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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]

Magnetorheological elastomers (MRE) can change their shape and properties when activated by an external magnetic field. The attractive tunable properties of this stimuli-responsive composite can be further amplified by utilizing the magneto-mechanical instability phenomenon, frequently leading to dramatic microstructure transformation. In this work, we investigate the buckling behavior of the composite system consisting of a magnetoactive layer embedded into an inactive elastomeric matrix. The composite is subjected to compressive strains in the presence of a high magnetic field. Our experimental results show that the critical buckling strain is highly tunable by the applied magnetic field. In particular, the composite buckles significantly earlier when the field is applied, leading to well-developed controllable wavy patterns in the post-buckling regime. To elucidate the mechanisms associated with the experimentally observed magneto-mechanical instability, we investigated the stability using numerical analysis. The developed computational model utilizes our new experimental data on the mechanical and magnetic properties of the composite (including magnetization and the magnetic susceptibility of the MRE composite as a function of the volume fraction of magnetic particles). The numerical model is verified against the experimental results, showing its capability to predict the onset of the magneto-mechanical instability and the post-buckling behavior of the MRE. Collectively, the study demonstrates MRE instability tuning in a laminate form factor and outlines the strategy and benefits of harnessing two field physics for controlling bifurcations. [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]

We study the buckling of soft 3D-fiber composites (FCs) with varying in-plane microstructure periodicity. Through our experiments and simulations, we find that the out-of-plane buckling orientation of fibers is determined by the constituent material properties, volume fractions, and the in-plane periodicity. The examples are given for the FCs with rectangular in-plane arrangement of fibers, i.e., the fibers are periodically situated at distance a from each other in one principal direction and distance b along the other principal direction (b > a). We provide a buckling configuration map in the design-space of geometric parameters (fiber volume fraction and in-plane periodicity aspect ratio, b / a). Pre-determined by the microstructure parameters, the fibers buckle towards (i) the first principal direction along which the fibers are closer to each other, or (ii) the second principal direction, or (iii) towards a non-principal direction. Furthermore, we find that the characteristics of the buckling plane map is governed by the shear modulus contrast between the phases of FCs. We anticipate that the distinct instability patterns reported here will enrich the design-space for building deformation-controlled tunable materials. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability of microstructured dielectric elastomer (DE) plates under electro-mechanical finite deformations. We examine the influence of the DE composite microstructure parameters on the stability of the DE composite plate. In particular, we analyze the DE plates made out of laminated ideal dielectric phases. We use an exact solution for the incompressible DE laminates to determine the effective material behavior of the composite plates. The corresponding micromechanics-based energy density functions are used in the subsequent analysis of the DE plate stability. The unstable domains for different materials compositions, volume fractions, and properties of the DE composite phases are determined. Finally, we compare these results for the onset of structural instabilities in DE plates with the material instabilities predicted based on the loss of ellipticity analysis. • The stability of microstructured DE laminated plates is examined. • The influence of material compositions are determinedStructural (plate) and microstructural (or material) instabilities in DE plates are compared. [ABSTRACT FROM AUTHOR]

• Onset of magnetoelastic instabilities is studied in magnetoactive laminates with ferromagnetic phases under magneto-mechanical loading • The analysis is performed using the small-amplitude perturbations superimposed on finite deformations in presence of magnetic field • Interplay between macroscopic and microscopic instabilities, and tunability of buckling pattern wavelengths by magnetic field is studied • Magnetoactive laminates are observed to develop antisymmetric buckling modes, in addition to classical symmetric mode • An explicit expression is derived for the magnetic field-induced deformation of magneto-active laminates [Display omitted] We investigate the microscopic and macroscopic instabilities developing in magnetoactive elastomer (MAE) composites undergoing large deformations in the presence of an external magnetic field. In particular, we consider the MAEs with bi-phasic layered microstructure, with phases exhibiting ferromagnetic behavior. We derive an explicit expression for the magnetic field-induced deformation of MAEs with hyperelastic phases. To perform the magnetoelastic instability analysis, we employ the small-amplitude perturbations superimposed on finite deformations in the presence of the magnetic field. We examine the interplay between the macroscopic and microscopic instabilities. We find that the layered MAEs can develop microscopic instability with antisymmetric buckling modes, in addition to the classical symmetric mode. Notably, the antisymmetric microscopic instability mode does not appear in a purely mechanical scenario (when a magnetic field is absent). Furthermore, our analysis reveals that the wavelength of buckling patterns is highly tunable by the applied magnetic field, and by the properties and volume fractions of the phases. Our findings provide the information for designing materials with reconfigurable microstructures. This material ability can be used to actively tune the behavior of materials by a remotely applied magnetic field. The results can be utilized in designing tunable acoustic metamaterials, soft actuators, sensors, and shape morphing devices. [ABSTRACT FROM AUTHOR]

• Multiscale analysis of elastic waves in soft microstructured materials is performed, including the underlying chain network mechanisms and micromechanics of hyperelastic fiber composites. • The interplay between the crosslinked and entangled polymer chains and elastic wave characteristics in finitely deformed soft materials is examined. • Shear wave propagation in transversely isotropic fiber composites is examined with phases characterized by the stiffening behavior stemming from the non-Gaussian statistics of polymer chains. • Explicit expressions for the phase velocities are derived by employing the micromechanics -based approach. • Illustrative examples are provided to show the influence of mechanisms under different loading conditions, wave propagation directionality, and material microstructure parameters. [Display omitted] We provide a multiscale analysis of elastic waves in soft microstructured materials including the underlying molecular chain network mechanisms and micromechanics of hyperelastic fiber composites. First, we examine the interplay between the crosslinked and entangled polymer chains and elastic wave characteristics in finitely deformed materials. Next, we study the shear wave propagation in a class of heterogeneous hyperelastic composites. In particular, we consider the transversely isotropic fiber composites with phases characterized by the stiffening behavior stemming from the non-Gaussian statistics of polymer chains. By employing a micromechanics-based approach, we derive explicit expressions for phase velocities in terms of material properties and volume fraction of the phases. Our results indicate the significant influence of the variety of length-scales mechanisms on the elastic wave characteristics. We provide examples to illustrate the influence of the mechanisms under different loading conditions, wave propagation directionality, and material microstructure parameters. [ABSTRACT FROM AUTHOR]

• Classical buckling in beam-based structure lattice designs. • Instability-induced microstructure transformations in periodic soft composites. • Wrinkling and folding of the thin film on a complaint soft substrate. • Creasing, fringe, and fingering instabilities in confined homogeneous soft layer. Large deformations of soft materials can give rise to the development of various elastic instabilities. The phenomenon is associated with a sudden and dramatic change in structure morphologies. The underlying mechanism is crucial for the formation of complex morphologies in biology. Moreover, the concept of instability-induced pattern transformations is promising for designing novel materials with switchable functions and properties. In this paper, we review the state of the art in elastic instability phenomena in soft materials. We start by considering the classical buckling in beam-based structure lattice designs. Then, we discuss the instability-induced microstructure transformations in soft porous materials, and heterogeneous multiphase and fiber composites. Next, the mechanisms – often involving the post-buckling consideration – leading to the wrinkling and folding, creasing, fringe, and fingering are discussed. [ABSTRACT FROM AUTHOR]

• The interplay between the material composition and deformation-induced effective permittivity in dielectric elastomer (DE) composites is studied. • DE composites with periodic microstructures of (a) circular and (b) elliptical inclusions, (c) pair of inclusions, and (d) randomly distributed inclusions with varying number of the particles in the unit cell, and periodic porous composites are analyzed. • An explicit relation between the effective permittivity and stretch is derived. • The permittivity tunability in DE periodic porous composites structures experiencing elastic instabilities is realized numerically. We study the interplay between the material composition and deformation in dielectric elastomer (DE) composites with periodically and randomly distributed particles embedded in a soft matrix. We focus on the deformation-induced tunability of the effective permittivity in DE composites. We examine the effects of microstructural periodicity and its transition towards random distribution. In particular, we analyze the DE composites with periodic microstructures of (a) circular and (b) elliptical inclusions, (c) pair of inclusions, and (d) randomly distributed inclusions with different numbers of the particles in the unit cell. The finitely deformed DE composites with ideal dielectric elastomer constituents are analyzed numerically. In addition, for the periodic DE composites with circular inclusions, we derive an explicit relation between the effective permittivity and stretch. The effective permittivity of DE composites with periodic microstructures changes with deformation, whereas in DE composites with randomly distributed inclusions, the permittivity is barely affected by deformation. For the latter case, the effective permittivity attains a certain value as the number of particles in the periodic cell increases. To provide the insights on the composite behavior, a two-particle periodic system is examined. The permittivity is found to be sensitive to the orientation of the pairs with respect to the applied electric field, and the distance between the particles. The geometrical effects amplify significantly as the inter-particle distance becomes less than their two diameters. Finally, we illustrate the permittivity tunability in DE periodic porous composites structures experiencing elastic instabilities. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the post-buckling development of instability-induced patterns in soft particulate composites. Upon reaching the critical strain level, the composite experiences microstructural buckling. Interestingly, in the post-buckling regime, the initial buckling mode may evolve into different new patterns. These transformations are governed by the initial microstructure parameters. In particular, depending on the initial distance between the columns of inclusions, the initial instabilities may develop into (i) inclusion chains with a zigzag or wavy shapes, (ii) a combination of inclusion sets in different length scales, (iii) seemingly disordered inclusion sets, (iv) and structures with strictly doubled periodicity. The different post-buckling patterns are further characterized via the discrete Fourier transform (DFT) analysis. Our results also show that the initially formed post-buckling patterns can further evolve into rather complex new shapes beyond a simple amplification in deformation. [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]

• We report the magnetic field-enabled propagation of solitary waves. • We propose to exploit the unique magneto-mechanical coupling of hard-magnetic active elastomers to remotely tune the width, amplitude, and velocity of the nonlinear solitary waves propagating within. • This work provide a fundamental understanding of the effects of magneto-mechanical coupling on the unusual nonlinear vector solitary wave phenomenon. We propose a design of a metamaterial for magnetically tunable propagation of nonlinear vector solitary waves. The metamaterial consists of a periodic array of units of hard-magnetic inclusion embedded in a soft matrix. The units are connected via thin and highly deformable ligaments. Our theoretical and numerical modeling results show that the configuration of the metamaterial undergoes drastic transformations when activated by a magnetic field. These controllable microstructural transformations significantly influence the propagation of vector solitary waves in the proposed metamaterial system. We report the magnetic field-enabled propagation of solitary waves. We show that the proposed soft magnetoactive metamaterial allows us to tune the key characteristics of the enabled nonlinear solitary waves, including their pulse width and amplitude. Our findings also highlight the potential of magneto-mechanical coupling in the development of untethered mechanical metamaterial systems for applications in nondestructive testing, energy harvesting, and smart soft wave devices. [ABSTRACT FROM AUTHOR]