Effective balance equations for elastic composites subject to inhomogeneous potentials

Penta, R. , Ramírez-Torres, A. , Merodio, J. and Rodríguez-Ramos, R. (2018) Effective balance equations for elastic composites subject to inhomogeneous potentials. Continuum Mechanics and Thermodynamics, 30(1), pp. 145-163. (doi: 10.1007/s00161-017-0590-x)

Abstract

We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and nonstandard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ramirez Torres, Dr Ariel and Penta, Dr Raimondo
• Authors: Penta, R., Ramírez-Torres, A., Merodio, J., and Rodríguez-Ramos, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Continuum Mechanics and Thermodynamics
• Publisher: Springer
• ISSN: 0935-1175
• ISSN (Online): 1432-0959
• Published Online: 21 August 2017
• Copyright Holders: Copyright © 2017 Springer-Verlag GmbH Germany
• First Published: First published in Continuum Mechanics and Thermodynamics 30(1): 145-163
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.