Recent developments in numerical homogenization

  • Daniela P. Boso
  • Marek Lefik
  • Bernhard A. Schrefler


This paper deals with homogenization of non linear fibre-reinforced composites in the coupled thermomechanical field. For this kind of structures, i.e. inclusions randomly dispersed in a matrix, the self consistent methods are particularly suitable to describe the problem. Usually, in the framework of the self consistent scheme the homogenized material behaviour is obtained with a symbolic approach. For the non linear case, that method may become tedious. This paper presents a different, fully numerical procedure. The effective properties are determined by minimizing a functional expressing the difference (in some chosen norm) between the solution of the heterogeneous problem and the equivalent homogenous one. The heterogeneous problem is solved with the Finite Element method, while the second one has its analytical solution. The two solutions are written as a function of the (unknown) effective parameters, so that the final global solution is found by iterating between the two single solutions. Further, it is shown that the considered homogenization scheme can be seen as an inverse problem and Artificial Neural Networks are used to solve it.


Generalized Self-Consistent-Like method, non-linear homogenization, Artificial Neural Networks, inverse problems, thermo-mechanical analysis, multiscale modelling, unsmearing,


Jan 25, 2017
How to Cite
BOSO, Daniela P.; LEFIK, Marek; SCHREFLER, Bernhard A.. Recent developments in numerical homogenization. Computer Assisted Methods in Engineering and Science, [S.l.], v. 16, n. 3–4, p. 161-183, jan. 2017. ISSN 2299-3649. Available at: <>. Date accessed: 26 jan. 2022.