Asymptotic comparison of the strain-gradient and micromorphic models when loading forces are widely spread

Pierre Seppecher (1) , Lukáš Jakabčin (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 LaMé - Laboratoire de Mécanique Gabriel Lamé

In this paper we reconciliate different homogenization results which describe the effective behavior of a heterogeneous material either by a strain-gradient model either by a micromorphic one. Indeed we prove that the solutions of both models are asymptotically very close when considering a loading with increasing wavelength. This result is obtained using the Fourier analysis on the tensor spaces and applies to a large class of micromorphic models. However, we provide an example of a micromorphic model that does not belong to this class and thus cannot be approximated by a strain-gradient model.

Mots clés: Continuum mechanics; Strain-gradient; Micromorphic model

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des matériaux [physics.class-ph]

Pierre Seppecher, Lukáš Jakabčin. Asymptotic comparison of the strain-gradient and micromorphic models when loading forces are widely spread. 2021. ⟨hal-03432329⟩