Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study

Penta, R. and Gerisch, A. (2015) Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study. Computing and Visualization in Science, 17(4), pp. 185-201. (doi: 10.1007/s00791-015-0257-8)

Abstract

Asymptotic homogenization is employed assuming a sharp length scale separation between the periodic structure (fine scale) and the whole composite (coarse scale). A classical approach yields the linear elastic-type coarse scale model, where the effective elastic coefficients are computed solving fine scale periodic cell problems. We generalize the existing results by considering an arbitrary number of subphases and general periodic cell shapes. We focus on the stress jump conditions arising in the cell problems and explicitly compute the corresponding interface loads. The latter represent a key driving force to obtain nontrivial cell problems solutions whenever discontinuities of the coefficients between the host medium (matrix) and the subphases occur. The numerical simulations illustrate the geometrically induced anisotropy and foster the comparison between asymptotic homogenization and well established Eshelby based techniques. We show that the method can be routinely implemented in three dimensions and should be applied to hierarchical hard tissues whenever the precise shape and arrangement of the subphases cannot be ignored. Our numerical results are benchmarked exploiting the semi-analytical solution which holds for cylindrical aligned fibers.

• Item Type: Articles
• Additional Information: This work was supported by the DFG priority program SPP 1420, Project GE 1894/3 and RA 1380/7 Multiscale structure-functional modeling of musculoskeletal mineralized tissues, PIs Alf Gerisch and Kay Raum.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Penta, Dr Raimondo
• Authors: Penta, R., and Gerisch, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Computing and Visualization in Science
• Publisher: Springer
• ISSN: 1432-9360
• ISSN (Online): 1433-0369
• Published Online: 02 January 2016
• Copyright Holders: Copyright © 2015 Springer
• First Published: First published in Computing and Visualization in Science volume 17(4): 185–201
• Publisher Policy: Reproduced in accordance with the publisher copyright policy