Surface stress and surface energy are two fundamental parameters that determine the surface properties of any materials. While it is commonly believed that the surface stress and surface energy of liquids are identical, the relationship between the two parameters in soft polymeric gels remains debatable. In this work, we measured the surface stress and surface energy of soft silicone gels with varying weight ratios of crosslinkers in soft wetting experiments. Above a critical density, $k_0$, the surface stress was found to increase significantly with crosslinking density while the surface energy remained unchanged. In this regime, we can estimate a non-zero surface elastic modulus that also increases with the ratio of crosslinkers. By comparing the surface mechanics of the soft gels with their bulk rheology, the surface properties near the critical density $k_0$ were found to be closely related to the underlying percolation transition of the polymer networks.
Intermediate filaments are cytoskeletal proteins that are key regulators of cell mechanics, a role which is intrinsically tied to their hierarchical structure and their unique ability to accommodate large axial strains. However, how the single-filament response to applied strains translates to networks remains unclear, particularly with regards to the crosslinking role played by the filaments' disordered "tail" domains. Here we test the role of these noncovalent crosslinks in the nonlinear rheology of reconstituted networks of the intermediate filament protein vimentin, probing their stress- a…
Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving deformation to establish contact and bulk elasticity resisting this. However, it has recently been shown that surface stresses provide an additional restoring force that can compete with and even dominate over elasticity in highly compliant materials, especially when length scales are small compared to the ratio of the surface stress to the elastic modulus, $Υ/…
In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample to sample fluctuations that grow without bound with the system size. More relevant however for experiments are the conditions of stress control. In the present Communication we show that also under stress control the shear modulus exists but higher order moduli show unbounded sample to sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments sho…
We study the stress fluctuations in simulations of a two-dimensional amorphous solid under a cyclic drive. It is known that this system organizes into a reversible state for small driving amplitudes and remains in an irreversible state for high driving amplitudes, and that a critical driving amplitude separates the two regimes. Here we study the time series of the stress fluctuations below and above the reversible-irreversible transition. In the irreversible regime above the transition, the power spectrum of the stress fluctuations is broad and has a $1/f^α$ shape with $1< α<2$. We find that t…
It is now well-established that mechanical equilibrium in athermal disordered solids gives rise to anisotropic spatial correlations of the coarse-grained stress field that decay in space as $1/r^d$, where $r$ is the distance from the origin, and $d$ denotes the spatial dimension. In this note we present a simple, geometry based argument for the scaling form of the emergent spatial correlations of the stress field in disordered solids.
In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the stress fields of i) a parallel cylindrically-symmetric distribution of screw dislocations in infinite orthotropic and monoclinic media, ii) a cylindrically-symmetric distribution of parallel wedge disclinations in an infinite orthotropic medium, iii) a distribution of edge dislocations in an orthotropic medium, and iv) a spherically-symmetric distribution of point defects in a transversely isotropic spherical ball.
In this article, we propose a mathematical model which explains the formation of strong bonds during the relaxation process of a soft solid on a hard surface. As a result, the soft solid relaxes to a non zero residual stress level. The model assumes that formation of strong bonds occurs owing to transition from weak to strong bonds at a critical time. Parametric studies are carried out to understand the effect of different friction parameters related with the model on the relaxation process. The relaxation model is, in turn, validated with experiments and corresponding numerical values are jus…
Yield stress materials fail when the imposed stress crosses a critical threshold. A well-known dynamical response to the applied stress is the phenomenon of creep where the cumulative deformation grows sublinearly with time, prior to failure or arrest. Using extensive molecular dynamics simulations, we study such response for a model amorphous system, in the athermal limit, and probe how the annealing history of the initial state determines the observed behaviour to an applied shear stress. Further, we analyze the microscopic dynamics in the vicinity of the yield threshold, using large systems…
The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress {\em differences} between plastic events. Results f…
It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play an central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresse…
We numerically study the local stress distribution within athermal, isotropically stressed, mechanically stable, packings of bidisperse frictionless disks above the jamming transition in two dimensions. Considering the Fourier transform of the local stress, we find evidence for algebraically increasing fluctuations in both isotropic and anisotropic components of the stress tensor at small wavenumbers, contrary to recent theoretical predictions. Such increasing fluctuations imply a lack of self-averaging of the stress on large length scales. The crossover to these increasing fluctuations define…
We find that unjammed packings of frictionless particles with rather weak attraction can always be driven into solid-like states by shear. The structure of shear-driven solids evolves continuously with packing fraction from gel-like to jamming-like, but is almost independent of the shear stress. In contrast, both the density of vibrational states (DOVS) and force network evolve progressively with the shear stress. There exists a packing fraction independent shear stress $σ_c$, at which the shear-driven solids are isostatic and have a flattened DOVS. Solid-like states induced by a shear stress …
The response to shear of the dense soft solids features a stress overshoot and a persistent shear banding before reaching a homogeneously flowing state. In 3D large scale simulations we analyze the time required for the onset of homogeneous flow, the normal stresses and structural signatures at different shear rates and in different flow geometries, finding that the stress overshoot, the shear band formation and its persistence are controlled by the presence of overconstrained microscopic domains in the initially solid samples. Being able to identify such domains in our model by prevalently ic…
The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a 'small-on-large' acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose b…
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit.
We demonstrate that irreversible structural reorganization is not necessary for the observation of yield behaviour in an amorphous solid. While the majority of solids strained to their yield point do indeed undergo an irreversible reorganization, we find a significant fraction of solids exhibit yield via a reversible strain. We also demonstrate that large instantaneous strains in excess of the yield stress can result in complete stress relaxation, a result of the large non-affine motions driven by the applied strain. The empirical similarity of the dependence of the ratio of stress over strain…
We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space leading to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis for the model particulate gels at low particle volume fr…
In soft amorphous materials, shear cessation after large shear deformation leads to structures having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the s…
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation gradient $\mathbf{F}$ and initial stress $\boldsymbol τ$, i.e. $W:= W(\mathbf F, \boldsymbol τ)$. The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not depend upon an arbitrary choice of reference configuration. We call this restriction: initial stress reference independence (ISRI). It transpires t…
A theory for the non-local stress in liquids captures the crossover from viscous to elastic correlations upon supercooling. It explains the emergence of long-ranged stress fields in glass which originate from the coupling of shear stress to transverse deformations. The Goldstone mode in colloidal glass is shown to be diffusive.
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress vs. strain curves, and pro…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the form of collective avalanches. We investigate their characterization through energy vs. stress drops and at multiple stages of deformation, thus revealing a change of spatial extent of the avalanches and degree of stress correlations as deformation progresses. We show that the statistics of stress and energy drops only become comparable for large events in …
One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a deep connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular…
Rate-effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size $L$. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent $1/β$, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure $β$ …
We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al, Soft Matter 2018). Following a Green's function approach, we extend the surface-stress regularized Flamant-Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two…
When submitted to a constant mechanical load, many amorphous solids display power law creep followed by fluidization. A fundamental understanding of these processes is still far from being achieved. Here, we characterize creep and fluidization on the basis of a mesoscopic viscoplastic model that includes thermally activated yielding events and a broad distribution of energy barriers, which may be lowered under the effect of a local deformation. We relate the creep exponent observed before fluidization to the width of barrier distribution and to the specific form of stress redistribution follow…
