Sensitivity of the macroscopic thermal conductivity tensor to topological microstructural changes
✍ Scribed by S.M. Giusti; A.A. Novotny; E.A. de Souza Neto; R.A. Feijóo
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 553 KB
- Volume
- 198
- Category
- Article
- ISSN
- 0045-7825
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✦ Synopsis
This paper proposes a closed form expression for the sensitivity of the macroscopic heat conductivity tensor for two-dimensional problems to topological microstructural changes of the underlying material. The sensitivity formula is remarkably simple. It is derived by applying the concept of topological derivative within a variational multi-scale framework for steady-state heat conduction where the macroscopic temperature gradient and heat flux are defined as volume averages of their microscopic counterparts over a representative volume element (RVE) of material. The classical Fourier law is assumed to hold at the scale referred to as microscopic (the RVE). The derived sensitivity -a symmetric second order tensor field over the RVE domain -measures how the estimated macroscopic conductivity tensor changes when a small circular inclusion is introduced at the micro-scale. The proposed formula finds potential application in the design and optimisation of heat conducting materials.