Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties
| Autor: | Manuel E. Cruz, Leslie D. Pérez-Fernández, Raúl Guinovart-Díaz, F. E. Álvarez-Borges, Reinaldo Rodríguez-Ramos, Julián Bravo-Castillero, Federico J. Sabina |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Partial differential equation
Applied Mathematics Mechanical Engineering Computation 02 engineering and technology 01 natural sciences Homogenization (chemistry) 010101 applied mathematics 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials Applied mathematics Imperfect 0101 mathematics Finite set Mathematics |
| Zdroj: | Applied Mathematics and Mechanics. 39:1119-1146 |
| ISSN: | 1573-2754 0253-4827 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|