Microscopic and long-wave instabilities in 3D fiber composites with non-Gaussian hyperelastic phases

Abstract

We investigate the microscopic and long-wave (or macroscopic) instabilities in fiber composites (FCs) with hyperelastic phases. To study the influence of the phase stiffening behavior, we employ the phase constitutive models that are developed based on the non-Gaussian statistics of polymeric molecular chains. These non-Gaussian models accurately predict the non-linear behavior of soft materials. Moreover, they can capture the essential soft material stiffening behavior arising due to the finite extensibility of the polymer chains. In turn, the non-linear behavior of the composite phases significantly influences the elastic instabilities and the buckling patterns. Here, we illustrate the phenomenon by the example of FCs with Gent phases. We derive an explicit closed-form expression – in terms of the phase properties and composition – for the onset of long-wave instabilities. To predict the onset of finite length scale (or microscopic) instabilities, we employ the Bloch-Floquet analysis superimposed on finite deformations. We find that the matrix stiffening behavior stabilizes the composites, and can even result in an absolutely stable scenario. Remarkably, Gent FCs with identical phase stiffening characteristics are found to be more stable than their neo-Hookean counterparts for morphologies at which the microscopic instabilities are to develop first. The stiffening behavior of the phases dictates the interplay between the long-wave and microscopic instabilities, and defines the wavelength of the buckling patterns. Thus, the pre-designed phase properties can be used in tailoring the instability-induced patterns in soft fiber composites.