We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface diffusion kinetics. This type of coupling can manifests as an integral aspect in diverse engineering processes encountered in optical interference coatings, tissue engineering, soft electronics, and can prove important in design process for the next generation of sensors and actuators, especially as the focus is shifted to systems in smaller lengthscales. The intricate interplay between solvent diffusion and deformation of the film is governed by surface poroelasticity, and the viscoelastic deformation of the substrate. While existing methodologies offer tools for studying coupled poroelasticity involving solvent diffusion and network deformation, there exists a gap in understanding how coupled poroelastic processes occurring in a film attached to the boundary of a highly deformable solid can influence its response. In this study, we introduce a non-equilibrium thermodynamics formulation encompassing the multiphysical processes of surface poroelasticity and bulk viscoelasticity, complemented by a corresponding finite element implementation. Our approach captures the complex dynamics between the finite deformation of the substrate and solvent diffusion on the surface. This work contributes valuable insights, particularly in scenarios where the coupling of surface diffusion kinetics and substrate elasticity is an important design factor.
Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the latt…
We demonstrate that plastic deformation in solids is associated with a dynamic transition that is reminiscent to the transition from a superconducting to a mixed phase in Type II superconductors. We report analytic calculations, extensive molecular dynamics and sequential umbrella sampling Monte Carlo simulations of a two dimensional triangular crystalline solid undergoing plastic deformation under strain. The solid consists of particles connected by harmonic springs. Non-affine displacement fluctuations of the solid are enhanced using an external field, causing a rich deformation behaviour. T…
Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent years. Investigations employing both unidirectional and cyclic deformation protocols reveal a strong dependence of yielding behaviour on the degree of annealing. Below a threshold degree of annealing, the nature of yielding changes qualitatively, to progressively more discontinuous yielding. Theoretical investigations of yielding in amorphous solids have almost e…
Deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotics. Expanding on this concept, beams can be designed so that the pressure in the channel-network is created directly from external forces acting on the beam, and thus can be viewed as passive solid-liquid composite structure. We obtain a continuous function relating the network geometry to the deformation. This enables design of networks creating arbitrary steady and time varying deformation-fields as well as to eliminate deformation created by external forces.
Understanding the particle-scale transition from elastic deformation to plastic flow is central to making predictions about the bulk material properties and response of disordered materials. To address this issue, we perform experiments on flow-stabilized solids composed of micron-scale spheres within a microfluidic channel, in a regime where particle inertia is negligible. Each solid heap exists within a stress gradient imposed by the flow, and we track the positions of particles in response to single impulses of fluid-driven compression or decompression. We find that the resulting deformatio…
We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system (PDMS with different degrees of crosslinking) allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation where the fingering wavelength only scales with the film thickness, and a bulk regime called "viscoelastic" where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and pres…
We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the …
We derive a Föppl-von Kármán-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustra…
We use the shear transformation zone (STZ) theory of dynamic plasticity to study the necking instability in a two-dimensional strip of amorphous solid. Our Eulerian description of large-scale deformation allows us to follow the instability far into the nonlinear regime. We find a strong rate dependence; the higher the applied strain rate, the further the strip extends before the onset of instability. The material hardens outside the necking region, but the description of plastic flow within the neck is distinctly different from that of conventional time-independent theories of plasticity.
Implicit rate-type constitutive relations utilizing discontinuous functions provide a novel approach to the purely phenomenological description of the inelastic response of solids undergoing finite deformation. However, this type of constitutive relations has been so far considered only in the purely mechanical setting, and the complete thermodynamic basis is largely missing. We address this issue, and we develop a thermodynamic basis for such constitutive relations. In particular, we focus on the thermodynamic basis for the classical elastic--perfectly plastic response, but the framework is f…
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate, particularly those at the contact-line. We construct a general solution using a displacement potential function for the elastic deformations within a finite elastic substrate associated with these wetting forces, and compare the results for several different contact-line models. Our work incorporates internal contributions to the surface stress from both liquid/soli…
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the uti…
Recently there has been an increase in demand for soft and biocompatible electronic devices capable of withstanding large stretch. Ionically conductive polymers present a promising class of soft materials for these emerging applications due to their ability to realize charge transport across the polymer network, while preserving the desired mechanical and chemical features. As opposed to electron transfer in traditional electrical conductors, the charge transport across these polymers is achieved through ion migration. When such materials are used in combination with electrical systems, they a…
Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft sub…
Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of …
We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and…
Multiple speckle diffusing wave spectroscopy (MSDWS) can be applied to measure spatially heterogeneous mechanical behavior in soft solids, with high sensitivity to deformation and both spatial and temporal resolution. In this paper, we discuss the mathematical approach behind the quantification of the deformation rate from MSDWS data and provide guidelines for optimizing the selection of experimental parameters in measurements. After validating the method in extensional tests on an elastomer, we provide an example of the potentiality of MSDWS by measuring the spatial distribution of the deform…
We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic droplets embedded in soft solids are particularly attractive, because they avoid intrinsic nonlinearities associated with previous experiments such as the equilibrium of contact lines and the relaxation of patterned surfaces. We derive analytical solutions for the shape of droplets under uniaxial deformation and for the radius of droplets upon hydrostatic in…
From hydrogels and plastics to liquid crystals, soft solids cover a wide array of synthetic and biological materials that play key enabling roles in advanced technologies such as 3D printing, soft robotics, wearable electronics, self-assembly, and bioartificial tissues. Their elasticity and stimuli-induced changes in mechanical, optical, or electrical properties offer a unique advantage in designing and creating new dynamically functional components for sensing, micro-actuation, colour changes, information, and mass transport. To harness the vast potential of soft solids, a thorough understand…
The most profound effect of disorder on the elastic response of solids is the nonaffinity of local displacements whereby the atoms (particles, network junctions) do not simply follow the macroscopic strain, as they do in perfect crystals, but undergo additional displacements which result in a softening of response. Whether disorder can produce further effects has been an open and difficult question due to our poor understanding of nonaffinity. Here we present a systematic analysis of this problem by allowing both network disorder and lattice coordination to vary continuously under account of n…
In this work, the mechanical response oF an one-dimensional active solid -- defined as a network of active stochastic particles interacting by nonlinear hard springs -- subject to an external deformation force, is numerically studied and rationalized with a minimal model. It is found that an active solid made of linear springs and subject to an external stress, presents an average deformation which is independent of the system's activity. However, when the active solid is made of nonlinear hard springs, the solid's average deformation decreases with respect to a passive system under the same c…
We study a model amorphous solid that is subjected to repeated athermal cyclic shear deformation. It has previously been demonstrated that the memory of the amplitudes of shear deformation the system is subjected to (or trained at) is encoded, and can be retrieved by subsequent deformation cycles that serve as read operations. Here we consider different read protocols and measurements and show that single and multiple memories can be robustly retrieved through these different protocols. We also show that shear deformation by a larger amplitude always erases the stored memories. These observati…
Liquid adsorption in nanoporous materials induces their deformation due to strong capillary forces. The linear relationship between the liquid pressure and the solid strain (pore-load modulus) provides an experimental technique to determine the mechanical properties of nanosized solids. Puzzling experimental results have often been reported, leading to a severe reconsideration of the mechanical properties of the thin walls, the introduction of surface stresses, and the suggestion of a mutual influence of fluid adsorption and matrix deformation. This work presents a molecular simulation examina…
Amorphous solids are known to fail catastrophically and in some situations, nano-scaled cavities are believed to play a significant role in the failure. In a recent work, using numerical simulations, we have shown the correspondence between cavitation under uniform expansion of amorphous solids and the yielding under shear. In this study, we probe the stability of spatially-homogeneous states sampled from expansion trajectories to alternate modes of driving, viz. macroscopic cyclic shear or local random deformation via activity. We find that, under cyclic shear and activity, the cavitation ins…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain…
The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; na…
Plastic deformation in solids induced by external shear stress is of huge practical interest. Presence of local crystalline order in polycrystals, consisting of many grains, distinguishes its deformation pattern from that of amorphous materials. Despite strong anisotropy, induced by external stress, the plastic flow and the consequent deformation field show strong dynamical heterogeneity. The distribution $P(u)$ of particle displacements ($u$) shows three distinct regimes including a power law scaling regime at moderate displacements. Using a phase field simulation we show how polycrystals gen…
Molecular dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkabl…
Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively[1-14], observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transiti…
Polymer self-adhesion due to the interdiffusion of macromolecules has been an active area of research for several decades [70, 43, 62, 42, 72, 73, 41]. Here, we report a new phenomenon of sub-Tg, solid-state, plasticity-induced bonding; where amorphous polymeric films were bonded together in a period of time on the order of a second in the solid-state at ambient temperatures nearly 60 K below their glass transition temperature (Tg) by subjecting them to active plastic deformation. Despite the glassy regime, the bulk plastic deformation triggered the requisite molecular mobility of the polymer …
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging for standard continuum formulations for solids that are meant for situations with a fixed amount of material. Recent approaches to handle this have used time-evolving reference configurations. In t…
On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the initial stress and in general, for a compressible material, it requires 10 invariants, reducing to 9 for an incompressible material. Expressions for the Cauchy and nominal stress tensors in a finitely deformed configuration are given along with the elasticity tensor and its specialization to the initially stressed undeformed configuration. The equations gov…
We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of dissipation and of material and geometric stability. In particular, the analysis provides bounds on the constitutive parameters and on the pre-deformation that ensure linearized stability in the neighbourhood of a large pre-stretch. This type of result is relevant to the imaging of biological soft tissues using acoustical techniques, where pre-deformation is known to increase contr…
Elastic materials with holes and inclusions are important in a large variety of contexts ranging from construction material to biological membranes. More recently, they have also been exploited in mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson's ratio, mechanical cloaking, and tunable phononic band gaps. Understanding how such structures deform in response to applied external loads is thus crucial for designing novel mechanical metamaterials. Here we present a method for predicting the linear re…
The understanding of sliding friction for wet, patterned surfaces from first principles is challenging. While emerging applications have sought design principles from biology, a general framework is lacking because soft interfaces experience a multiphysics coupling between solid deformation and fluid dissipation. We investigate the elastohydrodynamic sliding of >50 patterned sliding pairs comprising elastomers, thermosets, and hydrogels, and discover that texturing induces a critical transition in the macroscopic friction coefficient. This critical friction scales universally, without any fitt…
Activated solids: Spontaneous deformations, non-affine fluctuations, softening, and failure
Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, Odisha, India（印度物理研究所）；Georg-August-Universität Göttingen, Wilhelmsplatz 1, 37073 Göttingen, Germany（哥廷根大学）；Tata Institute for Fundamental Research Hyderabad, 36/P Gopanapally, Hyderabad 500107, India.（塔塔基础研究院海得拉巴分校）；Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India（霍米·巴巴国立研究所）
The equilibrium amorphous solid state -- formed, e.g., by adequately randomly crosslinking the constituents of a macromolecular fluid -- is a heterogeneous state characterized by a universal distribution of particle localization lengths. Near to the crosslink-density-controlled continuous amorphous-solidification transition, this distribution obeys a scaling form: it has a single peak at a lengthscale that diverges (along with the width of the distribution) as the transition is approached. The modulus controlling macroscale elastic shear deformations of the amorphous solid does not depend on t…
Unravelling the multiscale surface mechanics of soft solids
Universite Lyon 1（里昂第一大学）；CNRS（法国国家科学研究中心）；Institut Lumière Matière（光与物质研究所）；ETH Zürich（苏黎世联邦理工学院）；Yale University（耶鲁大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）；Cornell University（康奈尔大学）
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of large solid-like deformations, in any dimension, of the type that might otherwise require the finite element method. The generality of the method stems from its ability to easily compute kinematic quantities essential to solid mechanics, that are elusive outside of Lagrangian frame. This introductory work focuses on large-strain, hyperelastic materials. After…
We use Shear Transformation Zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts…
The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is not oriented along the liquid vapor interface nor perpendicular to the solid surface, as usually assumed, but points towards the liquid. It is shown that the elastic deformations induced by this force can only be explained if, contrary to an incompressible liquid, the surface stress is different from the surface energy. Using thermodynamic variations we show that the the surface stress and the surface …
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 …
Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited statistical sampling. On the other hand, while existing elasto-plastic depinning models give precise exponent values, these models to date have been limited to a scalar approximation of plasticity which is difficult to reconcile with the statistical isotropy of amorphous materials. Here we introduce for the first time a fully tensorial mesoscale model for the ela…
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses and liquids based on non-affine displacements and the consequent Goldstones phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field -- non-affinity -- which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topologic…
Bonding between polymeric interfaces is encountered widely in several industrial applications. Many of these bonding processes rely on time-consuming and temperature-dependent classical mechanism of polymer interdiffusion via reptation in a melt state. Here, for the first time, we report a new mechanistic pathway for achieving solid-state polymer bonding by triggering rapid macromolecular acceleration through mechanical deformation. Large-scale molecular simulations reveal that active plastic deformation in glassy polymers, at temperatures well-below the bulk (and surface) glass transition tem…
Micromotor and nanomotor particles are typically made using dense solid particles that can sediment or be trapped in confined flow environments. Creation of much larger motors should be possible if a very low-density system is used with sufficient strength to carry liquid and still experience propulsive motion. Light, dense millimotors should also be able to deform more than dense solid ones in constrictions. Millimotors are created from permeable capsules of bacterial cellulose that are coated with catalase-containing metal-organic frameworks, enabling reactive propulsion in aqueous hydrogen …
The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatio-temporal correlations in the undeformed glass that may trigger plastic instability. In contrast, here we show that the topological defects which correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dis…
