Thick Elastic Layer Research Articles

Modified double cantilever beam test method for mode-I energy release rate of elastic adhesive layers

This study proposes a Mode I double cantilever beam (DCB) test method for debonding thick elastic adhesive layers. The approach integrates Bernoulli–Euler beams connected via spring elements akin to Winkler’s foundation. Energy release rate determination considers crack length correlation with elastic deformation in the crack-front region, accounting for both beam rotation and lateral movement. Evaluation of Ti6Al4V samples bonded with FM 309 adhesive revealed higher initial energy release rates with the conventional beam theory and conservative values with the modified beam theory. The proposed method offered improved consistency, and less conservative energy release rate values compared to the modified theory.

Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system

Modern transducers and actuators may have functional layers with multi-field coupling and some elastic layers. This paper considers a tubular bilayer system consisting of a thin dielectric tube coated with a thick elastic layer. We study the nonlinear electromechanical response and the linear axisymmetric vibration of the system subject to different applied voltages and inner/outer pressures within the framework of the general nonlinear theory of electro-elasticity, the related linear incremental theory, and by considering the continuity conditions at the interface. We investigate instability behaviour using the same basic formulae. The state-space method provides efficient and accurate free vibration analysis, considering the dynamic response at the lowest frequencies, so we can neglect the viscous and damping effects, which is well suited to this problem. New results indicate that the bilayer system improves its frequency capability and stability compared to the monolayer dielectric tube. The thick outer elastic layer stiffens the bilayer system against axisymmetric bifurcation, bulging and necking instabilities. It also performs better in front of axisymmetric instability, increasing the system’s capability to receive or produce higher voltages, especially for long waves.This work thoroughly explains bilayer functional systems’ behaviour when exposed to extreme environments such as high voltage or pressure.

An adhesive detachment paradox: Does the substrate thickness matter?

A normal adhesive contact between a flat-ended cylindrical punch with elliptical cross-section and the surface of an elastic substrate, which can be regarded as an elastic layer of finite thickness, is considered. The experimental evidence published elsewhere indicates that the initiation of detachment can occur at the ends of the minor axis of the elliptical contact area, which eventually comes into contradiction with the surface energy theory developed so far. This paradox of adhesive detachment is examined in the framework of the JKR-type model formulated in terms of the stress intensity factor (SIF) of the contact normal stress. Based on the asymptotic model for a relatively thick elastic layer, the contact SIFs at the ends of the minor axis are shown to grow with decreasing the relative layer thickness faster than those at the ends of the major axis of the initial contact area. A plausible explanation for the observed inconsistency between experiment and state-of-the-art theory is found in the effect of the nonuniform elastic deformations on the square root singularity of the contact pressure at the punch edge.

Post‐Rifting Relaxation During 2015–2020 Following the Bárðarbunga‐Holuhraun Dike Intrusion and Eruption in Iceland

AbstractPost‐rifting ground deformation may be driven by viscoelastic relaxation of stresses generated by dike intrusions. The single‐dike intrusion of the 2014–2015 Bárðarbunga eruption in Iceland presents an opportunity for a detailed study of this process. We use continuous Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) velocity fields to analyze the 2015–2020 post‐rifting deformation, showing uplift on both sides of the dike and horizontal displacement away from the dike after correcting for background deformation. Two GNSS stations experience baseline lengthening at a rate of 19 mm/yr in the direction perpendicular to the strike of the dike. A two‐layer viscoelastic model with a 0.4 × 1019 Pa s viscoelastic half‐space overlain by an 18 km thick elastic layer best explains the observed horizontal and vertical InSAR and GNSS displacements. The model misfit space shows a second regime of good fit, likely driven by deformation near the dike that may result from cooling compaction of the emplaced dike.

Ground Deformation After a Caldera Collapse: Contributions of Magma Inflow and Viscoelastic Response to the 2015–2018 Deformation Field Around Bárðarbunga, Iceland

AbstractImprovement of our understanding of the role of ground deformation due to viscoelastic relaxation following eruptions is important, as the generated signals can resemble renewed magma inflow. We study post‐eruptive unrest at the subglacial Bárðarbunga volcano, Iceland, after a caldera collapse and major magma drainage in 2014–2015. Elevated seismicity began about 6 months after the eruption ended, including nine Mlw > 4.5 earthquakes. Global Navigation Satellite System and Sentinel‐1 Interferometric Synthetic Aperture Radar geodesy are applied to evaluate post‐eruptive ground deformation from 2015 to 2018. Horizontal velocities locally exceed 10 cm/year and rapidly decay with distance away from the caldera. We explore two end‐member models and their combination to explain the post‐eruptive deformation field: 1) viscoelastic relaxation caused by the co‐eruptive caldera collapse and magma withdrawal, and 2) renewed magma inflow. We find parameter combinations for each model that explain the observed ground deformation. The purely viscoelastic relaxation model, consisting of a half‐space composed of a 7‐km thick elastic layer on top of a viscoelastic layer with a viscosity of 3.0 × 1018 Pa s reproduces broadly the observations. A simple magma inflow model consisting of a single point source with an inflow rate of 1 × 107 m3/year at 0.7 km depth broadly fits the observations, but may be unrealistic. A more elaborate model of magma inflow into a 10‐km deep sill combined with slip on the caldera ring fault explains the observations well. Our results suggest that the co‐eruptive deformation field is likely influenced by viscoelastic relaxation, renewed magma inflow, or a combination of both processes.

Failure of a pre-cracked epoxy sandwich layer in shear

Adhesive joints are frequently used in automotive, maritime and construction applications, yet joint reliability remains a concern. The purpose of this study is to develop a fracture mechanics methodology for the failure of an elastic-brittle lap-shear joint comprising a thick adhesive layer (an epoxy, of thickness on the order of 10 mm) sandwiched between thick steel adherends. This configuration is of practical application to ship-building, such as the bonding of a superstructure to the underlying hull. A modified thick-adherend shear test (TAST) is designed, and specimens are fabricated, with a range of interfacial pre-crack length and a range of adhesive layer thickness. The failure of samples with no pre-crack is governed by a critical value of corner singularity, whereas the failure of samples with long pre-cracks is governed by a critical value of interfacial stress intensity factor. Predictions for the dependence of failure load upon layer thickness and pre-crack length are obtained by analysing the elastic stress state for both a corner singularity and for an interfacial crack. Both the experimental results and the theoretical framework are useful in the design and fabrication of reliable lap-shear joints that comprise a thick elastic adhesive layer.

Sensitivity of elastic thickness to water in the Martian lithosphere

Ancient Mars likely hosted oceans similar to those on Earth; however, such water is not presently observed on Mars. One possible explanation for the lack of present-day oceans is that surface water was transported into and stored within the interior of Mars throughout the geological history. As water can influence the rheological structure of the Martian lithosphere, we investigated the sensitivity of the elastic thickness of the lithosphere to water using recent laboratory data. Calculations indicate that the presence of water results in a significant decrease in elastic thickness relative to dry conditions at a given thermal structure. Gravity and topographic data acquired by the Mars Global Surveyor and other orbiters indicate a temporal change in elastic thickness during the geological history of Mars. The extremely thin elastic layer during the planet’s early history can be explained by a water-rich rheological model, whereas a dry rheology can account for the relatively thick elastic layer inferred during the later evolution of Mars. Although thermal evolution of Mars has a large uncertainty, the strong sensitivity of elastic lithospheric thickness to water suggests possible sequestered water into deeper levels during the early history of Mars.

Buckling of a compliant hollow cylinder attached to a rotating rigid shaft

Bifurcations in the equilibrium shape of a thick elastic layer attached to a circular rigid cylinder rotating about its axis are investigated analytically and numerically. The centrifugal force breaks the symmetry of the system leading to deformations invariant along the axis as the result of an instability. The instability threshold depends at linear order on the relative thickness of the compliant layer, and on a dimensionless control parameter based on the elastic modulus, the angular velocity and the outer radius. A weakly non linear analysis, carried out for layers following the Mooney–Rivlin constitutive law, points out the discontinuous (sub-critical) features of the bifurcation, except for relative thickness laying in a very narrow range in which the bifurcation is super-critical. Numerical simulations in the fully post-buckled regime yield the absolute instability threshold, and the order in the rotational symmetry of the developed equilibrium shape.

In situ X-ray diffraction of lead zirconate titanate piezoMEMS cantilever during actuation

Synchrotron X-ray diffraction (XRD) was used to probe the electric-field-induced response of a 500nm lead zirconate titanate (52/48, Zr/Ti) (PZT) based piezoelectric microelectromechanical system (piezoMEMS) device. 90° ferroelectric/ferroelastic domain reorientation was observed in a cantilever comprised of a 500nm thick PZT film on a 3μm thick elastic layer composite of SiO2 and Si3N4. Diffraction data from sectors both parallel- and perpendicular-to-field showed the presence of ferroelastic texture, which is typically seen in in situ electric field diffraction studies of bulk tetragonal perovskite ferroelectrics. The fraction of domains reoriented into the field direction was quantified through the intensity changes of the 002 and 200 diffraction profiles. The maximum induced volume fraction calculated from the results was 20%, which is comparable to values seen in previous bulk and thin film ferroelectric diffraction studies. The novelty of the present work is that a fully released ferroelectric thin film device of micron scale dimensions (down to 60,000μm3) was interrogated in situ with an applied electric field using synchrotron XRD. Furthermore, the experiment demonstrates that 90° ferroelectric/ferroelastic domain reorientation can be characterized in samples of such small dimensions.

Effect of Prestresses on the Dispersion of Waves in a System Consisting of a Viscous Liquid Layer and a Compressible Elastic Layer

The propagation of acoustic waves in a prestrained compressible elastic layer that interacts with a compressible viscous liquid layer is considered. Use is made of the three-dimensional equations of the linearized theory of finite deformations for the elastic layer and the three-dimensional linearized Navier–Stokes equations for the liquid layer. The problem statement and problem-solving method used are based on the general solutions of the linearized equations for the elastic and liquid layers. A dispersion equation describing the propagation of harmonic waves in the hydroelastic system over a wide frequency range is derived for both thin and thick elastic layers. The effect of the prestresses and the thickness of the layers on the phase velocities and damping factors of modes is analyzed for thin and thick elastic layers. It is established that for all the modes beginning from the second one, there are certain values of fluid thicknesses and frequency at which the pretension in the elastic layer do not affect their phase velocities and damping factors. If the elastic layer is thick, each mode generated by the fluid is shown to have three such frequencies. The approach developed and the results obtained allow us to identify the limits of applicability of models based on various theories of small initial deformations and the ideal-fluid model

Wave Propagation in an Elastic Layer Interacting with a Viscous Liquid Layer

The Navier–Stokes three-dimensional linearized equations for a viscous fluid and the linear equations of classical elasticity for an elastic layer are used to plot dispersion curves and to study the propagation of acoustic waves over a wide frequency range. The effect of the viscosity of the fluid and the thickness of the elastic and liquid layers on the phase velocities and the damping factors of the modes is analyzed for both thin and thick solid layers. It is shown that for the thick elastic layer, there are certain thicknesses of the liquid layer and certain frequencies at which the effect of the viscosity of the fluid on the phase velocities and damping factors of all the modes is the weakest. It is also revealed that for a number of modes, there are certain frequencies and certain frequency ranges for which the effect of the viscosity of the fluid on the phase velocities and damping factors of the modes is strong. The approach developed and the results obtained allow identifying the limits of applicability of the model of ideal compressible fluid. The numerical results are presented in the form of plots and analyzed

Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part II. Control Problems of Field of Transverse Dynamic Displacements of Layer

Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part II. Control Problems of Field of Transverse Dynamic Displacements of Layer

Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part I. Mathematical Modeling of the Field of Transverse Dynamic Displacements of Layer

Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part I. Mathematical Modeling of the Field of Transverse Dynamic Displacements of Layer

A partitioned scheme for fluid–composite structure interaction problems

We present a benchmark problem and a loosely-coupled partitioned scheme for fluid–structure interaction with composite structures. The benchmark problem consists of an incompressible, viscous fluid interacting with a structure composed of two layers: a thin elastic layer with mass which is in contact with the fluid and modeled by the Koiter membrane/shell equations, and a thick elastic layer with mass modeled by the equations of linear elasticity. An efficient, modular, partitioned operator-splitting scheme is proposed to simulate solutions to the coupled, nonlinear FSI problem, without the need for sub-iterations at every time-step. An energy estimate associated with unconditional stability is derived for the fully nonlinear FSI problem defined on moving domains. Two instructive numerical benchmark problems are presented to test the performance of numerical FSI schemes involving composite structures. It is shown numerically that the proposed scheme is at least first-order accurate both in time and space. This work reveals a new physical property of FSI problems involving thin interfaces with mass: the inertia of the thin fluid–structure interface regularizes solutions to the full FSI problem.

Is there a discrepancy between geological and geodetic slip rates along the San Andreas Fault System?

AbstractPrevious inversions for slip rate along the San Andreas Fault System (SAFS), based on elastic half‐space models, show a discrepancy between the geologic and geodetic slip rates along a few major fault segments. In this study, we use an earthquake cycle model representing an elastic plate over a viscoelastic half‐space to demonstrate that there is no significant discrepancy between long‐term geologic and geodetic slip rates. The California statewide model includes 41 major fault segments having steady slip from the base of the locked zone to the base of the elastic plate and episodic shallow slip based on known historical ruptures and geologic recurrence intervals. The slip rates are constrained by 1981 secular velocity measurements from GPS and L‐band intereferometric synthetic aperture radar. A model with a thick elastic layer (60 km) and half‐space viscosity of 1019Pa s is preferred because it produces the smallest misfit to both the geologic and the geodetic data. We find that the geodetic slip rates from the thick plate model agrees to within the bounds of the geologic slip rates, while the rates from the elastic half‐space model disagree on specific important fault segments such as the Mojave and the North Coast segment of the San Andreas Fault. The viscoelastic earthquake cycle models have generally higher slip rates than the half‐space model because most of the faults along the SAFS are late in the earthquake cycle, so today they are moving slower than the long‐term cycle‐averaged velocity as governed by the viscoelastic relaxation process.

On an Integral Model of the Transverse Dynamic Displacements of a Thick Elastic Layer

On an Integral Model of the Transverse Dynamic Displacements of a Thick Elastic Layer

On Construction of Differential Model of Transversal Dynamic Displacements of Thick Elastic Layer

On Construction of Differential Model of Transversal Dynamic Displacements of Thick Elastic Layer

Upper mantle rheology from GRACE and GPS postseismic deformation after the 2004 Sumatra‐Andaman earthquake

Mantle rheology is one of the essential, yet least understood, material properties of our planet, controlling the dynamic processes inside the Earth's mantle and the Earth's response to various forces. With the advent of GRACE satellite gravity, measurements of mass displacements associated with many processes are now available. In the case of mass displacements related to postseismic deformation, these data may provide new constraints on the mantle rheology. We consider the postseismic deformation due to the Mw = 9.2 Sumatra 26 December 2004 and Mw = 8.7 Nias 28 March 2005 earthquakes. Applying wavelet analyses to enhance those local signals in the GRACE time varying geoids up to September 2007, we detect a clear postseismic gravity signal. We supplement these gravity variations with GPS measurements of postseismic crustal displacements to constrain postseismic relaxation processes throughout the upper mantle. The observed GPS displacements and gravity variations are well explained by a model of viscoelastic relaxation plus a small amount of afterslip at the downdip extension of the coseismically ruptured fault planes. Our model uses a 60 km thick elastic layer above a viscoelastic asthenosphere with Burgers body rheology. The mantle below depth 220 km has a Maxwell rheology. Assuming a low transient viscosity in the 60–220 km depth range, the GRACE data are best explained by a constant steady state viscosity throughout the ductile portion of the upper mantle (e.g., 60–660 km). This suggests that the localization of relatively low viscosity in the asthenosphere is chiefly in the transient viscosity rather than the steady state viscosity. We find a 8.1018 Pa s mantle viscosity in the 220–660 km depth range. This may indicate a transient response of the upper mantle to the high amount of stress released by the earthquakes. To fit the remaining misfit to the GRACE data, larger at the smaller spatial scales, cumulative afterslip of about 75 cm at depth should be added over the period spanned by the GRACE models. It produces only small crustal displacements. Our results confirm that satellite gravity data are an essential complement to ground geodetic and geophysical networks in order to understand the seismic cycle and the Earth's inner structure.

On the frictionless axi-symmetric contact of a thick elastic layer and the associated squeeze film problem

The problem of the frictionless axi-symmetric indentation between a thick elastic layer (the contact radius does not exceed the layer thickness) and a rigid spherical indenter is investigated. The kernel of the governing integral equation was broken down into two parts. The first corresponds to the Hertzian solution and the second represents the contribution due to the finite layer thickness. The second part was approximated by an absolute and uniform convergent series. Hence, the governing elasticity equation was reduced to a set of linear equations. A set of simple formulae for the contact pressure, total load, and penetration depth are presented. The obtained formulae were compared with the existing numerical results where good agreement was found. Furthermore, the associated squeeze film problem is examined. Expressions for the variation of the film thickness with time were derived using two different pressure conditions.

Equivalences in the Analysis of Thermally Induced Vibrations of Sandwich Structures

Thermally induced flexural vibrations of sandwich structures composed of three moderately thick elastic layers are studied. Alternative formulations of various higher-order theories are introduced that offer complete analogies between the corresponding initial-boundary value problems and those of homogenized single layer structures of effective parameters. Also the effects of geometrically nonlinear large deflection and elastic interlayer slip are considered within appropriate equivalences.