Macro- and micro-instabilities in incompressible bioinspired composite materials with nacre-like microstructure

In this work, we study the macroscopic and microscopic instabilities in 2D incompressible nacre-like composite materials induced by uniaxial loadings. The interchange between macro- and micro-instabilities in bioinspired composite materials has been investigated by examining different combinations of platelets volume fraction, aspect ratio, and shear modulus contrast between the stiff (platelets) and soft (matrix) phases. It has been highlighted that the critical instability mode shapes, together with their critical load factors and wavelengths, are highly influenced by the microscopic geometrical arrangement and the material composition. For a wide range of geometrical and material parameters, the instabilities are found to be global with an in-phase mode shape. It has been shown that the out-of-phase instability mode shapes occur at a significantly higher magnitude of the homogenized energy compared to the in-phase ones. The results indicate that, adopting a small unit cell assembly, the microscopic stability analysis provides in most of cases strong underestimates of the critical stretch ratios, and that an accurate and efficient instability prediction can be instead obtained based on the loss of strong ellipticity condition of the homogenized incremental moduli tensor, except for few cases in which local modes occur.