Stability analysis at the micro- And macro-scales in periodic bioinspired composites

This work deals with the onset of instabilities at the microscopic and macroscopic scales in uniaxially compressed bioinspired composite materials with periodic microstructure. particular, the interchange between macro- and micro-instabilities in incompressible nacre-like composite materials has been investigated for different combinations of platelets aspect ratio, platelets volume fraction and shear modulus contrast between platelets and soft matrix. It has been demonstrated that the critical stretch ratios and the critical mode shapes are highly influenced by both the geometrical and materials parameters. The stability analyses highlighted that the microscopic stability analysis provides in most cases strong underestimates of the critical stretch ratios (adopting a small unit cell assembly), and that, by performing a macroscopic stability analysis based on the strong ellipticity condition of the homogenized tangent moduli tensor, a more accurate evaluation of the load associated with the primary instability can be instead obtained with less computational efforts. In addition, for a wide range of the investigated parameters, the instabilities are found to be characterized by long wavelengths with an in-phase critical mode shape.