Coupling Of Elasticity Research Articles

Deformation dynamics of nanopores upon water imbibition

Capillarity-driven transport in nanoporous solids is widespread in nature and crucial for modern liquid-infused engineering materials. During imbibition, curved menisci driven by high negative Laplace pressures exert an enormous contractile load on the porous matrix. Due to the challenge of simultaneously monitoring imbibition and deformation with high spatial resolution, the resulting coupling of solid elasticity to liquid capillarity has remained largely unexplored. Here, we study water imbibition in mesoporous silica using optical imaging, gravimetry, and high-resolution dilatometry. In contrast to an expected Laplace pressure-induced contraction, we find a square-root-of-time expansion and an additional abrupt length increase when the menisci reach the top surface. The final expansion is absent when we stop the imbibition front inside the porous medium in a dynamic imbibition-evaporation equilibrium, as is typical for transpiration-driven hydraulic transport in plants, especially in trees. These peculiar deformation behaviors are validated by single-nanopore molecular dynamics simulations and described by a continuum model that highlights the importance of expansive surface stresses at the pore walls (Bangham effect) and the buildup or release of contractile Laplace pressures as menisci collectively advance, arrest, or disappear. Our model suggests that these observations apply to any imbibition process in nanopores, regardless of the liquid/solid combination, and that the Laplace contribution upon imbibition is precisely half that of vapor sorption, due to the linear pressure drop associated with viscous flow. Thus, simple deformation measurements can be used to quantify surface stresses and Laplace pressures or transport in a wide variety of natural and artificial porous media.

Roles of chain stretch and concentration gradients in capillary thinning of polymer solutions

Abstract Polymers inhibit the breakup of a liquid filament thinning under surface tension. The coupling of elasticity, capillarity and inertia leads to the well-known beads-on-a-string (BOAS) formation. Additionally, under different conditions, smaller satellite drops can form along the liquid bridge between the main beads. The development of BOAS and satellite drops is controlled by the rheology of the polymer solution. In this study, we consider the roles played by finite extensibility and anisotropic drag on the formation of satellite beads. In particular, we show that the more stretching a polymer chain can undergo, satellite beads are suppressed. The latter stages of capillary thinning has been shown to result in a phase separation resulting in what is referred to as a blistering pattern. We thus also conduct simulations of an inhomogeneous dilute polymer model that considers the competing effects of diffusion and stress gradients. We show that polymer is pulled axially towards the region connecting string and bead. This simple model does not predict a phase separation, but does reveal that pinchoff could be inhibited by the buildup of polymer concentration.

Simulation of droplet bouncing on flexible substrate in 2D and 3D with WC-TL SPH method

Droplet impacts on super-hydrophobic surfaces play an important role in many fields. Previous studies have focused on rigid substrates and ignored the effect of substrate deformation. Simulating droplet impacts on a flexible substrate is a challenge to numerical methods due to the coupling of free surface, elasticity, large deformation and surface tension. In this study, a fully meshfree model of fluid–solid interaction is developed based on the smoothed particle hydrodynamics (SPH) method. The liquid droplet is modeled by the weakly compressible (WC) SPH method, and the flexible substrate is modeled by the total Lagrangian (TL) SPH method. Liquid surface tension is modeled by the continuum surface force (CSF) method through reconstructing the free surface of the droplet. The surface geometry reconstruction process is given for both 2D and 3D cases, enabling the model to simulate the bouncing of droplets in both 2D and 3D cases. Furthermore, in order to reduce the computational cost of 3D simulation, the TL-SPH model combined with shell theory established the TL-SPH-shell model, thus achieving the simulation of 3D droplet impact on thin plates. For verification and testing, the established WC-TL SPH model is used to simulate the process of droplet impact on various substrates, including fixed-fixed and curved beams, micro-pillar substrates, and cantilever beams. The results show that the spreading, retraction and bouncing processes of the droplets interact with the deformation and recovery of the flexible substrate, accompanied by large deformation and dynamic characteristics, which can be effectively simulated by the model.

Piezosuperconductivity: Novel effects in noncentrosymmetric superconductors

We study novel effects in non-centrosymmetric superconductors arising from their unique coupling of Cooper-pair condensate and elasticity. We show that although the much discussed Lifshitz coupling is not observable in a uniform bulk state, it strikingly endows dislocations with a fractional magnetic flux. We also predict a generation of voltage-free strain by a DC current in a P and T-breaking Josephson junction. Viewing superconductors through the lens of higher-form symmetries we identify the Lifshitz coupling as a chemical potential for the approximately conserved winding number, drawing an analogy with pyroelectric insulators.

Coupling Approaches for Classical Linear Elasticity and Bond-Based Peridynamic Models

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. This paper studies the continuous and discrete formulations of three existing approaches for the coupling of classical linear elasticity and bond-based peridynamic models, namely (1) a method that enforces matching displacements in an overlap region, (2) a variant that enforces a constraint on the stresses instead, and (3) a method that considers a variable horizon in the vicinity of the interfaces. The performance of the three coupling approaches is compared on a series of one-dimensional numerical examples that involve cubic and quartic manufactured solutions. Accuracy of the presented methods is measured in terms of the difference between the solution to the coupling approach and the solution to the classical linear elasticity model, which can be viewed as a modeling error. The objective of the paper is to assess the quality and performance of the discrete formulation for this class of force-based coupling methods.

A phase-field multirate scheme with stabilized iterative coupling for pressure driven fracture propagation in porous media

Phase-field methods have the potential to simulate large scale evolution of networks of fractures in porous media without the need to explicitly track interfaces. Practical field simulations require however that robust and efficient decoupling techniques can be applied for solving these complex systems. In this work, we focus on the mechanics-step that involves the coupling of elasticity and the phase-field variable. We develop a multirate scheme in which a coarser time grid is employed for the mechanics equation (i.e., the displacements) and a finer time grid is taken for the phase-field problem. The performance of this algorithm is demonstrated for two test cases.

In-Plane Second-Order Topologically Protected States in Elastic Kagome Lattices

Second-order topological insulators, which exhibit capability of hosting topologically protected zero-dimensional corner states distinct from the well-studied topological edge states, unveil a horizon beyond the conventional bulk-edge correspondence. Motivated by recent experimental observation of Wannier-type second-order corner states in acoustic structures, we investigate numerically and demonstrate experimentally the in-plane edge and corner states in a mechanical kagome lattice. By manipulating simply lattice geometry and quantized characterization, we exploit that the emerging corner states are topologically robust against disorders. We further present a second-order topological insulator with multi-interfaces such that the mechanical energy can be localized in multiple locations, which provides the possibility of practical application in energy harvesting devices. The present study is the physical observation to extend the second-order topological insulator to in-plane elastic dynamics, and modal coupling of in-plane elasticity makes it more challenging to be measured experimentally.

An adaptive finite element method for elastoviscoplastic fluid flows

Elastoviscoplastic fluids are a class of yield-stress fluids that behave like neoHookean (or viscoelastic) solids when the imposed stress is less than the yield stress whereas after yielding, their behaviour is described by a viscoplastic fluid with an additional elastic history. This exceptional behaviour has been recently observed by many yield-stress fluids in rheometric tests such as waxy crude oil, Carbopol gel, etc. Moreover, interesting phenomena have been evidenced experimentally such as the presence of a negative wake and a loss of fore-aft symmetry about a settling particle which are predominantly related to the elastic behaviour of yield-stress fluids (i.e., coupling of elasticity and plasticity). Here, we present a numerical scheme based on the so-called augmented Lagrangian method for numerical simulation of elastoviscoplastic fluid flows. The method is benchmarked by two rheometric flows: Poiseuille and circular Couette flows for which analytical solutions are derived. Moreover, anisotropic adaptive mesh procedure (which was previously introduced for viscoplastic fluid flows by Saramito and Roquet, Comput. Meth. Appl. Mech. Eng., vol. 190, 2001, pp. 5391–5412) is coupled to obtain a fine resolution of the yield surfaces. Finally, the presented method is applied to study more complex flows: elastoviscoplastic fluid flow in a wavy channel.

Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

In this paper, a coupled peridynamic-finite element method for modeling mechanical behavior and damage growth in materials is developed. Peridynamics is a nonlocal continuum model which, in contrast to other continuum models, uses integration instead of spatial derivations in its governing equations. Utilizing integration instead of derivatives is advantageous in modeling fracture since the governing equations remain valid even after the initiation or growth of discontinuities. Although peridynamics can capture material fracture effectively, however due to its nonlocal formulation peridynamics is computationally expensive. To reduce the computational costs, we propose to couple peridynamics with finite elements and use peridynamics only in small zones where higher accuracy is needed. The main challenge in developing such a coupling method is to eliminate the artifacts introduced by the interface of the two subdomains. One of the main issues is spurious wave reflections which occurs because high frequency waves traveling from peridynamic region cannot enter the finite element zone and spuriously reflect back into the peridynamic zone. This will lead to an increase in the energy of the peridynamic zone and will drastically reduce the computational accuracy. The main feature of the proposed method is eliminating the spurious wave reflections such that the coupled method is as accurate as the pure peridynamics.

Boundary control of small solutions to fluid–structure interactions arising in coupling of elasticity with Navier–Stokes equation under mixed boundary conditions

We consider a coupled system of a linearly elastic body immersed in a flowing fluid which is modeled by means of the incompressible Navier–Stokes equations with mixed Dirichlet–Neumann-type boundary conditions. For this system we formulate an optimal control problem which amounts to a minimization under constraints of a hydro-elastic pressure at the interface between the two environments. The corresponding functional lacks convexity and radial unboundedness — a serious obstacle to the solution of the optimization problem. The approach taken to solve it is based on transforming the variable domain occupied by the fluid into a fixed domain corresponding to the undeformed elastic inclusion. This leads to a free boundary elliptic problem. Mathematical challenge also results from the fact that the corresponding quasilinear elliptic model is equipped with mixed (Zaremba type) boundary conditions, which intrinsically lead to compromised regularity of elliptic solutions. It is shown that under the assumption of small strains, the controlled structure is wellposed in suitable Sobolev’s spaces and the nonlinear control-to-state map is well defined and continuous. The obtained wellposedness result provides thus foundation for proving existence of an optimal control, where the latter is based on compensated compactness methods. The change in the boundary conditions makes the analysis different and substantially more challenging — particularly at the level of wellposedness of both uncontrolled and controlled dynamics. A key to the existence/uniqueness theory is a suitable localization of the spatial domain and of the resulting PDE. The geometry of the fluid domain plays a critical role in the arguments. The analysis of optimal control is nonstandard due to the lack of convexity and of radial unboundedness of the associated functional cost — main tools for proving weak lower-semicontinuity of the functional. This difficulty is dealt with the help of compensated compactness.

Molecular Coupling of the Lipid Membrane Elasticity and In-plane Dynamics

Molecular Coupling of the Lipid Membrane Elasticity and In-plane Dynamics

Multi-phase-field method for surface tension induced elasticity

A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases including different types of spherical heterogeneities and a thin plate suspending in a gas environment. It is then used to study the stress distribution inside elastic bodies with non-spherical geometries, such as a solid ellipsoid and a sintered structure. In these latter cases, it is shown that the interplay between deformation and spatially variable surface curvature leads to heterogeneous stress distribution across the specimen.

Sodium Ion Batteries Particles: Phase-Field Modeling with Coupling of Cahn-Hilliard Equation and Finite Deformation Elasticity

The cathode material NaxFePO4 of sodium-ion batteries shows phase changes during intercalation. In this work, a phase-field model for NaxFePO4 is studied for the first time. The Cahn-Hilliard diffusion equation coupled to finite deformation elasticity is derived. Two finite deformation elasticity formulations based on elastic Green strain and logarithmic elastic strain, respectively, are compared. The material parameters for NaxFePO4 are determined. We implemented the model in COMSOL Multiphysics for a spherically symmetric problem of sodium insertion into or extraction from a cathodic particle made of NaxFePO4. The model captures the important feature of phase segregation into a sodium-poor phase FePO4 and a sodium-rich phase Na2/3FePO4. There is a visible difference for the concentration and stress between the small deformation theory and the finite deformation theories. Furthermore, we compare the two cathode materials NaxFePO4 and LixFePO4 of lithium-ion batteries to each other in terms of phase changes and stresses, and show that although the miscibility gap of NaxFePO4 is smaller than that of LixFePO4, the stresses in the cathode material NaxFePO4 are higher in the phase segregated state. As a result, the suppression of phase segregation by the elastic strain energy is more easily achieved in NaxFePO4 compared to LixFePO4.

Coupling of lipid membrane elasticity and in-plane dynamics.

Biomembranes exhibit liquid and solid features concomitantly with their in-plane fluidity and elasticity tightly regulated by cells. Here, we present experimental evidence supporting the existence of the dynamics-elasticity correlations for lipid membranes and propose a mechanism involving molecular packing densities to explain them. This paper thereby unifies, at the molecular level, the aspects of the continuum mechanics long used to model the two membrane features. This ultimately may elucidate the universal physical principles governing the cellular phenomena involving biomembranes.

Effects of inertia on the deformation of drops enclosed by elastic interfaces in linear shear flow

Droplets enclosed by elastic interfaces can be extensively found in nature and engineering applications. For instance, oil-water droplets in petroleum engineering can be surrounded by Asphaltene thin film; biological cells are usually surrounded by elastic biological membranes consisting of lipid bilayers with spectrin proteins; droplets enclosed by polymer membranes or lipid bilayers are also widely found in materials science and engineering. This type of droplets is also an excellent structure for encapsulation, transport and release of active agents due to the presence of elastic interface, thus they are widely used in applications such as cosmetics and drug delivery. To study the deformation behavior of single droplet enclosed by complex interfaces under shear flow is fundamental for understanding rheological characteristics of droplet suspensions and for developing droplet-based substance transport technologies. The presence of various molecules confers the drop interfaces various special mechanical properties, such as resistances to shear deformation, area dilatation and bending deformation. Those special mechanical properties significantly influence the transport characteristics of momentum and energy between droplets and surrounding fluids, thus conventional theories based on surface tension are no longer valid for understanding the dynamics of droplets enclosed by elastic interfaces. Generally, the deformation of droplets enclosed by elastic interfaces under shear flow is mainly governed by the coupling of fluid inertia, interface elasticity and fluid viscosity. Current literatures mostly focus on the deformation of drops with elastic interfaces with inertia neglected, which is based on the assumption of Stokes flow. However, the effects of fluid inertia are of great importance in many cutting edge technologies and in vivo bioprocesses, such as inertial microfluidic technologies for separation and manipulation of droplets, blood flow with moderate Reynolds number in arterial vessel. As such, in this study, a three-dimensional direct numerical simulation model able to simultaneously consider fluid inertia and interface elasticity is developed for two-phase flow by combining the front tracking method and the finite element method. Using this model, we study the effects of particle Reynolds number on the deformation behavior of elastic interface enclosed drops in linear shear flow. It is found that oscillations in transient deformation are presented at high Reynolds numbers, and the amplitude and period of such oscillations increase with the Reynolds number. Both the maximum deformation and steady-state deformation increase with the Reynolds number. Besides, the three-dimensional shapes of drops are alternated with the Reynolds number increased. The physical mechanisms underlying the effects of fluid inertia on the deformation of elastic interface enclosed droplets are also discussed by analyzing the distribution of streamline and pressure inside and outside the droplets at different Reynolds number. In summary, the fluid inertia has significant influences on the deformation behavior of elastic interface enclosed drops, especially at moderate to high Reynolds numbers. These results provide new insights into the deformation and motion of droplets enclosed by elastic interfaces under shear flow. Besides, the numerical method developed in the present study can be further used to study the flow characteristics of complex droplet suspensions such as blood and crude oil emulsions and to develop microfluidic technologies for manipulation and separation of complex droplets such as blood cells.

Linearized hydro-elasticity: A numerical study

In view of control and stability theory, a recently obtained linearization around a steady state of a fluid-structure interaction is considered. The linearization was performed with respect to an external forcing term and was derived in an earlier paper via shape optimization techniques. In contrast to other approaches, like transporting to a fixed reference configuration, or using transpiration techniques, the shape optimization route is most suited to incorporating the geometry of the problem into the analysis. This refined description brings up new terms---missing in the classical coupling of linear Stokes flow and linear elasticity---in the matching of the normal stresses and the velocities on the interface. Later, it was demonstrated that this linear PDE system generates a $C_0$ semigroup, however, unlike in the standard Stokes-elasticity coupling, the wellposedness result depended on the fluid's viscosity and the new boundary terms which, among other things, involve the curvature of the interface. Here, we implement a finite element scheme for approximating solutions of this fluid-elasticity dynamics and numerically investigate the dependence of the discretized model on the ``new terms present therein, in contrast with the classical Stokes-linear elasticity system.

Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?

The `stick-slip' phenomenon is the unsteady relative motion of two solids in frictional contact. Tentative explanations were given in the past by enriching the friction law (for example, introducing static and dynamic friction coefficients). In this article, we outline an approach for the analysis of the `stick-slip' phenomenon within the simple framework of the coupling of linear elasticity with the Coulomb dry friction law. Simple examples, both discrete and continuous, show that the solutions of the steady sliding frictional contact problem may exhibit bifurcations (loss of uniqueness) when the friction coefficient is taken as a control parameter. It is argued that such a bifurcation could account, in some cases, for the `stick-slip' phenomenon. The situations of a single point particle, of a linear elastic bounded body with homogeneous friction coefficient and of the elastic half-space with both homogenous and piecewise constant friction coefficient are analysed and compared.

Mechanical coupling of cytoskeletal elasticity and force generation is crucial for understanding the migrating nature of keloid fibroblasts.

One of the key features of keloid is its fibroblasts migrating beyond the original wound border. During migration, cells not only undergo molecular changes but also mechanical modulation. This process is led by actin filaments serving as the backbone of intra-cellular force and transduces external mechanical signal via focal adhesion complex into the cell. Here, we focus on determining the mechanical changes of actin filaments and the spatial distribution of forces in response to changing chemical stimulations and during cell migration. Atomic force microscopy and micropost array detector are used to determine and compare the magnitude and distribution of filament elasticity and force generation in fibroblasts and keloid fibroblasts. We found both filament elasticity and force generation show spatial distribution in a polarized and migrating cell. Such spatial distribution is disrupted when mechano-signalling is perturbed by focal adhesion kinase inhibitor and in keloid fibroblasts. The demonstration of keloid pathology at the nanoscale highlights the coupling of cytoskeletal function with physical characters at the subcellular level and provides new research directions for migration-related disease such as keloid.

The Simulation Study of Fluid Physical Properties on Drop Formation of Drop-on-demand Inkjet Printing

Inkjet printing is a method for directly patterning and fabricating patterns without the need for masks. However, the physical phenomenon in inkjet printing process is very complicated with the coupling of piezoelectricity, elasticity, and free surface fluid dynamics. The authors use the volume of fluid (VOF) method as implemented in the commercial code FLUENT to model the details of the drop formation process. The influence of viscosity and surface tension of the liquid on the droplet formation process is investigated. Consequently, we find that the speed of liquid plays an important role for the jet stability. The viscosity of liquid greatly influences the final speed of droplet. However, the surface tension of liquid does not much affect the speed of droplet. It changes the shape of the liquid thread and final droplet.

Type-IV Pilus deformation can explain retraction behavior.

Polymeric filament like type IV Pilus (TFP) can transfer forces in excess of 100 pN during their retraction before stalling, powering surface translocation(twitching). Single TFP level experiments have shown remarkable nonlinearity in the retraction behavior influenced by the external load as well as levels of PilT molecular motor protein. This includes reversal of motion near stall forces when the concentration of the PilT protein is loweblack significantly. In order to explain this behavior, we analyze the coupling of TFP elasticity and interfacial behavior with PilT kinetics. We model retraction as reaction controlled and elongation as transport controlled process. The reaction rates vary with TFP deformation which is modeled as a compound elastic body consisting of multiple helical strands under axial load. Elongation is controlled by monomer transport which suffer entrapment due to excess PilT in the cell periplasm. Our analysis shows excellent agreement with a host of experimental observations and we present a possible biophysical relevance of model parameters through a mechano-chemical stall force map.