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 

机构地区：[1]Facultad de Matematica y Computacion,Departamento de Matematica,Universidad de La Habana,San Lazaro y L,Habana 4,La Habana,CP 10400,Cuba [2]Departamento de Matematicas y Mecanica,Universidad Nacional Autonoma de Mexico,Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas,01000 CDMX,AP 20-126,M′exico [3]Departamento de Engenharia Mecanica,Universidade Federal do Rio de Janeiro,Politecnica/COPPE,Caixa Postal 68503,Rio de Janeiro,RJ,CEP 21941-972,Brasil [4]Departamento de Matematica e Estatistica,Universidade Federal de Pelotas,Caixa Postal 354,Pelotas,Rio Grande do Sul,CEP 96010-900,Brasil

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第8期1119-1146,共28页应用数学和力学（英文版）

基　　金：Project supported by the Desenvolvimento e Aplicaoes de Mtodos Matemticos de Homogeneizaao(CAPES)(No.88881.030424/2013-01);the Homogeneizao Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases(CNPq)(Nos.450892/2016-6and 303208/2014-7);the Caracterizacin de Propiedades Efectivas de Tejidos Biolgicos Sanos y Cancerosos(CONACYT)(No.2016–01–3212)

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.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 

分 类 号：O241.82[理学—计算数学]