Homogenization of very rough interfaces for the micropolar elasticity theory. (English) Zbl 1480.74262
Summary: In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar isotropic micropolar elastic solids is investigated. The interface is assumed to oscillate between two parallel straight lines. The main aim is to derive homogenized equations in explicit form. These equations are obtained by the homogenization method along with the matrix formalism of the theory of micropolar elasticity. Since obtained homogenized equations are totally explicit, they are a powerful tool for solving various practical problems. As an example, the reflection and transmission of a longitudinal displacement plane wave at a very rough interface of tooth-comb type is investigated. The closed-form formulas for the reflection and transmission coefficients have been derived. Based on these formulas, some numerical examples are carried out to show the dependence of the reflection and transmission coefficients on the incident angle and the geometry parameter of the interface.
MSC:
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74A35 | Polar materials |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
homogenized equations; very rough interfaces; theory of micropolar elasticity; reflection and transmission of wavesReferences:
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