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• The elastic instability phenomenon in hyperelastic layered materials with the phases exhibiting stiffening behavior is studied • A closed-form expression for the critical stretch of macroscopic instability is derived • An analytical prediction based on Bloch-Floquet analysis for the microscopic instability is exhibited • The critical parameters and transition of instability modes are found to be highly tunable with phase stiffening This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain rates, and experiences microstructural buckling upon exceeding the critical strain level. We characterize the dependence of the critical strain and wavelength on the applied strain rate through our numerical analysis. In the simulations, we employ the single and multiple-branch visco-hyperelastic models. We find that the critical strain and wavelength – characterized by the single-branch model – show a non-monotonic dependence on the strain rate, reaching a maximum at a specific strain rate. Remarkably, different buckling patterns (with different critical wavelengths) can be activated by changing strain rates. The space of admissible buckling modes widens in composites with higher instantaneous shear modulus. In the composites characterized by the multiple-branch model, the critical strain function exhibit multiple local maxima following a superposition of the single-branch responses. Typically, the branch with a larger relaxation time has a more significant effect on the critical strain. Moreover, the local maximum (of the critical strain function) is amplified by increasing the strain–energy factor of the corresponding branch term. Finally, we perform the experiments on the 3D-printed particulate soft composite characterized by a broad spectrum of relaxation times. The comparison of the experimental and simulation results demonstrates the ability of the numerical model to predict the critical buckling characteristics. [ABSTRACT FROM AUTHOR]