Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures

Gabriele Barbagallo (1) , Domenico Tallarico (1) , Marco Valerio d'Agostino (2) , Alexios Aivaliotis (1) , Patrizio Neff (3) , Angela Madeo (2)

1 GEOMAS - Géomécanique, Matériaux et Structures
2 M2S - Mécanique des Matériaux et des Structures
3 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]

In this paper, we show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced by a corresponding generalised continuum of the relaxed micromorphic type. Specifically, we compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties: (i) the relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic continuum. We show that, while the Cauchy theory is able to describe the overall behaviour of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency band-gap and at frequencies intersecting the optical branches. In addition, we observe a computational time reduction associated with the use of the relaxed micromorphic continuum, compared to the sensible computational time needed to perform a transient computation in a micro-structured domain.

Mots clés: relaxed micromorphic model; elastic metamaterials; anisotropy; transient dynamic response

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]

Gabriele Barbagallo, Domenico Tallarico, Marco Valerio d'Agostino, Alexios Aivaliotis, Patrizio Neff, et al.. Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures. International Journal of Solids and Structures, 2019, 162, pp.148-163. ⟨10.1016/j.ijsolstr.2018.11.033⟩. ⟨hal-01874167⟩