Elastic Interface Research Articles

Sequential Linear Analysis for the Prediction of the Symmetrical or Non-Symmetrical Character of the Debond Onset and Propagation Along a Fiber-Matrix Interface

In this work, a recently proposed numerical tool is used to predict the onset and growth of debonds appearing along a single glass/carbon fiber embedded in an epoxy matrix subjected to transverse loads. The fiber-matrix system is modelled using the FEA commercial code ABAQUS, together with a solving algorithm programmed in Python and named Sequential Linear Analysis (SLA). Besides, the interface behavior is modeled using the Linear Elastic Brittle Interface Model (LEBIM) included in ABAQUS by means of a UMAT subroutine. The developed models are able to reproduce the non-symmetrical (one-side) debond at the fiber-matrix interface. Moreover, the results obtained show that the appearance of a unilateral debond may be affected both by the material employed and the size of the matrix cell where the fiber is embedded.

An Elastic Interface Model for the Delamination of Bending-Extension Coupled Laminates

The paper addresses the problem of an interfacial crack in a multi-directional laminated beam with possible bending-extension coupling. A crack-tip element is considered as an assemblage of two sublaminates connected by an elastic-brittle interface of negligible thickness. Each sublaminate is modeled as an extensible, flexible, and shear-deformable laminated beam. The mathematical problem is reduced to a set of two differential equations in the interfacial stresses. Explicit expressions are derived for the internal forces, strain measures, and generalized displacements in the sublaminates. Then, the energy release rate and its Mode I and Mode II contributions are evaluated. As an example, the model is applied to the analysis of the double cantilever beam test with both symmetric and asymmetric laminated specimens.

Seismiclike organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks.

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

Elastic–slip interface effect on the diffraction of plane waves around a saturated lining structure in saturated soil

By combining Biot's dynamic wave theory with the elastic and slip interface theory, the scattering of plane waves around a saturated lining structure embedded in saturated soil is studied. The lining structure is assumed to be arbitrary shape. Separating variable method of Helmholtz equations leads to the semi-analytical solutions of the potentials. By using the conformal mapping method, the lining structures of arbitrary shape can be mapped to the cirque at the same centre with different radii. The elastic and slip material constants of interface are introduced to analyze the effect of interfacial properties. The dynamic stress and pore pressure are solved by applying the displacement and stress boundary conditions with interface effect. In numerical examples, the dynamic stress and pore pressure under different interface coefficients (normal and circumferential spring coefficients and slip coefficient) are analyzed. It is found that the effect of normal spring coefficient is larger than that of circumferential spring coefficients. The imperfect interface effect on the dynamic stress and pore pressure is also related with the wave frequencies.

Elastic stiffness of metallic multilayers studied by picosecond ultrasonics: improved interpretation of interface elasticity

In metallic multilayers, elastic stiffness is often reported to decrease with an increasing number of interfaces. This phenomenon is generally attributed to softening at interfaces, and a decrease of 50% or more in interface stiffness is expected. This interpretation of the elastic stiffness of metallic multilayers is commonly accepted; however, we propose that the decrease of interface stiffness is doubtful because it is difficult to explain the large decrease using existing models. In the present study, to confirm the validity of the decrease of interface stiffness, the longitudinal-wave elastic stiffness in the stacking direction is measured using picosecond ultrasonics. The elastic stiffness of Cr/Fe, Cu/Co, and Nb/Cu multilayers with several thickness ratios is measured, and the decrease in multilayer stiffness is experimentally demonstrated to arise from the decrease in stiffness of each layer, not from a decrease in interface stiffness.

Effects of surface/interface elasticity on the screw dislocation-induced stress field in an elastic film–substrate system

In the analysis of continuum-based models describing the dislocation mechanism for a film–substrate system, it is customary to treat the surface of the film as ‘traction-free’ or ‘perfectly bonded’ to the substrate. For an ultra-thin film, however, the appreciable surface to volume ratio is known to be responsible for considerable surface energies which contribute significantly to the overall deformation of the structure. Consequently, in order to ensure a sufficiently accurate account of the corresponding dislocation behavior, it becomes necessary to incorporate the contribution of surface/interface effects into the description of deformation of the film surface or film–substrate interface. In this paper, we study the effects of surface/interface elasticity on the mechanical behavior of a screw dislocation embedded in a thin film bonded to an elastic substrate. Using conformal mapping techniques, we derive a semi-analytical solution for the dislocation-induced stress field in the film–substrate system. Our results show that when the thickness of the film approaches the nanoscale, failure to incorporate surface/interface elasticity into the description of the corresponding surface or interface may induce significant errors in the stress field and in any predictions involving the mobility of the dislocation. More specifically, we show that whereas the incorporation of surface elasticity with positive shear modulus always relieves the stress concentration on the surface of the film–substrate system, interface elasticity with positive shear modulus can either relieve or intensify the stress concentration (for the film) on the film–substrate interface depending on the stiffness of the substrate. In particular, for an ultra-thin film bonded to a soft substrate, we find that the presence of interface elasticity greatly influences the (unstable) equilibrium position of the dislocation in the film.

Elastic field at a rugous interface of a bimaterial with surface effects

The two-dimensional problem of elasticity incorporating surface effect at a rugous interface of bimaterial is considered. The current study is directed towards developing the theoretical model for analysing the stress distribution along nanosized interface irregularities of isotropic bimaterial systems, as the fracture of heterogeneous materials is strongly influenced by the stress concentrations around topological defects in an interface region. Based on the simplified Gurtin-Murdoch model of surface elasticity and the boundary perturbation method combined with the complex variable technique, the original boundary value problem is reduced to the sequence of hypersingular integral equations for any-order approximation. For the first-order approximation and periodic shape of the interface, the solution is obtained in an explicit form of Fourier series. The closed form expression for the hoop stress at the interface is derived in the case of the harmonic shape of the interface. Some detailed numerical investigations of the influence of mechanical characteristics of the interface, the shape and the size of interface asperities, and the elastic properties of the bimaterial components on the hoop stress and stress concentration are presented. It is shown that the incorporation of an interfacial energy exhibits properties that cannot be obtained using classical approach. For instance, the size effect is revealed, namely, the stress concentration depends on the deviation amplitude of the interface undulation at the nanoscale when the ratio of this amplitude to the period is constant; allowing for the interface elasticity reduces the concentration of the hoop stresses if the interface tension is neglected; if external loading is absent or relatively small, the elastic field at the interphase region is determined by the value of the interface tension and depends on geometric and elastic properties of the interface.

Transient magnetic-domain-wall ac dynamics by means of magneto-optical Kerr effect microscopy

The domain wall response under constant external magnetic fields reveals a complex behavior where sample disorder plays a key role. Furthermore, the response to alternating magnetic fields has only been explored in limited cases and analyzed in terms of the constant field solution. Here we unveil phenomena in the evolution of magnetic domain walls under the application of alternating magnetic fields within the creep regime, well beyond a small fuctuation limit of the domain wall position. Magnetic field pulses were applied in ultra-thin ferromagnetic films with perpendicular anisotropy, and the resulting domain wall evolution was characterized by polar magneto-optical Kerr effect microscopy. Whereas the DC characterization is well predicted by the elastic interface model, striking unexpected features are observed under the application of alternating square pulses: magneto-optical images show that after a transient number of cycles, domain walls evolve toward strongly distorted shapes concomitantly with a modification of domain area. The morphology of domain walls is characterized with a roughness exponent when possible and contrasted with alternative observables which result to be more suitable for the characterization of this transient evolution. The final stationary convergence as well as the underlying physics is discussed.

Accurate modelling of instabilities caused by multi-site interface-crack onset and propagation in composites using the sequentially linear analysis and Abaqus

Even well-established non-linear FEM codes may present convergence issues when solving highly unstable problems, e.g. fracture mechanics problems, especially in the presence of a pronounced snap-back behaviour. In composites, at lamina level, the debonds occurring between the fibres and matrix, lead to multiple-crack configurations. Each individual debond growth is an unstable process. Then, when multiple debonds occur the problem becomes highly unstable. Moreover, experimental evidence shows that a sequence of multiple debonds originates a macro-crack that extends over the whole lamina thickness. In this article a new Python based numerical tool implementing a Sequentially Linear Analysis (SLA) procedure, which is able to call the FEM software Abaqus, is described and tested. The Linear Elastic Brittle Interface Model (LEBIM) is also included in Abaqus by means of a UMAT subroutine. Numerical results for a representative 100-fibre model show that the tool is able to adequately model simultaneous onset and propagation of multiple debonds resulting in a completely unstable process composed by a series of instability events. Eventually, these numerical results together with some previous experimental results for transverse failure loads for unidirectional carbon fibre-epoxy matrix plies allow us to estimate the tensile strength and critical fracture energy of the fibre-matrix interface by a simple inverse analysis.

Simulation of spatially variable seismic underground motions in saturated double-phase media with overlying water excited by SV-wave and difference from P-wave incidence

The spatial seismic excitations affected by water-saturated soil, a double-phase medium, and overlying water are desirable to be considered for evaluating the seismic response of some typical structures such as large-span cross-sea bridges considering soil-structure interaction. This paper focuses on the study of a theoretical method and numerical simulation of multi-support seismic underground excitations in saturated soil with overlying water for obliquely incident SV waves that can produce P1, P2 and SV waves in saturated soil. First, the reflection coefficients (results are different from the case for P waves incidence) of three kinds of waves (P1, P2, SV) at the interface between saturated soil and overlying water are derived. Based on the reflection coefficients and the boundary conditions at the elastic solid-saturated soil interface, the transfer functions of soil layers with arbitrary depths are proposed to calculate the key elements (i.e., the underground power spectral density, response spectrum function and underground coherency function) for generating the multi-support seismic underground motions. Second, these three key elements are used to establish the underground power spectral matrix, and then the underground motions are generated by decomposing the matrix. Finally, the method is verified by numerical examples and the influences of overlying water depth and incident angle on ground motions are investigated. The effect of incident angle on transfer functions show great difference between the small-angle and large-angle case. Moreover, the phenomenon that is diffrent from P-waves incidence case is investigated,found and emphasized, and the reasons are given.

A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals

In this paper, we propose a Petrov-Galerkin finite element interface method (PGFEIM) to solve the elliptic and elastic interface problems with Bloch-periodic boundary conditions. The main idea of this method is to choose the standard finite element basis independent of the interface to be the test function basis, and choose a piecewise linear function satisfying the jump conditions across the interface to be the solution basis. The grid we use is a non-body-fitted grid. The PGFEIM is capable of dealing with sharp-edged interface problems with matrix coefficients and nonhomogeneous jump conditions. Further, we extend this method to compute the band structure of anti-plane transverse waves and in-plane elastic waves in phononic crystals. Different acoustic impedance ratios, arbitrary complex scatterer geometries and various material properties are considered and discussed. Numerical experiments demonstrate that the PGFEIM is nearly second order accurate in the L∞ norm for interface problems, and it is accurate and efficient for computing the band structure of phononic crystals.

Stress Controllability in Thermal and Electrical Conductivity of 3D Elastic Graphene‐Crosslinked Carbon Nanotube Sponge/Polyimide Nanocomposite

AbstractStress controllability in thermal and electrical conductivity is important for flexible piezoresistive devices. Due to the strength‐elasticity trade‐off, comprehensive investigation of stress‐controllable conduction in elastic high‐modulus polymers is challenging. Here presented is a 3D elastic graphene‐crosslinked carbon nanotube sponge/polyimide (Gw‐CNT/PI) nanocomposite. Graphene welding at the junction enables both phonon and electron transfer as well as avoids interfacial slippage during cyclic compression. The uniform Gw‐CNT/PI comprising a high‐modulus PI deposited on a porous templated network combines stress‐controllable thermal/electrical conductivity and cyclic elastic deformation. The uniform composites show different variation trends controlled by the porosity due to different phonon and electron conduction mechanisms. A relatively high k (3.24 W m−1 K−1, 1620% higher than PI) and suitable compressibility (16.5% under 1 MPa compression) enables the application of the composite in flexible elastic thermal interface conductors, which is further analyzed by finite element simulations. The interconnected network favors a high stress‐sensitive electrical conductivity (sensitivity, 973% at 9.6% strain). Thus, the Gw‐CNT/PI composite can be an important candidate material for piezoresistive sensors upon porosity optimization based on stress‐controllable thermal or electrical conductivity. The results provide insights toward controlling the stress‐induced thermal/electrical conductivities of 3D interconnected templated composite networks for piezoresistive conductors or sensors.

Dry-bonding to dentin using alternative conditioners based on iron-containing solutions or nitric acid

ObjectivesTo evaluate the effect of experimental conditioners (10–3 solution − 10–3, 6.8% ferric oxalate - FOX, and 1.4% nitric acid - NI) on dentin elastic modulus, flexural strength, bond strength, failure mode, and adhesive interface morphology of two etch-and-rinse adhesives (XP Bond, Dentsply or One-Step, Bisco) applied on etched dry dentin. MethodsSound human third molars were used for the microtensile bond strength test (n = 8), performed at 24 h and after one year of water storage. Failure modes were evaluated by scanning electron microscopy. Dentin bonding interface was analyzed by confocal laser scanning microscopy (n = 3). Adhesive systems were applied on phosphoric acid-etched, wet (positive control) and dry (negative control) dentin, and on etched and dry dentin previously treated with 10–3 (15s), FOX (60s), or NI (15s). Bovine dentin bars (n = 15) were immersed into the conditioning solutions and subjected to a three-point bending test. ResultsXP Bond + 10–3 or NI resulted in lower bond strength than phosphoric acid. One-Step + 10–3 or NI resulted in bond strengths equivalent to the positive control. Experimental conditioners presented no bond strength reduction after one year, regardless of the bonding agent tested. One-Step resulted in more adhesive failures than XP Bond at 24 h, and mixed failures increased after storage. All experimental conditioners promoted hybridization and resin tags formation, except FOX. Dentin elastic modulus was not affected by the conditioners, whereas flexural strength was significantly reduced by FOX. ConclusionsAdequate and stable dentin bonds were achieved when the bonding agents were applied on 10–3 or NI-treated dentin. None of the experimental conditioners reduced dentin elastic modulus, but dentin flexural strength was significantly reduced by FOX-conditioning.

Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods

Many interface formulations, e.g. based on asymptotic thin interphase models or material surface theories, involve higher-order differential operators and discontinuous solution fields. In this article, we are taking first steps towards a variationally consistent discretization framework that naturally accommodates these two challenges by synergistically combining recent developments in isogeometric analysis and cut-cell finite element methods. Its basis is the mixed variational formulation of the elastic interface problem that provides access to jumps in displacements and stresses for incorporating general interface conditions. Upon discretization with smooth splines, derivatives of arbitrary order can be consistently evaluated, while cut-cell meshes enable discontinuous solutions at potentially complex interfaces. We demonstrate via numerical tests for three specific nontrivial interfaces (two regimes of the Benveniste–Miloh classification of thin layers and the Gurtin–Murdoch material surface model) that our framework is geometrically flexible and provides optimal higher-order accuracy in the bulk and at the interface.

Understanding the role of general interfaces in the overall behavior of composites and size effects

The objective of this contribution is to investigate the role of generalized interfaces in the overall response of particulate composites and the associated size effects. Throughout this work, the effective properties of composites are obtained via three-dimensional computational simulations using the interface-enhanced finite element method for a broad range of parameters. The term interface corresponds to a zero-thickness model representing the interphase region between the constituents and accounting for the interfaces at the micro-scale introduces a physical length-scale to the effective behavior of composites, unlike the classical first-order homogenization that is missing a length-scale. The interface model here is general in the sense that both traction and displacement jumps across the interface are admissible recovering both the cohesive and elastic interface models. Via a comprehensive computational study, we identify extraordinary and uncommon characteristics of particle reinforced composites endowed with interfaces. Notably, we introduce the notion of critical size at which the overall behavior, somewhat surprisingly, shows no sensitivity with respect to the inclusion-to-matrix stiffness ratio. Our study, provides significant insight towards computational design of composites accounting for interfaces and in particular, nano-composites.

Interfacial Activity and Self-Assembly Behavior of Dissolved and Granular Octenyl Succinate Anhydride Starches.

The mechanisms of granular octenyl succinate anhydride (GOSA) and dissolved OSA (DOSA) starches in emulsion stabilization were investigated. In general, DOSA starch offered better emulsification activity by generating greater ζ-potential, lower particle size as well as long-term stability in comparison to GOSA starch of close degree of substitution (DS). A compact interface in DOSA starches was determined, resulting from an increased surface loading value of 2.37 mg/m2 in comparison to that of GOSA of 1.6 mg/m2. Additionally, the irreversibly adsorbed and predominantly elastic interface of both DOSA and GOSA starches indicated that the DOSA starch may be a Pickering emulsifier rather than a biopolymer surfactant. This assumption was confirmed by transmission electron microscopy. Spherical micelles with average diameters of 100 nm were observed above the critical micelle concentration of 1 mg/mL. Moreover, samples G28 (representing DS of 0.028), D28, G16, and D16 could reach equilibrium interfacial tensions of 19.4, 16.5, 20.0, and 19.3 mN/m, respectively. However, due to the misleading contact angle as a result of rough surfaces and nonignorable gravity of GOSA starch, the energy escape equation failed to be employed in this study.

Evolution equation for nonlinear Lucassen waves

A nonlinear, fractional, surface-wave equation was developed recently by Kappler et al. [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible medium. Linear theory for attenuation and dispersion of such a wave was developed originally by Lucassen [Trans. Faraday Soc. 64, 2221 (1968)]. Kappler et al. employ a fractional derivative to account for the Lucassen attenuation and dispersion, and they include quadratic and cubic nonlinearity of the elastic interface. Presented here is a simplified form of their model equation for plane progressive waves. The resulting nonlinear evolution equation has the form of a Burgers equation but with a fractional derivative in place of the second derivative for viscosity, and with cubic as well as quadratic nonlinearity. In addition to facilitating analytical and numerical calculations, the evolution equation enables interpretation of a threshold phenomenon, revealed in numerical simulations presented by Kappler et al., as competition between quadratic and cubic nonlinearity. It is also suitable for determining critical source amplitudes above which Lucassen attenuation and dispersion alone cannot preclude formation of unphysical multivalued waveforms [Cormack and Hamilton, Wave Motion 85, 18 (2019)]. [BES and JMC were supported by the ARL:UT McKinney Fellowship in Acoustics.]

Nonlinear buckling analysis of damaged laminated composite plates

An updated Lagrangian-based nonlinear finite element method is developed to study the buckling behavior of damaged laminated composite plates under uniaxial compression. In this study, material imperfections are treated as existing static damage and a continuum damage mechanics-based approach is used to model such imperfections. The laminated plate is modeled as a set of elementary layers bonded together by matrix-rich elastic interface. This allows to model different modes of damage present at both elementary ply level and interply interface separately. A layerwise plate model is used to model both elementary ply and interface layers of the laminate. The effect of different forms of existing static damage on the limit point loads and the corresponding displacements of laminated plates are studied. It is observed that for the chosen modes and size of the damaged regions, the limit point load does not change much as compared to the undamaged plate. However, the deformed shapes show significant changes and some very interesting phenomena like local wrinkling behaviour of the damaged region is observed. The effect of ply orientation along with different modes of damage on the limit points and the corresponding deformed shapes of laminated plates are also discussed.

Insight into the Interfacial Elastic Contact in Stacking Perovskite Solar Cells

AbstractStacking perovskite solar cells (PSCs) are emerging cells with two detached electrodes during fabrication process, in which the crucial step is the intimate mechanical and electronic contact between the laminated parts. The interfacial elastic contact of stacking PSCs with four different p‐type organic semiconductors has been systematically studied. Studies confirm that poly(3,4‐ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) is an elastic interface material with excellent performance. The convex–concave morphology of PEDOT:PSS surface and the interfacial elastic deformation make a contribution to a desirable conductive contact between two electrodes with sufficient contact area, thereby providing a highly reliable connection and efficient charge transport channel between the semi‐cells. Based on conducting polymer PEDOT:PSS, planar‐structured stacking PSCs are fabricated exhibiting power conversion efficiency of 13.49% with 1.0 cm2 area. Connecting electrodes with excellent conductivity and elasticity are also proved to be essential to the flexible assembly and readily detachment.

Wrinkling and folding patterns in a confined ferrofluid droplet with an elastic interface.

A thin elastic membrane lying on a fluid substrate deviates from its flat geometry on lateral compression. The compressed membrane folds and wrinkles into many distinct morphologies. We study a magnetoelastic variant of such a problem where a viscous ferrofluid, surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity comes into play when the fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. A perturbative linear stability theory is used to investigate how the combined action of magnetic and elastic forces can lead to the development of smooth, low-amplitude, sinusoidal wrinkles at the elastic interface. In addition, a nonperturbative vortex sheet approach is employed to examine the emergence of highly nonlinear, magnetically driven, wrinkling and folding equilibrium shape structures. A connection between the magnetoelastic shape solutions induced by a radial magnetic field and those produced by nonmagnetic means through centrifugal forces is also discussed.