Effective properties of homogenised nonlinear viscoelastic composites

Roque-Piedra, A., Rodríguez-Ramos, R., Penta, R. and Ramírez-Torres, A. (2023) Effective properties of homogenised nonlinear viscoelastic composites. Materials, 16(11), 3974. (doi: 10.3390/ma16113974) (PMID:37297108) (PMCID:PMC10254655)

Abstract

We develop a general approach for the computation of the effective properties of nonlinear viscoelastic composites. For this purpose, we employ the asymptotic homogenisation technique to decouple the equilibrium equation into a set of local problems. The theoretical framework is then specialised to the case of a strain energy density of the Saint-Venant type, with the second Piola–Kirchhoff stress tensor also featuring a memory contribution. Within this setting, we frame our mathematical model in the case of infinitesimal displacements and employ the correspondence principle which results from the use of the Laplace transform. In doing this, we obtain the classical cell problems in asymptotic homogenisation theory for linear viscoelastic composites and look for analytical solutions of the associated anti-plane cell problems for fibre-reinforced composites. Finally, we compute the effective coefficients by specifying different types of constitutive laws for the memory terms and compare our results with available data in the scientific literature.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Roque Piedra, Alejandro and Ramirez Torres, Dr Ariel and Penta, Dr Raimondo
• Authors: Roque-Piedra, A., Rodríguez-Ramos, R., Penta, R., and Ramírez-Torres, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Materials
• Publisher: MDPI
• ISSN: 1996-1944
• ISSN (Online): 1996-1944
• Published Online: 25 May 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Materials 16(11): 3974
• 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