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A general homogenization result of spectral problem for linearized elasticity in perforated domains

Mohamed Mourad Lhannafi Ait Yahia; Hamid Haddadou — 2021

Applications of Mathematics

The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the $H^{0}$ -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor $A^{0}$ , the $H^{0}$ -limit of $A^{ε}$ , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method...

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