Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials

Giusteri, G. G. and Penta, R. (2022) Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials. Mechanics Research Communications, 126, 104001. (doi: 10.1016/j.mechrescom.2022.104001)

Abstract

In the design and analysis of composite materials based on periodic arrangements of sub-units it is of paramount importance to control the emergent material symmetry in relation to the elastic response. The target material symmetry plays also an important role in additive manufacturing. In numerous applications it would be useful to obtain effectively isotropic materials. While these typically emerge from a random microstructure, it is not obvious how to achieve isotropy with a periodic order. We prove that arrangements of inclusions based on a rhomboidal cell that generates the Face-Centered Cubic lattice do in fact preserve any material symmetry of the constituents, so that spherical inclusions of isotropic materials in an isotropic matrix produce effectively isotropic composites.

• Item Type: Articles
• Additional Information: RP is partially supported by EPSRC research grants EP/S030875/1 and EP/T017899/1 and conducted the research according to the inspiring scientific principles of the national Italian mathematics association INdAM (“Istituto nazionale di Alta Matematica”). GGG acknowledges the support of the National Group of Mathematical Physics (GNFM–INdAM) through the funding scheme “GNFM Young Researchers’ Projects 2020”.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo
• Authors: Giusteri, G. G., and Penta, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mechanics Research Communications
• Publisher: Elsevier
• ISSN: 0093-6413
• ISSN (Online): 1873-3972
• Published Online: 13 October 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Mechanics Research Communications 126: 104001
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
303232		EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)	Xiaoyu Luo	Engineering and Physical Sciences Research Council (EPSRC)	EP/S030875/1	M&S - Mathematics
308255		The SofTMech Statistical Emulation and Translation Hub	Dirk Husmeier	Engineering and Physical Sciences Research Council (EPSRC)	EP/T017899/1	M&S - Statistics