Effective properties of fractional viscoelastic composites via two-scale asymptotic homogenization

Ramírez-Torres, A. , Penta, R. and Grillo, A. (2023) Effective properties of fractional viscoelastic composites via two-scale asymptotic homogenization. Mathematical Methods in the Applied Sciences, 46(16), pp. 16500-16520. (doi: 10.1002/mma.9457)

Abstract

Driven by the growing interest in fractional constitutive modeling, we adopt a two-scale asymptotic homogenization approach to study the effective properties of fractional viscoelastic composites. We focus on a purely mechanical setting and derive the cell and homogenized problems corresponding to the balance of linear momentum equation in the absence of body forces and inertial terms. In doing this, we reformulate the original framework in the Laplace–Carson domain and discuss how to obtain the effective coefficients in the time domain. We particularize the general setting of our work by considering memory functions that describe special types of fractional linear viscoelastic behaviors, and after presenting the limit cases of our selections, we framed the homogenization results to account for benchmark problems with different combinations of constitutive models. Specifically, these latter involve elastic, fractional Kelvin–Voigt, fractional Zener and fractional Maxwell constituents. Our results permit us to reinforce the interpretation of the theoretical findings and to elucidate the role of the fractional constitutive models on the effective properties of the composites under investigation.

• Item Type: Articles
• Additional Information: R.P. is partially funded by EPSRC Grants EP/S030875/1 and EP/T017899/1. A.G. acknowledges the Dipartimento di Scienze Matematiche (DISMA) “G.L. Lagrange” of the Politecnico di Torino, “Dipartimento di Eccellenza 2018–2022” (“Department of Excellence 2018–2022”), Project No. E11G18000350001, and the PRIN projects “Mathematics for industry 4.0 (Math4I4)” (MUR, Italy) (2020F3NCPX) and “Mathematics of active materials: From mechanobiology to smart devices.” (MUR, Italy) (2017KL4EF3).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo and Ramirez Torres, Dr Ariel
• Authors: Ramírez-Torres, A., Penta, R., and Grillo, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematical Methods in the Applied Sciences
• Publisher: Wiley
• ISSN: 0170-4214
• ISSN (Online): 1099-1476
• Published Online: 03 July 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Mathematical Methods in the Applied Sciences 46(16): 16500-16520
• 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