Mathematical and numerical multi-scale modelling of multiphysics problems

  • Bernhard A. Schrefler Department of Structural and Transportation Engineering, University of Padova
  • Daniela P. Boso Department of Structural and Transportation Engineering, University of Padova
  • Francesco Pesavento Department of Structural and Transportation Engineering, University of Padova
  • Dariusz Gawin, Technical University of Łódź
  • Marek Lefik Technical University of Łódź

Abstract

In this paper we discuss two multi-scale procedures, both of mathematical nature as opposed to purely numerical ones. Examples are shown for the two cases. Attention is also devoted to thermodynamical aspects such as thermodynamic consistency and non-equilibrium thermodynamics. Advances for the first aspect are obtained by adopting the thermodynamically constrained averaging theory TCAT as shown in the case of a stress tensor for multi-component media. The second aspect has allowed to solve numerically, with relative ease, the case of non-isothermal leaching. The absence of proofs of thermodynamic consistency in case of asymptotic theory of homogenization with finite size of the unit cell is also pointed out.

Keywords

multiphysics problems, multi-scale models, asymptotic homogenisation,

References

Published
Jan 25, 2017
How to Cite
SCHREFLER, Bernhard A. et al. Mathematical and numerical multi-scale modelling of multiphysics problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 18, n. 1–2, p. 91–113, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/123>. Date accessed: 26 jan. 2022.
Section
Articles