Ramírez-Torres, A. , Di Stefano, S., Grillo, A., Rodríguez-Ramos, R., Merodio, J. and Penta, R. (2018) An asymptotic homogenization approach to the microstructural evolution of heterogeneous media. International Journal of Non-Linear Mechanics, 106, pp. 245-257. (doi: 10.1016/j.ijnonlinmec.2018.06.012)
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Abstract
In the present work, we apply the asymptotic homogenization technique to the equations describing the dynamics of a heterogeneous material with evolving micro-structure, thereby obtaining a set of upscaled, effective equations. We consider the case in which the heterogeneous body comprises two hyperelastic materials and we assume that the evolution of their micro-structure occurs through the development of plastic-like distortions, the latter ones being accounted for by means of the Bilby–Kröner–Lee (BKL) decomposition. The asymptotic homogenization approach is applied simultaneously to the linear momentum balance law of the body and to the evolution law for the plastic-like distortions. Such evolution law models a stress-driven production of inelastic distortions, and stems from phenomenological observations done on cellular aggregates. The whole study is also framed within the limit of small elastic distortions, and provides a robust framework that can be readily generalized to growth and remodeling of nonlinear composites. Finally, we complete our theoretical model by performing numerical simulations.
| Item Type: | Articles |
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| Additional Information: | AR has been funded by the Istituto Nazionale di Alta Matematica “Francesco Saveri” (National Institute for High Mathematics “Francesco Saveri”) through a research project MATHTECH-CNR-INdAM and is currently employed in the research project “Mathematical multi-scale modeling of biological tissues” (N. 64) financed by the Politecnico di Torino (Scientific Advisor: Alfio Grillo). RR gratefully acknowledges the Proyecto Nacional de Ciencias Básicas No. 7515, Cuba 2015–2018. JM and RP acknowledge support from the Ministry of Economy in Spain (project reference DPI2014-58885-R). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Penta, Dr Raimondo and Ramirez Torres, Dr Ariel |
| Authors: | Ramírez-Torres, A., Di Stefano, S., Grillo, A., Rodríguez-Ramos, R., Merodio, J., and Penta, R. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | International Journal of Non-Linear Mechanics |
| Publisher: | Elsevier |
| ISSN: | 0020-7462 |
| ISSN (Online): | 1878-5638 |
| Published Online: | 02 July 2018 |
| Copyright Holders: | Copyright © 2018 Elsevier Ltd. |
| First Published: | First published in International Journal of Non-Linear Mechanics 106:245-257 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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