Micromorphic model for mechanical metamaterials

Abstract: Metamaterials, with their internal composition carefully designed to feature exotic and often counterintuitive properties such as cloaking or band gaps, are the prime example of a pronounced influence of material’s microstructure on its macroscopic response. Regarding mechanical responses, metamaterials have already delivered high stiffness-to-weight ratio, negative compressibility, and tunable auxetic behaviour. These mechanical metamaterials often rely on internal instability mechanisms that trigger transformation of their periodic microstructure into predefined patterns, which introduces strong kinematic coupling among adjacent periodic metamaterial cells and leads to significant size and boundary effects. As a result, the standard first-order computational homogenization fails to provide an effective model of such metamaterials.

This talk presents a micromorphic computational homogenization scheme that has been recently developed specifically for the instability-driven mechanical metamaterials. The scheme introduces characteristic deformation patterns at microscale, whose magnitudes are communicated across adjacent macroscopic material points by scalar modulation fields, which are added to the standard continuum formulation at the macroscale and for which an additional micromorphic-like conservation law emerges at macroscale. Consequently, the presented scheme captures the above-mentioned size effect and boundary layers and accounts for with spatial mixing of multiple patterns. Combined with the bifurcation analysis, the scheme also correctly predicts local to global (i.e. micro vs. macro) buckling transitions.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).