Soft Solids Research Articles

A numerical study of Mullins softening effects on mode I crack propagation in viscoelastic solids

This paper presents a finite element analysis of steady-state crack propagation in viscoelastic soft solids exhibiting Mullins softening. A cohesive-zone model is employed to simulate the localized processes at the tip of a Mode I crack in materials governed by viscoelastic behavior and damage-induced Mullins effects. The study numerically evaluates the intrinsic dissipation characteristics of typical rubber-like materials, focusing on the influence of key factors such as Mullins damage, relaxation modulus, and relaxation time. The impact of these factors on material toughening is examined, with particular emphasis on their role in crack propagation. The results reveal that crack propagation velocity is highly sensitive to the interplay between energy dissipation mechanisms. Specifically, Mullins damage parameters are shown to increase fracture toughness by raising the local energy release rate threshold at the crack tip. Additionally, the relaxation modulus enhances viscous dissipation, further elevating this threshold and subsequently reducing crack propagation velocity. Interestingly, an inverse relationship between relaxation time and crack propagation velocity is observed. The study provides a detailed analysis of the dissipation mechanisms at the crack tip, offering valuable insights for improving material toughness.

Effective medium theory for viscoelasticity of soft jammed solids

The viscoelastic properties of soft jammed solids, such as foams, emulsions, and soft colloids, have been extensively studied in experiments. A particular focus has been placed on the phenomenon of anomalous viscous loss, characterized by a storage modulus and a loss modulus , where ω represents the frequency of the applied strain. In this work, we aim to develop a microscopic theory that explains these experimental observations. Our approach is based on effective medium theory (EMT), also referred to as coherent potential approximation theory. By incorporating the effects of contact damping, a key characteristic of soft jammed solids, into the EMT, we offer new insights into the viscoelastic behavior of these materials. The theory not only explains the observed viscoelastic properties but also links the anomalous viscous loss to the marginal stability inherent in amorphous systems. This research lays the groundwork for a microscopic theory that effectively describes the impact of damping on soft jammed solids and their characteristic viscoelastic behaviors.

Fluid-mediated impact of soft solids

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity, and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we elucidate why nearly incompressible solids feature (a) substantial ‘gliding’ prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

Ultra-soft cellular solids inspired by marine mussel plaques: scaling of the mechanical properties

The porous core of the marine mussel provides mechanical advantages of achieving substantial deformation and high toughness. Inspired by the unique mechanical behaviours of mussel plaque cores, the present study develops ultra-soft, stretchable and tough cellular solids by bio-mimicking their porosity and properties. Although scaling laws to correlate the mechanical properties of cellular solids with bulk materials have been established, they are primarily based on experimental data from stiff cellular solids. In this article, the scaling law for soft cellular solids is studied to relate tensile properties and toughness with volume fractions. Unlike conventional stiff cellular solids, the scaling law shows that soft lattices experience bending-dominated deformation at the elastic state and fail under stretching-dominated deformation. Uniaxial and planar tensile tests demonstrate that the proposed soft lattices achieved Young’s modulus of 0.04 ∼ 0.17 MPa, failure strain of 135.5 ∼ 213.9 % and toughness of 582 ∼ 941 J m −2 by manipulating the volume fraction ( 0.2 ∼ 0.5 ), positioning them as softer, more stretchable and tougher than the majority of engineering foams in the Ashby diagram. In addition, the toughness of soft lattices is found to be sensitive to volume fraction but insensitive to initial crack length, thickness and height ( ≥ 20 m m ). Two distinct failure modes, truss failure and joint failure, are correlated with volume fraction. The soft lattice with a volume fraction (around 0.4) similar to mussel plaque fails at the transition of these two failure modes and achieves the highest toughness. This study contributes new insights to the materials science community and lays the foundation for the development of lightweight, damage-tolerant and high-performance metamaterials.

On the Cover: Y Shaped Cutting of Soft Solids: History and Best Practices

On the Cover: Y Shaped Cutting of Soft Solids: History and Best Practices

Emergence and growth dynamics of wetting-induced phase separation on soft solids

Liquid droplets on soft solids, such as soft polymeric gels, can induce substantial surface deformations, leading to the formation of wetting ridges at contact points. While these contact ridges have been shown to govern the rich surface mechanics on compliant substrates, the inherently divergent characteristics of contact points and the multiphase nature of soft reticulated gels pose great challenges for continuum mechanical theories in modeling soft wetting phenomena. In this study, we report experimental characterizations of the emergence and growth dynamics of the wetting-induced phase separation. The measurements demonstrate how the migration of free chains prevents the stress singularities at contact points. Based on the Onsager variational principle, we present a phenomenological model that effectively captures the extraction process of free chains, including a crossover from a short-term diffusive state to a long-term equilibrium state. By comparing model predictions with experimental results for varied crosslinking densities, we reveal how the intrinsic material parameters of soft gels dictate phase-separation dynamics. Published by the American Physical Society 2024

Making the Cut: End Effects and the Benefits of Slicing

Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting of a parallelepiped sample is the simplest model system to analyse the cutting resistance of a soft material. However, even for this simple system, the complex failure mechanisms that underpin cutting are still not completely understood. Several models that connect the critical cutting force to the radius of the wire and the key mechanical properties of the cut material have been proposed. An almost ubiquitous simplifying assumption is a state of plane (and anti-plane) strain in the material. In this paper, we show that this assumption can lead to erroneous conclusions because even such a simple cutting problem is essentially three-dimensional. A planar approximation restricts the analysis to the stress distribution in the midplane of the sample. However, through threedimensional finite element modelling, we reveal that the maximal tensile stress – and thus the likely location of cut initiation – is located in the front face of the sample (end effect). Friction reduces the magnitude of this tensile stress, but this detrimental effect can be counteracted by large “slice-to-push” (shear-to-indentation) ratios. The introduction of the “end effect” helps reconcile a recent controversy around the role of friction in wire cutting, for it implies that slicing can indeed reduce required cutting forces, but only if the slice-push ratio and the friction coefficient are sufficiently large.

Containment strategy for subsurface H2 storage based on time-dependent soft solids

We propose an innovative containment strategy based on time-dependent soft solids, namely 2 wt% Laponite suspensions, to reinforce natural subsurface seals and engineer flow barriers, with an eye toward making H2 subsurface storage scalable and geographically agnostic. This suspension can be injected at its initial low viscosity and elasticity into a porous medium, allowing for easy pumping and targeted delivery. Once inside the target zone, it matures into a soft solid with much higher viscosity and elasticity, acting as a potential flow barrier. We discuss the rheological properties of the suspensions and demonstrate that hydrogen does not adversely affect their microstructure, but rather increases the suspensions’ viscosity and elasticity. Moreover, the suspensions enhance the rock samples’ compressive strength, while hydrogen exposure increases their stiffness and ductility. The ability of rock samples saturated with the suspensions to contain higher injected gas pressures is enhanced by aging at higher temperatures.

Decoupling the rheological responses of a soft solid emulsion with liquid inclusions

Soft solid emulsions are liquid droplets encapsulated in a soft solid material. Typical of dispersed systems, they can combine properties from both the liquid inclusions and the soft solids. The relative importance of the two phases in the rheological response is captured through the elastocapillary number, which compares capillary forces in the liquid inclusions to the matrix rigidity. We work with solid emulsions formed of poly(ethylene glycol) droplets in a poly(dimethylsiloxane) (PDMS) continuous phase. We create three families of emulsions with varying elastocapillary numbers, and range of inclusion volume fractions from 0 to 0.5. Through oscillatory rheology we probe both the elastic response and the dissipative effects of liquid droplets. In the case of a dominant response from the continuous phase or the drops, the results can be described with Palierne’s model. However, for the intermediate elastocapillary series we show that the evolution of the storage and loss moduli decouple with dispersed phase volume fraction. We attribute the increase of loss factor with volume fraction to the high polydispersity in droplet size. We can further modulate the response of the materials by cooling to freeze the droplets. This approach allows us to compare these soft solid emulsions with theories related to solid dispersions.

Y-Shaped Cutting of Soft Solids: History and Best Practices

Y-Shaped Cutting of Soft Solids: History and Best Practices

Transition to plastic regime for Rayleigh-Taylor instability in soft solids.

Rayleigh-Taylor instability (RTI) is observed in soft materials that have significant resistance to yield. Estimating the instability threshold is critical to several engineering applications and has been the topic of several studies in past decades. However, limited attention has been given to the elastic-to-plastic (EP) transition threshold, where material properties vary significantly. This study explores the phase transition between the pure elastic and stable plastic regimes in RTI in a soft solid (mayonnaise) using a rotating wheel experimental setup with a time-varying acceleration profile. The material properties of the soft solid are characterized using rheological techniques. Different initial perturbation wavelength and amplitude combinations are used to analyze their role in the EP transition threshold and the subsequent maximum fully recoverable elastic strain. The effects of the initial perturbation dimensions, the steepness of the perturbation, and the mass of the perturbation on the stability of the samples, the EP transition thresholds, and the maximum fully recoverable elastic strains are analyzed. The samples with the largest full elastic recovery potentials and the parameters governing this phenomenon are identified, and the physics behind it is discussed. It is observed that increasing the initial perturbation wavelength decreases the required phase transition acceleration while increasing the maximum fully recoverable elastic strain. Finally, nondimensional parameters that involve the perturbation dimensions, as well as the mechanical properties of the material, are introduced to provide a generalized approach to the problem.

Reversible shape transformations through continuous deformations in soft responsive self-repairing solids using voxel techniques

Voxel modeling is a technique in which an object is represented by an array of cubes. One advantage in design-for-manufacturing is that selected voxels may be assigned desired responsive properties through additive manufacturing. It allows for achieving reversible shape transformation in soft responsive self-repairing solids within a strategic sequence. The first step in the sequence involves selecting an equivalent geometric shape. The second step involves mapping shapes to preserve properties during continuous deformation. The third step involves transforming the shape from one form to another. The fourth step involves defining changes in dimensions. The final step involves correlating the flow of stress with the stretch of the solid. This research also considers self-repair or self-healing as part of the transformation process because the splitting or joining of solids involves continuous deformation. The newly transformed shape can also be considered as the intermediate shape, or first shape for next transformation. This leads to a chain of shapes that are topologically equivalent, and interchangeable. The iterative steps involved in shape transformation finds applications in topology optimization, generative design, metastructures, among others. One application of shape transformation in these domains is that it serves as an alternative to material reduction techniques.

The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic

Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in forms which are not quite suitable for the analysis of actual data. Here, we propose a linear viscoelastic approach which consistently exploits the dynamic mechanical analysis data. We apply this method to four sets of results documenting fracture or adhesion rupture in soft solids with various degrees of viscoelasticity. For elastomers, the results reproduce the well-known inconsistency of the process zone size. In more viscoelastic systems, however, the present approach is able to match the measured velocity dependence of the rupture energy with physically acceptable process zone sizes. Moreover, our predictions agree with the damage zone sizes measured by mechanoluminescence. Building on these results, we discuss various issues arising when evaluating the linear viscoelastic contribution to the rupture/adhesion energy in soft solids: data quality, physical interpretation of the parameters, validity of simpler approximations and limitations of the present approach.

Exploring the influence of friction in the puncture mechanics of soft solids

AbstractFriction is an ever-present force in our lives, affecting the interaction between objects in numerous ways. The common hypothesis of frictionless contact between a foreign rigid object (needle) and a target material during puncturing leads to a constant penetration force. However, experimental observations reveal a linear increase in penetration force as the needle tip delves deeper. This force increment arises from the interplay of friction and adhesion at needle-solid interface. The present work provides an insight into the measure of friction and adhesion quasi-static characteristics at the needle-solid interface through puncture experiments. To this end, an axisymmetric hyperelastic model is presented to describe the expansion of a cavity under the contact pressure of the penetrating needle. In addition, the competing mechanisms of cavity expansion and mode I cracking during needle penetration in a soft solid are discussed.

Why soft contacts are stickier when breaking than when making them.

Soft solids are sticky. They attract each other and spontaneously form a large area of contact. Their force of attraction is higher when separating than when forming contact, a phenomenon known as adhesion hysteresis. The common explanation for this hysteresis is viscoelastic energy dissipation or contact aging. Here, we use experiments and simulations to show that it emerges even for perfectly elastic solids. Pinning by surface roughness triggers the stick-slip motion of the contact line, dissipating energy. We derive a simple and general parameter-free equation that quantitatively describes contact formation in the presence of roughness. Our results highlight the crucial role of surface roughness and present a fundamental shift in our understanding of soft adhesion.

Unsteady wetting of soft solids

HypothesisSpreading of liquids on soft solids often occurs intermittently, i.e., the liquid's wetting front switches between sticking and slipping. Studies of this so-called stick-slip wetting on soft solids mostly are confined within quasi-static or forced spreading conditions. In these situations, because the sticking duration is set much larger than the viscoelastic relaxation time of the solid, a ridge is persistently and fully developed at the wetting front as the soft solid yields to the liquid's surface tension. The sticking duration and spreading velocity, therefore, were shown to have little impact to the contact angle change required for stick-to-slip transitions. For unsteady wetting of soft solids, a commonly encountered but largely unexplored situation, we hypothesize that the stick-to-slip transition is controlled not only by a combination of sticking duration and the spreading velocity, but also by an increasing depinning threshold caused by the growing ridge at the wetting front. ExperimentWe performed unsteady wetting experiment on soft solids by letting water droplets spread freely on soft solid surfaces of various stiffness. We capture both the stick-slip spreading behavior and growing wetting ridges using synchronous high-speed imaging and high-speed interferometry. Recorded data of liquid spreading and solid deforming at the wetting front were analyzed to shed light on the relation between stick-slip characteristics and the growing wetting ridge. FindingsWe find that intermittent wetting on a soft solid surface results from a competition between three key factors: liquid inertia, capillary force change during sticking, and growing pinning force caused by the solid's viscoelastic response. We theoretically formulate their quantitative contributions to predict how stick-to-slip transitions occur, i.e., how the contact angle change and sticking duration depend on the liquid's spreading velocity and the solid's viscoelastic characteristics. This provides a mechanistic understanding and methods to control unsteady wetting phenomena in diverse applications, from tissue engineering and fabrication of flexible electronics to biomedicine.

Direct, model-free acoustic evaluation of stresses and strains in loaded nonlinear soft solids

We show analytically and experimentally that the states of stress and strain existing in a mechanically loaded elastic material can be accessed directly from elastic wave speed measurements, without having to determine, or even know, its material linear and nonlinear elastic parameters. These techniques are expected to have important applications in the health monitoring of loaded structures. Examples include stressed hydrogels, muscles, and thin membranes, such as a stretched rubber sheet, a piece of cling film (∼10 μm thick), and the animal skin of a bodhrán, a traditional Irish drum.

REVIEW: THE USE OF TOFU RESIDUE IN THE PHARMACEUTICS

Tofu is a processed soy product consisting of soft solids made by clumping soy protein extracts. The residual result of tofu processing is called the tofu dredging waste. In Indonesia, tofu waste remains an unsolved problem. Many people argue that the waste from tofu processing (tofu residue waste) does not have high economic value and is only used as feed for livestock and is even thrown carelessly into the river, which causes damage to the ecosystem. Tofu pulp has high nutritional content, such as protein (26.6%), fat (18.3%), carbohydrates (41.3%), phosphorus (0.29%), calcium (0.19%), iron (0.04%), and water (0.09%). The purpose of this journal review is to determine the use of tofu residue waste and solve the problem of tofu residue waste in the community. The method used was collecting various research journals through the Google Scholar website with keywords for the use of tofu residue in the pharmaceutical field. Based on the 7 journals reviewed, tofu pulp can be used as an anti-aging, adsorbent, anti-diabetes, anti-inflammatory, bioethanol, and excipient in tablet production. Keywords: Tofu, tofu residue, pharmaceutical

Elasticity-controlled jamming criticality in soft composite solids

Soft composite solids are made of inclusions dispersed within soft matrices. They are ubiquitous in nature and form the basis of many biological tissues. In the field of materials science, synthetic soft composites are promising candidates for building various engineering devices due to their highly programmable features. However, when the volume fraction of the inclusions increases, predicting the mechanical properties of these materials poses a significant challenge for the classical theories of composite mechanics. The difficulty arises from the inherently disordered, multi-scale interactions between the inclusions and the matrix. To address this challenge, we systematically investigated the mechanics of densely filled soft elastomers containing stiff microspheres. We experimentally demonstrate how the strain-stiffening response of the soft composites is governed by the critical scalings in the vicinity of a shear-jamming transition of the included particles. The proposed criticality framework quantitatively connects the overall mechanics of a soft composite with the elasticity of the matrix and the particles, and captures the diverse mechanical responses observed across a wide range of material parameters. The findings uncover a novel design paradigm of composite mechanics that relies on engineering the jamming properties of the embedded inclusions.

Sensitive Thermochromic Behavior of InSeI, a Highly Anisotropic and Tubular 1D van der Waals Crystal.

Thermochromism, the change in color of a material with temperature, is the fundamental basis of optical thermometry. A longstanding challenge in realizing sensitive optical thermometers for widespread use is identifying materials with pronounced thermometric optical performance in the visible range. Herein, it is demonstrated that single crystals of indium selenium iodide (InSeI), a 1D van der Waals (vdW) solid consisting of weakly bound helical chains, exhibit considerable visible range thermochromism. A strong temperature-dependent optical band edge absorption shift ranging from 450 to 530 nm (2.8 to 2.3 eV) over a 380 K temperature range with an experimental (dEg/dT)max value extracted to be 1.26 × 10-3 eV K-1 is shown. This value lies appreciably above most dense conventional semiconductors in the visible range and is comparable to soft lattice solids. The authors further seek to understand the origin of this unusually sensitive thermochromic behavior and find that it arises from strong electron-phonon interactions and anharmonic phonons that significantly broaden band edges and lower the Eg with increasing temperature. The identification of structural signatures resulting in sensitive thermochromism in 1D vdW crystals opens avenues in discovering low-dimensional solids with strong temperature-dependent optical responses across broad spectral windows, dimensionalities, and size regimes.