Abstract
The mechanical behaviour of periodic three-dimensional non-homogeneous solids can be functionally designed by optimizing their cellular composite microstructure. The present contribution aims at establishing a theoretical and methodological framework to determine the dispersion properties of periodic Cauchy materials, characterized by a generic microstructured repetitive cell. First, two conceptually alternative strategies are formulated to state the continuous complex-valued eigenproblem, governing the free undamped propagation of Bloch waves, in the finite domain of the periodic cell. Second, a consistent mathematical procedure to convert the governing field equations into an equivalent discrete eigenproblem, suited to be computationally attacked through the finite element method, is outlined.
I would like to take this opportunity to wish from the deep of my heart the best to professor Peter Wriggers on occasion of his 70th birthday and every happiness on this special day. Peter has always been a world-renowned, brilliant researcher, an excellent example for our computational mechanics community; however, in the years I have appreciated more and more his friendship, his willingness and easiness in sitting down, coding, exploring new ideas and concepts, as well as enjoying life, traveling, sailing, having a beer and laugh all together. With this completeness I think Peter is a wonderful friend and example for me and for all of us. So, dear Peter, best wishes for many other opportunities to spend time together and for you to enjoy good time with Claudia and your family. Ferdinando
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Acknowledgements
The authors gratefully acknowledge the financial support from National Group of Mathematical Physics (GNFM-INdAM), from Compagnia San Paolo, project MINIERA no. I34I20000380007 and from University of Trento, project UNMASKED 2020.
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Auricchio, F., Bacigalupo, A., Lepidi, M., Morganti, S. (2022). Free Bloch Wave Propagation in Periodic Cauchy Materials: Analytical and Computational Strategies. In: Aldakheel, F., Hudobivnik, B., Soleimani, M., Wessels, H., Weißenfels, C., Marino, M. (eds) Current Trends and Open Problems in Computational Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-87312-7_5
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DOI: https://doi.org/10.1007/978-3-030-87312-7_5
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