Effective properties of periodic media in elastodynamic problems

Rolando Yera1, Carlos G. Méndez1, Pablo J. Sánchez1,2, Alfredo E. Huespe1,3

1CIMEC-UNL-CONICET, Predio Conicet Dr Alberto Cassano, CP 3000 Santa Fe, Argentina.

2Gimni UTN-FRSF, Lavaise 610, CP 3000 Santa Fe, Argentina.

3FIQ-UNL, Santiago del Estero 2800, CP 3000 Santa Fe, Argentina.




This paper describes a homogenization model for evaluating the effective elastodynamic properties of acoustic metamaterials in problems involving wave propagation. The methodology is based on determining the constitutive equations in terms of averaged quantities observed at the macroscale. In this sense, the approach very closely follows the pioneering ideas introduced by Willis, and afterwards, followed by several authors in the last ten years. The distinctive characteristic of our approach is that we write the microscale equation in the spatial domain. The model is validated with previous results published in the literature, and our results replicate them almost exactly. The resulting homogenization model could be used as an additional tool for the topology design of acoustic metamaterials.

Cite as:

Yera, R., Méndez, C. G., Sánchez, P. J., & Huespe, A. E. (2021). Effective properties of periodic media in elastodynamic problems. Computer Methods in Materials Science, 21(3), pages. https://doi.org/10.7494/cmms.2021.3.0753

Article (PDF):

Key words:

Effective properties of acoustic metamaterials, Qave propagation in periodic media, Bloch waves, Phononic crystals


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