Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization

Kaczmarczyk, L., Pearce, C. J. and Bicanic, N. (2008) Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization. International Journal for Numerical Methods in Engineering, 74(3), pp. 506-522. (doi: 10.1002/nme.2188)

Abstract

Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pearce, Chris J and Kaczmarczyk, Professor Lukasz and Bicanic, Professor Nenad
• Authors: Kaczmarczyk, L., Pearce, C. J., and Bicanic, N.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• ISSN: 0029-5981
• ISSN (Online): 1097-0207
• Published Online: 21 September 2007

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
39767	1	Computational homogenisation for modelling heterogeneous multi-phase materials	Christopher Pearce	Engineering & Physical Sciences Research Council (EPSRC)	EP/D500273/1	Infrastructure and Environment