Extraction of effective material parameters with application to sandwich structures

Abstract

In this contribution we present a first‐order numerical homogenization approach which allows for extracting effective linear elastic properties of heterogeneous materials. The approach is based on the window or self consistency method where a representative microscopic subdomain is embedded into a window of effective properties. Since these properties are not known in advance they have to be determined iteratively. For the discretization of the micro structures we use the Finite Cell Method, which is a fictitious domain method of higher‐order. It is very well suited for efficiently discretizing complicated geometries stemming, for example, from tomography (CT‐scans). In the numerical examples we will investigate a bending test of a sandwich plate which is composed of a polymeric core with thin faceplates made of Aluminum. Firstly, effective properties of the core are extracted and then applied to a macroscopic numerical model. The numerical results are validated by experiments. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An efficient integration technique for the voxel‐based finite cell method

“…The following contribution introduces an extension of the finite cell method (FCM) , a high order fictitious domain method that favorably applies the simple nature of Cartesian grids and turns out to be highly suited for time‐critical voxel‐based simulations of complex structures in various fields of numerical simulation. The FCM recently has been successfully applied for geometrically nonlinear analyses of foam‐like structures with various refinement strategies , advection–diffusion problems and applications in the field of bone mechanics , as well as to the numerical homogenization of heterogeneous and foamed materials . With the extension of a pre‐computation scheme, the method is even capable to produce sufficient update rates for user‐interactive simulations in patient‐specific femur analyses .…”

“…to the numerical homogenization of heterogeneous and foamed materials [23,24]. With the extension of a pre-computation scheme, the method is even capable to produce sufficient update rates for user-interactive simulations in patient-specific femur analyses [25].…”