An isogeometric approach for analysis of phononic crystals and elastic metamaterials with complex geometries
An isogeometric analysis (IGA) framework is presented to construct and solve dispersion relations for generating the band structure of periodic materials with complicated geometries representing phononic crystals and elastic metamaterials. As the dispersive properties depend on the microstructural geometry, an accurate representation of microstructural geometrical features is paramount. To this end, the ability of isogeometric analysis to exactly model complex curved geometries is exploited, and wave propagation in infinitely periodic solids is combined with isogeometric analysis. The benefits of IGA are demonstrated by comparing the results to those obtained using standard finite element analysis (FEA). It is shown that the IGA solutions can reach the same level of accuracy as FEA while using significantly fewer degrees of freedom. IGA is applied to phononic crystals and elastic metamaterials and the band structure for a variety of unit cells with complex microstructural geometries is investigated to illustrate the desirable dispersive effects in these metamaterials.
KeywordsIsogeometric analysis Bloch waves Phononic crystals Elastic metamaterials Bandgaps and local resonance
The presented work is supported in part by the US National Science Foundation through Grant CMMI-1055314. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.
- 2.Pierre AD (2013) Acoustic metamaterials and phononic crystals. Springer, BerlinGoogle Scholar
- 3.Hussein MI, Leamy MJ, Ruzzene M (2014) Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Appl Mech Rev 66:040802-040802-38Google Scholar
- 6.Kushwaha MS, Halevi P, Dobrzynski L, Djafarirouhani B (1993) Acoustic band-structure of periodic elastic composites. Phys Rev Lett 71:2022–2025. https://doi.org/10.1103/PhysRevLett.71.2022
- 27.Zhang G, Khandelwal K (2016) Modeling of nonlocal damage-plasticity in beams using isogeometric analysis. Comput & Struct 165:76–95. https://doi.org/10.1016/j.compstruc.2015.12.006
- 32.Hughes TJR, Reali A, Sangalli G (2008) Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput Methods Appl Mech Eng 197:4104–4124. https://doi.org/10.1016/j.cma.2008.04.006 MathSciNetCrossRefzbMATHGoogle Scholar
- 36.Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis, New YorkGoogle Scholar
- 37.Piegl L, Tiller W (1997) The NURBS book. 1997. Monographs in Visual CommunicationGoogle Scholar
- 38.Rogers DF (2000) An introduction to NURBS: with historical perspective. Elsevier, AmsterdamGoogle Scholar