We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.
We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the volumetric deviatoric separation of the strain energy used, for example, in many Finite Element (FE) codes in that it does not fully represent the behavior of anisotropic materials in the linear regime. This limitation has important consequences. We show that, in the small deformation regime, a FE code based on the volumetric-deviatoric separation assumption predict…
We theoretically study the effect of external deformation on activated structural relaxation and elementary aspects of the nonlinear mechanical response of glassy hard sphere fluids in the context of the nonequilibrium version of the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. ECNLE theory describes activated relaxation as a coupled local-nonlocal event involving local caging and longer range collective elasticity, with the latter becoming more important with increasing packing fraction. The central new question is how this physical picture, and the relative importance o…
We propose a model for a thermally driven microswimmer in which three spheres are connected by two springs with odd elasticity. We demonstrate that the presence of odd elasticity leads to the directional locomotion of the stochastic microswimmer.
Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius $a$ in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth ($δ$) of the bead inside the softest gels as $δ\sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean model of elastic deformation, according to which the displacement fields must diverge, i…
Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial to understand on the one hand how a glass may become unstable due to increased plasticity under shear deformations; on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released. Here we focus on assemblies of hard spheres as the simplest model of amorph…
The synthetic actin network arouses great interest as bio-material due to its soft and wet nature that mimics many biological scaffolding structures. Inside the cell, the actin network is regulated by tens of actin-binding proteins (ABP's), which make for a highly complex system with several emergent behaviours. In particular, calponin is an ABP that was identified as an actin stabiliser, but whose mechanism is still poorly understood. Recent experiments using an in vitro model system of cross-linked actin with calponin and large deformation bulk rheology, found that networks with basic calpon…
We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{θ_e}$ the force distribution of such pairs and $ϕ_c$ the packing fraction at which pressure diverges, we predict that (i…
The flow of colloidal suspensions is ubiquitous in nature and industry. Colloidal suspensions exhibit a wide range of rheological behavior, which should be closely related to the microscopic structure of the systems. With in-situ small-angle neutron scattering complemented by rheological measurements, we investigated the deformation behavior of a charge-stabilized colloidal glass at particle level undergoing steady shear. A short-lived, localized elastic response at particle level, termed as transient elasticity zone (TEZ), was identified from the neutron spectra. The existence of the TEZ is a…
We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directiona…
The shear response of soft solids can be modeled with linear elasticity, provided the forcing is slow and weak. Both of these approximations must break down when the material loses rigidity, such as in foams and emulsions at their (un)jamming point -- suggesting that the window of linear elastic response near jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs remains unclear. To answer these questions, we perform computer simulations of stress relaxation and shear startup experiments in athermal soft sphere packings, the canonical model for jamming. By systematical…
The conventional (Zwanzig-Mountain) expressions for instantaneous elastic moduli of simple fluids predict their divergence as the limit of hard sphere (HS) interaction is approached. However, elastic moduli of a true HS fluid are finite. Here we demonstrate that this paradox reveals the soft- to hard-sphere crossover in fluid excitations and thermodynamics. With extensive \emph{in-silico} study of fluids with repulsive power-law interactions ($\propto r^{-n}$), we locate the crossover at $n\simeq 10-20$ and develop a simple and accurate model for the HS regime. The results open novel prospects…
Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, w…
In the classic theory of solid adhesion, surface energy drives deformation to increase contact area while bulk elasticity opposes it. Recently, solid surface stress has been shown also to play an important role in opposing deformation of soft materials. This suggests that the contact line in soft adhesion should mimic that of a liquid droplet, with a contact angle determined by surface tensions. Consistent with this hypothesis, we observe a contact angle of a soft silicone substrate on rigid silica spheres that depends on the surface functionalization but not the sphere size. However, to satis…
An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are vi…
The elastic and adhesive properties of a solid surface can be quantified by indenting it with a rigid sphere. Indentation tests are classically described by the JKR-law when the solid is very stiff, while recent work highlights the importance of surface tension for exceedingly soft materials. Here we show that surface tension plays a crucial role even for stiff solids: it regularizes the crack-like singularity at the edge of the contact. We find that the edge region exhibits a universal, self-similar structure that emerges from the balance of surface tension and elasticity. The similarity theo…
Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not u…
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/…
Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitely considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand,…
The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that due to elasticity. This article studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The re…
We study the interaction of two parallel rigid cylinders on the surface of a thin elastic film supported on a pool of liquid. The excess energy of the surface due to the curvature of the stretched film induces attraction of the cylinders that can be quantified by the variation of their gravitational potential energies as they descend into the liquid while still floating on the film. Although the experimental results follow the trend predicted from the balance of the gravitational and elastic energies of the system, they are somewhat underestimated. The origin of this discrepancy is the hystere…
Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid particles embedded in a soft elastic polymeric matrix, leading to overall deformations. It is a major challenge in theory to correctly predict from the discrete particle configuration the type of deformation resulting for a finite-sized system. Considering an elastic sphere, we here present such an approach. The method is in principle exact, at least within the fr…
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational as well as translational order. The study of these structures is important for investigating the interplay between geometry, topology, and elasticity, and for their potential applications in materials science. In this work we numerically simulate a spherical monolayer of soft repulsive spherocylinders (SRS) and study the packing of rods and their ordering transition as a function of the packing fraction. In the model that we study, …
The packing problem of long thin filaments that are injected into confined spaces is of fundamental interest for physicists and biologists alike. How linear threads pack and coil is well known only for the ideal case of rigid containers, though. Here, we force long elastic rods into flexible spatial confinement borne by an elastic shell to examine under which conditions recently acquired knowledge on wire packing in rigid spheres breaks down. We find that unlike in rigid cavities, friction plays a key role by giving rise to the emergence of two distinct packing patterns. At low friction, the w…
How do we characterize the shape of a surface? It is now well understood that the shape of a surface is determined by measuring how curved it is at each point. From these measurements, one can identify the directions of largest and smallest curvature, i.e. the principal curvatures, and construct two surface invariants by taking the average and the product of the principal curvatures. The product of the principal curvatures describes the intrinsic curvature of a surface, and has profound importance in differential geometry - evidenced by the Gauss's Theorema Egregium and the Gauss-Bonnet theore…
