Entropy Correctors in Homogenization of Microheterogeneous Rigid Bodies
Abstract
Abstract. We propose an effective heat equation for an enhanced heat conduction problem that can account for thermal scale-size effects in miniaturized or nanofabricated metamaterials. The derivation of the proposed enhanced heat conduction problem is based on contributions to the global energy balance in the form of Gurtin’s microforce balance introduced in [M. E. Gurtin, Phys. D, 92 (1996), pp. 178–192] and was first proposed by S. Forest and M. Amestoy [ C. R. Méc., 336 (2008), pp. 347–353]. The resulting effective heat equation retains its classical form with temperature as the macroscopic variable; however, the effective conductivity tensor is constructed using the local entropy and the local gradient of entropy instead of the local temperature.
Fields of Study & Subjects
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Composite Material Mechanics
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- SIAM Journal on Applied Mathematics
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 86
- Issue
- 1
- Pages
- 260–278
- Publication date
- 20 January 2026
- Language
- EN