Grande do SulCEP 96010-900Brasil 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2018年第39卷第8期

页      面：1119-1146页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070102[理学-计算数学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the Desenvolvimento e Aplicaoes de Mtodos Matemticos de Homogeneizaao(CAPES)(No.88881.030424/2013-01) the Homogeneizao Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases(CNPq)(Nos.450892/2016-6and 303208/2014-7) the Caracterizacin de Propiedades Efectivas de Tejidos Biolgicos Sanos y Cancerosos(CONACYT)(No.2016–01–3212) 

主　　题：reiterated homogenization method(RHM) imperfect contact variational formulation effective coefficient gain 

摘      要：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.