A filter-based computational homogenization method for handling non-separated scales problems

Julien Yvonnet (1) , Amen Tognevi (2, 1) , Guy Bonnet (1) , Mohamed Guerich (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 Département de Mécanique des Systèmes

In this work, a computational homogenization framework based on filters is proposed to handle homogenization with arbitrary scale separation. Classical homogenization is extended by using low-pass filters instead of averaging operators, leading to a naturally nonlocal elastic framework, where the kernel function is fully constructed by means of computations on a unit cell describing the microstructure. An associated Finite Element Framework is proposed to deal with heterogeneous structures containing inclusions with characteristic length of the same order than loading fluctuation wavelength.

Mots clés: Homogenization; Non-separated scales; Filter-based homogenization

Domaines: Mécanique [physics]

Julien Yvonnet, Amen Tognevi, Guy Bonnet, Mohamed Guerich. A filter-based computational homogenization method for handling non-separated scales problems. 12e Colloque national en calcul des structures, CSMA, May 2015, Giens, France. ⟨hal-01515064⟩