Effective balance equations for electrostrictive composites

Di Stefano, S., Miller, L., Grillo, A. and Penta, R. (2020) Effective balance equations for electrostrictive composites. Zeitschrift für Angewandte Mathematik und Physik, 71, 166. (doi: 10.1007/s00033-020-01365-x)

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Abstract

This work concerns the study of the effective balance equations governing linear elastic electrostrictive composites, where mechanical strains can be observed due to the application of a given electric field in the so-called small strain and moderate electric field regime. The formulation is developed in the framework of the active elastic composites. The latter are defined as composite materials constitutively described by an additive decomposition of the stress tensor into a purely linear elastic contribution and another component, which is assumed to be given and quadratic in the applied electric field when further specialised to electrostrictive composites. We derive the new mathematical model by describing the effective mechanical behaviour of the whole material by means of the asymptotic (periodic) homogenisation technique. We assume that there exists a sharp separation between the micro-scale, where the distance among different sub-phases (i.e. inclusions and/or fibres and/or strata) is resolved, and the macro-scale, which is related to the average size of the whole system at hand. This way, we formally decompose spatial variations by assuming that every physical field and material property are depending on both the macro-scale and the micro-scale. The effective governing equations encode the role of the micro-structure, and the effective contributions to the global stress tensor are to be computed by solving appropriate linear-elastic-type cell problems on the periodic cell. We also provide analytic formulae for the electrostrictive tensor when the applied electric field is either microscopically uniform or given by a suitable multiplicative decomposition between purely microscopically and macroscopically varying components. The obtained results are consistently compared with previous works in the field, and can pave the way towards improvement of smart active materials currently utilised for engineering (possibly bio-inspired) purposes.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Penta, Dr Raimondo and Miller, Miss Laura
Authors: Di Stefano, S., Miller, L., Grillo, A., and Penta, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Zeitschrift für Angewandte Mathematik und Physik
Publisher:Springer
ISSN:0044-2275
ISSN (Online):1420-9039
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Zeitschrift für Angewandte Mathematik und Physik 71:166
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
172865EPSRC DTP 16/17 and 17/18Tania GalabovaEngineering and Physical Sciences Research Council (EPSRC)EP/N509668/1Research and Innovation Services
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics