Interface Displacement Research Articles

Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities

The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form of the boundary value problem formulated at the microscopic level, a polynomial expression of the virtual velocity is adopted as the minimum microscopic kinematics consistent with the selected macroscopic kinematics of the strain gradient effective continuum. The effective volumetric and interfacial mesoscopic strains and stress measures for the effective substitution are obtained versus the microscopic strains and stresses. The Hill macrohomogeneity condition is successively formulated for continuous interfaces and discontinuous interfaces witnessing strong discontinuities. It highlights the expressions of the effective stress measures associated to the volumetric and interfacial behavior for both classical and higher-order effects.

Behaviour analysis on the vertically loaded bored pile socketed into weak rocks using slip-line theory arc failure surface

Due to the advantages of high bearing capacity and small settlement, rock-socketed bored piles have been commonly used as the foundation for most structures. In this paper, for the vertically loaded bored pile socketed into weak rocks, the shear failure process of the concrete-rock interface was divided into two stages, e.g., a dilatant sliding stage and a post-peak sliding stage, and a bilinear shear model was proposed to describe the relationship between shear stress and concrete-rock relative displacement. The shape of the concrete-rock shear failure surface was determined using the dilatancy effect and the slip-line field theory, and the critical shear displacement of the concrete-rock interface was clarified. Load transfer method of the vertically loaded bored pile socketed into weak rocks was then established to capture the distribution of axial force. Moreover, a parameter study was conducted to assess the influence of the concrete-rock interface roughness, normal stiffness, and residual friction angle on the residual skin friction.

Frontal collision of two nonlinear internal solitary waves in a stratified fluid

Head-on collision of two internal solitary waves (ISWs) in a two-layer inviscid fluid with fully nonlinear free-surface (FS) condition is investigated numerically in this paper. The collision process of and nonlinear interaction of internal solitary waves is studied based on nonlinear potential flow theory and a series of numerical simulations are conducted using a multi-domain boundary element method (MDBEM). The numerical model is validated by experiment for the simulation of ISWs propagating. The computation results show that the collision of ISWs is the asymmetric and nonlinear process in which the rundown motion causes the interface displacement penetrates the interface. The collision leaves imprints on small dispersive trailing waves which accounts for the attenuation with each departing ISW tilting slightly backward with respect to the direction of its propagation. In addition, the characteristic of collision process including run up, residence time, surface wave feature is discussed. During the collision, the wave spends more time falling than rising for all cases and the residence time is very long for waves of small amplitude, large depth ratios and density ratios. Considering the free surface of the top layer whether or not makes contributions to the run up and the residence time is larger if the top boundary is free surface.

Sequential adsorption and interfacial displacement in emulsions stabilized with plant-dairy protein blends

HypothesisMany traditional or emergent emulsion products contain mixtures of proteins, resulting in complex, non-equilibrated interfacial structures. It is expected that protein displacement at oil-water interfaces depends on the sequence in which proteins are introduced during emulsion preparation, and on its initial interfacial composition. ExperimentsWe produced emulsions with whey, pea or a whey-pea protein blend and added extra protein post-emulsification. The surface load was measured indirectly via the continuous phase, or directly via the creamed phase. The interfacial composition was monitored over a three-day period using SDS-PAGE densitometry. We compared these findings with results obtained using an automated drop tensiometer with bulk-phase exchange to highlight the effect of sequential protein adsorption on interfacial tension and dilatational rheology. FindingsAddition of a second protein increased the surface load; especially pea proteins adsorbed to pre-adsorbed whey proteins, leading to thick interfacial layers. The addition of whey proteins to a pea protein- or whey-pea protein blend-stabilized emulsion led to significant displacement of the pea proteins by β-lactoglobulin. We determined that protein-protein interactions were the driving force for this displacement, rather than a decrease in interfacial tension. These outcomes could be instrumental in defining new strategies for plant-animal protein hybrid products.

Derivation of circumferential guided waves equations for a multilayered laminate composite hollow cylinder by state-vector and Legendre polynomial hybrid formalism

A new spectral method based on the hybrid formula system of the state-vector and Legendre polynomials are used to derive the explicit expressions of circumferential guided waves in the anisotropic multilayer composite cylinders with an arbitrary lay-up. In this hybrid method, the state vector was utilized to transform the wave equation, boundary conditions, and interface continuous conditions in the cylinder coordinate system to form the dispersion equation in terms of the state matrix. Then, following the principle of the Galerkin method, projecting the dispersion state matrix equations onto the weight functions consisting of Legendre polynomials, the system of algebraic equation is obtained. The dispersion curves and mode shape can be obtained by solving the eigenvalues and eigenvectors of the system of algebraic equations. This hybrid method uses the orthogonal and recursive properties of the Legendre polynomial to simplify the integral expressions involved in all the matrices and yields the closed-form solutions. Numerical verification, including the cases of isotropic and anisotropic viscoelastic/elastic multilayer cylinders, was conducted to evaluate the performance of the proposed method. The results show that the proposed method overcomes the cumbersome of the traditional Legendre polynomial method to treat the interface displacement and stress continuity. The results also confirm that the hybrid method has the exponential convergence.

Numerical modeling of diffusion-controlled phase transformation using the Darken method: Application to the dissolution/precipitation processes in materials

Many material phase transformations are controlled by mass transport induced by diffusion. To better understand such transformations, numerous modeling strategies at the scale of the moving interfaces exist, with their strengths and weaknesses. Phase-field approaches are based on diffuse interfaces that do not require any interface tracking, as opposed to those based on fixed-grid sharp interface tracking. In the case of binary two-phase systems, in this paper we address the key point of the mass balance equation at the interface involving a concentration jump, which determines the interface moving velocity. We propose a unique diffusion equation for both phases and their interface, based on the component’s chemical potentials which are continuous through the interface and a smooth volume-of-fluid phase representation. This model is achieved in the framework of the Darken method, which involves intrinsic diffusion of components and a drift velocity to which all compounds are subjected. This drift velocity is shown to be that of the interface displacement as well. This methodology is verified for 1D and 3D dissolution/precipitation problems and has a first-order spatial convergence. The 3D simulations of precipitation and dissolution processes of more complex microstructures clearly show a bifurcation of the particle morphology from the initial spherical shape when the diffusion edges of each particle interact with each other. An extension of the diffusion potential to mechanical driving forces should make it possible to deal with mechano-chemical coupling of mass transport.

A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures

We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations for the brittle fracture part. For the application to complex multipatch structures, we propose penalty formulations for imposing all the required interface constraints, i.e., displacement (C0) and rotational (C1) continuity for the structure as well as C0 and C1 continuity for the phase field, where the latter is required only in the case of the fourth-order phase-field model. All involved penalty terms are scaled with the corresponding problem parameters to ensure a consistent scaling of the penalty contributions to the global system of equations. As a consequence, all coupling terms are controlled by one global penalty parameter, which can be set to 103 independent of the problem parameters. Furthermore, we present a multistep predictor–corrector algorithm for adaptive local refinement with LR NURBS, which can accurately predict and refine the region around the crack even in cases where fracture fully develops in a single load step, such that rather coarse initial meshes can be used, which is essential especially for the application to large structures. Finally, we investigate and compare the numerical efficiency of loosely vs. strongly staggered solution schemes and of the second- vs. fourth-order phase-field models.

Microscale diffusion-mechanics model for a polymer-based solid-state battery cathode

A non-linear microscale diffusion-mechanics model combining mass transport and linear momentum balance equations, with elasto-viscoplastic polymer constitutive law and interfacial traction-separation law is proposed to provide a new insight into the effects of viscoplasticity and interfacial damage on the in situ diffusive-mechanical behaviour of a polymer-based cathode for a solid-state battery (SSB). Diffusion and mechanics are coupled through two mechanisms: (1) active particle (AP) volumetric change dependence on Li concentration, and (2) interfacial flux dependence on mechanical opening. The model is resolved for a simple cathode microstructure using an axisymmetric unit cell concept, and integrated with the non-linear finite-element solver ABAQUS with the help of its user subroutines (UMAT and UINTER). Finite-element simulations reveal that plastic deformations of the polymer due to volumetric changes of the AP reduce the value of the interfacial opening displacement, which is desirable for maintaining interfacial flux. The results also demonstrate that slower battery charging rates may lead to a softer polymer response, and thus a smaller interfacial gap. Moreover, a comparison between the linear elastic and current elasto-viscoplastic models for the polymer electrolyte shows that even 5% volumetric shrinkage of the AP leads to an overprediction of the interfacial opening with the linear elastic material law, which limits its validity in modelling polymer-based SSBs.

Interface Displacement and Dynamic Phasor Mapping Equivalence Based Hybrid Simulation for HVAC/DC Power Grids

In the electromagnetic transient (EMT) and transient stability (TS) hybrid simulation, the entire power system is artificially split into two sub-grids, and sub-grids interact with each other via an interface. Thus interface distortions emerge, including latency and errors. The influence of interface latency is quantitated based on a demo circuit containing delayed interaction. Moreover, the principles of improving hybrid simulation interface accuracy are concluded. Inspired by the principles, a novel interface displacement (ID) and dynamic phasor mapping equivalence (DP-ME) interface scheme is proposed. The scheme makes sub-grids at opposite sides of an interface loosely coupled and avoids interface variable form conversion by applying two techniques. 1) Displacement of the partition interface from the converter buses to the control loops and interior of the EMT sub-grid to utilize the built-in inertias. 2) Construction of the DP-ME model to calculate the injected power from EMT to TS sub-grid. Tests based on designed cases and an actual HVAC/DC power grid give credibility to the proposed ID & DP-ME scheme in comparison with full electromagnetic simulation.

Experimental investigation on the propagation characteristics of internal solitary waves based on a developed piecewise dynamic mode decomposition method

The propagation of internal solitary waves (ISWs) flowing over the submerged topography is a strongly nonlinear process. To extract the dynamic characteristics of this process, an improved dynamic mode decomposition method is proposed in this paper, which is named piecewise dynamic mode decomposition (PDMD). The innovation of this method is to split the entire evolution process into several quasi-linear segments before modal analyzing to reduce the requirements on the spatial and temporal resolutions of input measured data. A feasible criterion for linearity is introduced by combining the proper orthogonal decomposition method, which is an important basis of PDMD. The data used in the analysis are provided by the experiments conducted in a stratified wave tank. The experimental conditions are set as ISWs flowing over two typical bottom topographies. The interfacial displacement and flow field information are analyzed as the measured data. Through reconstruction and modal analysis of experimental data, the effectiveness and flexibility of PDMD are verified for the ISW problem. The physical meaning of segmentation points can be explained. Based on the results of model decomposition, the main propagation characteristics of ISWs under different conditions are discussed. The evolution of the waveform or local flow phenomena can be simplified to the superposition of linear modes with frequency information.

Elastocapillarity modeling of multiphase flow-induced solid deformation using volume of fluid method

The interaction between fluids and solids is of great importance in different fields of science and engineering. Such interactions have become of great interest not only at the macroscale, but also at the micro and sub-millimetric scales dominated by capillary forces. At the microscale, the effect of surface tension at the interfacial boundaries plays an important role in defining flow patterns and regimes for a system of immiscible multiphase fluids. Such dynamic forces bring about the deformation of surrounding solid structures. In this paper, we present a multiphase fluid solver, with preferential-wetting boundary conditions at the fluid–solid interface, coupled together with a hyperelastic solid solver via a partitioned approach. The multiphase fluid-solid interaction (FSI) problem is solved by employing the Volume of Fluid (VOF) method for transporting a scalar function which acts as a phase indicator in the multiphase problem. The scalar transport equation is solved on the same mesh as the Navier-Stokes equation to avoid errors from projection. Sharpening of the fluid-fluid interface is achieved algebraically using artificial compression, enforced by Multidimensional Universal Limiter with Explicit Solution (MULES). The surface tension forces are obtained using Filtered Surface Force (FSF) model which filters out unphysical fluxes. The formulation of the multiphase FSI problem is based on the use of Arbitrary Lagrangian Eulerian (ALE). FSI interface displacements are relaxed using the Interface Quasi-Newton with Inverse Least Square root-finding relaxation technique (IQN-ILS). We then validate the model by comparing the present numerical results to experimental data for a static droplet on a soft substrate. The model shows good agreement with experimental data and captures the resulting deformation due to excess Laplace pressure. The model is also tested for a dynamic droplet case, and deformation in a microchannel with obstacles.

Laser-induced ultrasonics for detection of low-amplitude grating through metal layers with finite roughness.

We report on the use of laser-induced ultrasonics for the detection of gratings with amplitudes as small as 0.5 nm, buried underneath an optically opaque nickel layer. In our experiments, we use gratings fabricated on top of a nickel layer on glass, and we optically pump and probe the sample from the glass side. The diffraction of the probe pulse from the acoustic echo from the buried grating is measured as a function of time. We use a numerical model to show how the various physical phenomena such as interface displacement, strain-optic effects, thermo-optic effects, and surface roughness influence the shape and strength of the time-dependent diffraction signal. More importantly, we use a Rayleigh-Rice scattering theory to quantify the amount of light scattering, which is then used as in input parameter in our numerical model to predict the time-dependent diffracted signal.

Lipolysis products formation during in vitro gastric digestion is affected by the emulsion interfacial composition

In this work, we report on the effect of the emulsion interfacial composition on the lipid digestion kinetics of in vitro gastric lipolysis. Emulsions (o/w) were formulated with triolein (5%, w/w) and emulsifiers of different chemical nature (1%, w/w). These emulsifiers included different low-molecular-weight surfactants: sodium taurodeoxycholate (NaTDC, ionic), soy lecithin (LEC, zwitterionic), and tween 80 (TW80, non-ionic); as well as biopolymers: soy protein isolate (SPI) and citrus pectin (CP). Emulsions were subjected to static gastric in vitro digestion. Samples were characterized as a function of digestion time in terms of physicochemical properties (droplet charge, microstructure and particle size analysis) and multiple lipolysis products (HPLC coupled to a charged aerosol detector). The kinetic analysis, based on the % of digested triolein, showed that emulsions stabilized by biopolymers did not represent a barrier for gastric lipase adsorption, reaching the highest extents of lipid digestion (25–28%) in the gastric phase. Emulsions stabilized by low-molecular-weight surfactants presented considerable different behaviors under gastric conditions: lipolysis extents of NaTDC- and TW80-based emulsions were low due to early instability or strong interfacial displacement of gastric lipase, respectively; while the LEC-based emulsion presented a higher lipolysis extent (15%) due to its stability and apparent moderate interfacial displacement of gastric lipase. The quantification of multiple lipolysis products allowed the validation of the gastric lipolysis molecular mechanism previously proposed. The results hereby presented constitute advanced insight in the effect of interfacial design on the kinetics of in vitro gastric lipid digestion.

Analytical model for thermal boundary conductance based on elastic wave theory

Interfacial phonon-mediated heat transport plays a key role in nanoscale materials and devices. We propose a model based on elastic wave theory, that considers the mode conversion of acoustic waves transmitted across an interface and combines isotropic dispersion relations to describe the interfacial phonon thermal transfer process and estimate the thermal boundary conductance (TBC). In this model, we calculate the amplitude ratios of all reflected and transmitted acoustic waves using the frequency-dependent interfacial displacement and stress components of the continuity equation; we then determine the energy transmission coefficient of the three modes of incident waves. Consequently, our model can produce the complete angular and frequency spectra of the phonon transmission coefficients for the three acoustic modes. These results show that the specular scattering dominates the transmission of low-frequency phonons at interfaces (e.g., the transmission coefficients of the Al–Si interface are close to 1 below 4 THz, and due to different elastic properties, the phonons at frequencies below 5 THz dominate the heat transfer for Al–diamond interfaces). In addition, the TBC numerical results by our model for Al–Si and Al–diamond interfaces are consistent with those found in previous experimental works. Compared with existing theoretical models, better prediction values were obtained at temperatures higher than 100 K, which verified the model’s feasibility for phonon transmission coefficients and TBC prediction. Finally, we quantitatively analyze the differences between various theoretical models by considering the mode conversion of interfacial acoustic waves, models using acoustic mismatch simplifications, and the importance of phonon dispersion relations for TBC analysis at high temperatures.

Finite deformation cohesive zone phase field model for crack propagation in multi-phase microstructures

This paper develops a unified phase field model for simulating finite deformation crack evolution and interfacial decohesion in multi-phase elastic materials. Crack propagation is formulated using a phase field model, in which the order parameter $$s=1$$ corresponds to the crack topology. The phase field model at the interface is enhanced with cohesive zone characteristics through a cohesive potential function. The interface displacement discontinuities are regularized using an auxiliary interface phase field order parameter. The cohesive potential is associated with this interface phase field for delineating interfacial decohesion. The model is numerically implemented using a multi-pass staggered solver. Numerical examples involving different failure mechanisms are simulated for examining the performance of the proposed model. Different failure mechanisms such as interfacial debonding, crack kinking and propagation in the brittle matrix, and their interactions are captured by the model. Limited verification tests are conducted with analytical results.

Experimental study on the vertical interface of thin-tile masonry

This article presents the results of an experimental study on the structural behaviour of the vertical mortar thin-tile interface in thin-tile masonry. Four compression tests involving two- and three-leaf prisms made of two different types of mortar were carried out. The Digital Image Correlation (DIC) technique was used to capture the full-field displacement of the mortar thin-tile interface. The experimental results revealed that, while all the leaves presented a similar deformation in the longitudinal direction, transversally, the deformations tended to separate the mortar and tile leaf. Thus, it could be concluded that the failure mode of the thin-tile masonry was due to tensile stress perpendicular to the vertical thin-tile mortar interface (mode I), which seemed to be associated with the transverse deformation of the horizontal mortar joints. An analytical approach for the compressive strength of thin-tile masonry based on the usual equation available in the literature for unreinforced multi-leaf masonry walls has been presented. This model seems suitable for determining the compressive strength of thin-tile masonry, but has a more relevant role for mortar leaf.

Thermoelastic contact of layered materials with interfacial imperfection

This paper reports an investigation of the thermoelastic frictional contact responses of an elastic sphere sliding on an elastic layer-substrate system involving imperfect interfaces. The theoretical solution and numerical modeling of the thermoelastic contact of such material systems include: (1) the mathematical derivation of the closed-form frequency response functions (FRFs) of the thermoelastic field in terms of temperature, thermoelastic displacements and stresses in the layer and the substrate, (2) the numerical contact pressure determination and heat partition evaluation by employing the conjugate gradient method (CGM), and (3) stress and temperature calculations by utilizing the discrete convolution-fast Fourier transform algorithm (DC-FFT). Numerical results from the proposed model indicate that, a stronger discontinuity of interface displacements causes the contact pressure, temperature, and in-plane compressive stress to decrease, but the in-plane tensile stress, out-of-plane (compressive and tensile) stress, and von Mises stress to increase. The results also reveal the behavior transition of the out-of-plane shear stress state due to the change of the interface discontinuity status.

Transport characteristics of liquid-gas interface in a capillary membrane pore

Interface displacement of two phases mainly caused by replacement of one fluid with another one can occur inside the membrane pore during membrane preparation and characterization. This phenomenon is exemplified by measurement of liquid entry pressure (LEP) in membrane distillation, measurement of pore size and pore size distribution by the bubble point method, measurement of pore size and pore size distribution by porometry, wetting of dry membrane and also drying of wet membrane. In most of the theoretical studies, focus was on the transmembrane pressure required for one phase to enter into the membrane pores filled with another phase and little attention was paid to the movement of interface in the capillary. This paper attempts to discuss quantitatively the movement of interface, water/air interface in particular. Therefore, movement of interface was tracked using a well-founded model and consequently the pressure and velocity at the interface and the required time for replacement were studied. In addition, the influence of different parameters including pore radius, contact angle, and membrane thickness was assessed. It was found that the low resistance for the air flow, assumed in Washburn's equation, can be justified as an approximation. Moreover, the model proposed in this work can predict that the pressure at the water/air interface (when air replaces liquid water) may become significantly lower than the atmospheric pressure at the pore exit, causing pore shrinkage. As well, the pressure at the air/water interface (when liquid water replaces air) may become significantly higher than the feed pressure applied at the pore entrance, causing pore expansion.

A CONSTITUTIVE MODEL OF STEEL FIBER REINFORCED CONCRETE UNDER UNIAXIAL TENSION

The addition of randomly distributed short fibers in plain concrete can significantly improve the tensile properties. A modified smeared crack constitutive model for steel fiber reinforced concrete (SFRC) is proposed for the simulation of the mechanical behavior under uniaxial loading. In this model, a two-phase composite law is introduced to modify the elastic stiffness matrix. When the tensile cracking occurs, the model considers the plastic deformation as the interfacial slip displacement on the fiber and employs the bond-slip model to simulate the fiber-bridging behavior on the crack surface. The constitutive model is achieved by a Fortran code in the user subroutine Umat of the finite element software ABAQUS. The comparison between the numerical simulation results and experimental data under uniaxial tension shows that the new model can be used to simulate the SFRC characteristic behavior with good accuracy. By the numerical simulations, we further explore the influence of the SFRC related parameters and provide suggestions for the SFRC practical applications.

A multiscale method for periodic structures using domain decomposition and ECM-hyperreduction

This paper presents a nonlinear multiscale approach for periodic structures in the quasi-static, small strain regime. The approach consists in combining a domain decomposition method in which interface conditions are established through a “fictitious” frame with reduced-order modeling (ROM). We propose to approximate interface displacements, subdomain displacements and Lagrange Multipliers as linear combinations of reduced sets of dominant modes, and to assign to the coefficients of such linear combinations the role of coarse-scale displacements, strains and stresses, respectively. We discuss and propose a method based on subspace rotations that ensures that these three modal approximations lead to stable formulations. The modes of such expansions are determined in an offline “training” stage by applying the truncated Singular Value Decomposition (SVD) to the solutions obtained from Finite Element (FE) analyses. In contrast to other multiscale approaches, such as FE-ROM homogenization schemes, which uses a single unit cell with periodic conditions, here the “training” structures are formed by several unit cells. This way, we allow the SVD to extract also dominant patterns of interaction between subdomains in terms of reactive forces and deformations. This original feature confers to the proposed approach three unique advantages over FE-ROM homogenization schemes, namely: (1) It can deal with unit cells of arbitrary size (no need for scale separation). (2) It can model, not only how forces are transmitted through the structure, but also local effects. (3) It can also handle domains which are only periodic along one or two directions (beam-like or shell structures, respectively). To deal with material nonlinearities, element-wise Gauss integration of reduced internal forces is replaced by an algorithmically improved version of the hyperreduction scheme recently proposed by the author elsewhere, called the Empirical Cubature Method(ECM). Furthermore, we demonstrate that the coarse-scale Degrees of Freedom (DOFs) of a subdomain can be expressed directly in terms of the (fine-scale) stresses and strains at the ECM integration points. This feature dispenses with the need of deploying a special algorithmic infrastructure of intertwined local/global problems, as it occurs in FE-ROM schemes, since the unit cell can be treated as a special type of finite element, in which the centroids of the interfaces and the ECM points play the role of nodes and Gauss points, respectively. To illustrate all these advantages, we present 4 distinct examples: two beam-like structures of rectangular-shape and I-shaped cross-sections, a 2D hexagonal cellular material, and a cylindrical shell made of a porous composite cell. In all 4 cases the proposed method is able to produce coarse-scale models reducing the number of DOFs and integration points by over two orders of magnitude, with errors below 5 %. Interestingly, in the case of the beam-like structures, we show that the method provides 2-node beam finite elements whose kinematics are identical to that predicted by “analytical” beam theories (6 DOFs per node in the case of the rectangular beam), and totally consistent with their 3D full-order counterparts.