Instability-induced patterns and their post-buckling development in soft particulate composites

Abstract

In this paper, we investigated elastic instabilities in soft particulate composites under finite strains. Through our numerical analysis, we find distinct instability modes developing in the composites upon the critical deformation level. In particular, fully predetermined by its initial geometry, the microstructures transform into (i) strictly doubled periodicity, (ii) seemingly non-periodic state, or (iii) longwave pattern. The latter may give rise to highly ordered domain formations. We analyze the various mechanisms leading to the development of the different instability modes and specifically focus on the seemingly non-periodic one. We illustrate the distinct features of their corresponding eigenmodes obtained from the Bloch-Floquet analysis. We further employ the quasi-convexification analysis and examine the energy landscapes of the soft composites developing the different instability modes. Finally, we examine the development of the predicted instability modes in the post-buckling regime. We find that, depending on the characteristic critical wavenumber, the post-buckling patterns can significantly diverge from those predicted by the Bloch-Floquet analysis. In the post-buckling regime, the instabilities may develop into various scenarios: from a combination of different repeating inclusion sets to disordered, seemingly chaotic patterns.