Nonlinear Interface Model Research Articles

A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities

In this work, an efficient numerical approximation for the solution of the time fractional nonlinear diffuse interface model is studied. The solution to this problem has a weak singularity near the initial time . The fractional order nonlinear diffusion model is transformed into a system of nonlinear functional equations. The Daftardar–Gejji and Jafari method is employed to solve the corresponding nonlinear system. The L1 scheme is used to discretize the Caputo fractional derivative on a graded mesh in the time direction. In contrast, the spatial derivative is approximated by applying a classical central finite difference scheme to a uniform mesh. The convergence analysis and the error bounds are carried out. The analysis and the computational findings exhibit the effectiveness of the proposed method.

A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models

In this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative is approximated by truncated Haar wavelet series, while for temporal derivative, the finite difference formula is used. The diffusion coefficients, advection coefficients, and reaction coefficients are considered discontinuously across the fixed interface. The newly established numerical technique is applied to both linear and nonlinear benchmark interface models. In the case of linear interface models, Gauss elimination method is used, whereas for nonlinear interface models, the nonlinearity is removed by using the quasi-Newton linearization technique. TheL∞errors are calculated for different number of collocation points. The obtained numerical results are compared with the immersed interface method. The stability and convergence of the method are also discussed. On the whole, the numerical results show more efficiency, better accuracy, and simpler applicability of the newly developed numerical technique compared to the existing methods in literature.

Constitutive framework for rheologically complex interfaces with an application to elastoviscoplasticity

A framework is presented for the formulation of a class of continuum constitutive models for sharp interfaces with non-linear viscoelastic behaviour due to a considerable isotropic interfacial microstructure. For the formulation of a thermodynamically consistent elastoviscoplastic interface constitutive model we adapt an approach successful in describing the behaviour of bulk polymer glasses. The model has a clear separation between dilatation and shear, and is used to predict phenomena related to the plasticity of interfaces observed in the experimental literature, which is relevant for many applications. Stress–strain predictions in standard interfacial rheological flows, i.e. shear and dilatation, are investigated numerically. A predominantly elastic response is obtained at small deformations, with a transition to primarily plastic flow at high stress levels. In interfacial shear flow, strain softening and eventually a plastic plateau occur upon further deformation beyond the yield point. The yield stress and strain and (the relative strength of) the stress overshoot in interfacial shear flow are shown to be controlled by two dimensionless groups of parameters in the model. In interfacial dilatation, the model predicts elastoviscoplastic behaviour with a stress maximum and a decreasing stress without a plateau at even larger deformations. These phenomena are studied for various choices for the parameters in the model. • Framework for non-linear viscoelastic interface models is developed. • Thermodynamic consistency is intrinsically respected in the framework. • Existing viscoelastic interface models are reviewed. • New elastoviscoplastic interface model is proposed. • Qualitative agreement with experiments in both shear and dilatation is found.

Soil‐structure interface modeling with the nonlinear incremental approach

AbstractThis paper aims to develop the nonlinear incremental modeling approach for describing both monotonic and cyclic behaviors of the soil‐structure interface. An exponential function is adopted as an example to reproduce the asymptotic relationship between the interface shear stress ratio and the shear displacement. A stress‐dilatancy relation is developed for the shear‐induced change of interface thickness. A shear stress reversal technique is incorporated for cyclic loading effect. Then, three numerical schemes for simulating constant thickness, constant normal load, and constant normal stiffness tests are established respectively. Next, three modifications are made to enhance the model by introducing a nonlinear shear modulus, the critical state concept, and the grain breakage effect. The enhanced model is evaluated with satisfactory performance in simulating interface tests under various loading conditions. Furthermore, the extensions to other nonlinear incremental interface model and clay‐structure interface modeling with rate effect relating to drainage conditions are successfully demonstrated and discussed.

Estimation of the response of piled raft using nonlinear soil and interface model

ABSTRACT In this research paper, the complex interaction mechanism between different components of CPRF was simulated through 3D finite element analyses using the nonlinear interface and soil model for three case histories. The interface behaviour between concrete and soil was accounted using combined adhesion and friction model. The nonlinear soil behaviour was included using cap plasticity model, which has stress-dependant shear and compression yield surface, and captures the effect of stress history and stress path. The computed response parameters for the three case histories resulted in reasonably close agreement with the field measurements and led to significant improvement in the estimation of the load sharing of piles. The comparison of the results with the different methods showed that the stiffer interface results in a higher pile-raft coefficient and lesser settlement. The pile and soil stiffness found to vary with their position below the raft due to the different interactions.

A non-linear interface model for monotonic shear coupling in granular soil–structure interaction problems

The accurate prediction of the behaviour of soil–structure interfaces that accounts for shear coupling is of concern in the design and analysis of soil–structure interaction problems. In this study, an interface constitutive model capable of simulating the non-linear behaviour of granular soil–structure interface systems under three-dimensional loading conditions is proposed. The proposed constitutive model is a state-dependent elasto-plastic model, and it is formulated in the framework of two-surface plasticity and critical state soil mechanics. The interface model considers the effect of shear coupling and is capable of predicting the monotonic behaviour of soil–structure interfaces over a wide range of normal and shear stresses, and under different stress paths using a single set of model parameters. It also captures other complex behaviour characteristics such as strain hardening and softening, volumetric compaction and dilation, and phase transformation responses of granular soil–structure interfaces under orthogonal shear application. The performance of the proposed constitutive model is evaluated by comparing its predictions for both gravelly and sandy soil–structure interfaces with available experimental results.

Numerical study of interface cracking in composite structures using a novel geometrically nonlinear Linear Elastic Brittle Interface Model: Mixed-mode fracture conditions and application to structured interfaces

Interface cracking is one of the most prominent failure modes in fibre reinforced polymer (FRP) composites. Recent trends in high-tech applications of FRP composites exploit the limits of the load bearing capacity, generally encompassing the development of notable nonlinear effects from geometrical and material signatures. In this investigation, we present a comprehensive assessment of the new Linear Elastic Brittle Interface Model (LEBIM) in geometrically nonlinear applications undergoing mixed-mode fracture conditions. This interface model for triggering fracture events is formulated through the advocation of continuum-like assumptions (for initial non-zero interface thickness) and allows the incorporation of the potential role of in-plane deformation effects. The performance of the present interface model is demonstrated through the simulation of specimens with mixed-mode delamination, with special attention to its application in samples equipped with structured interfaces. Predictions exhibit an excellent agreement with experimental data, validating the proposed methodology.

Multiscale modeling for analyzing slip weakening at material interfaces

A multiscale framework is proposed for analyzing slip weakening at material interfaces. In the proposed model, discrete granular assemblies are attached to Gauss integration points to capture micro-structural characteristics of granular material, which furnishes the multiscale constitutive formulation. Interface shear slip is performed via penalty method and elasto-plastic decomposition, which formulates the frictional contact relationship. Furthermore, both linear and non-linear interface models are provided to examine slip weakening behavior. In the numerical implementation, both the resulting multiscale constitutive formulation and the frictional contact relationship, are implicitly embedded in conventional continuum-based finite element method (FEM) for solution. The multiscale framework is verified using an interface direct shear test, which shows good agreement between the analytical and numerical results. Cross-scale analyses are performed based on the proposed multiscale framework, which comprises mesh dependency, a macro-micro slip-weakening mechanism and staged responses. The interplay between interface slip weakening and material strain localization is successfully captured, by presenting the global and local responses during shearing where fabric anisotropy, coordination number, particle rotation, void ratio and deviatoric strain are considered.

The influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressure

The local behavior of segment-to-segment interfaces has a significant influence on the overall structural behavior of segmental tunnel rings subjected to ground pressure. This is quantified by means of structural simulations, combining analytical solutions of the linear theory of slender circular arches with time-dependent and nonlinear interface models for unreinforced and bolted interfaces. The time-dependent behavior results from creep of concrete and the nonlinear behavior from interfacial separation, crushing of concrete, and yielding of steel. Structural sensitivity analyses are performed with respect to the coefficient of lateral ground pressure. The influence of creep of concrete at unreinforced interfaces on the overall structural behavior is demonstrated, based on the interface models by Gladwell and Janßen. Furthermore, the elastic limits and the bearing capacities of segmental tunnel rings are quantified both for unreinforced and bolted interfaces. The corresponding interface law is based on the Bernoulli-Euler hypothesis and on linear-elastic and ideal-plastic behavior of both concrete and steel. In order to underline the reliability of the computed bearing capacities, a bearing-capacity test on a real-scale segmental tunnel ring is re-analyzed. It is concluded that (i) creep of concrete at the interfaces results in an increase of the structural displacements, while the distributions of the inner forces remain practically the same, (ii) interfacial bolts improve the serviceability of segmental tunnel rings, because they ensure the position stability of the lining, and (iii) the bearing capacity of segmental tunnel rings subjected to ground pressure can be estimated reliably, based on the combination of realistic interface models and analytical solutions of the linear theory of slender circular arches.

The effect of non-zero initial displacement value on displacement jump and wave form based on the cubic nonlinear spring interface model

The effect of non-zero initial displacement value ondisplacement jump and wave form based on the cubic nonlinear spring interface model between two semi-infinite plates is studied. The wave forms of reflected and transmitted pulses are sensitive to the initial value. The phenonmenon for non-zero initial displacement valueis much different from the counterpart for zero initial displacement value.First, the displacement jump is larger in the case of linear spring than that of nonlinear spring, but the displacement jump goes across the curve for linear spring with the initial displacement value increasing. Second, when the initial displacement value is not zero, for reflected pulse, the curve for nonlinear spring interface is on the top of the curve for linear spring interface, but for transmitted wave, the curve for linear spring interface is on the top of the curve for nonlinear spring interface. This is opposite for zero initial displacement. The initial displacement value plays a great role in elastic wave reflecting. The results in this paper will be of help to nondestructive evaluation of the interface.

Towards nonlinear imperfect interface models including micro-cracks and smooth roughness

The present paper deals with a general asymptotic theory aimed at deriving some imperfect interface models starting from thin interphases. The novelty of this work consists in taking into account some non-standard constitutive behaviors for the interphase material. In particular, micro-cracks, surface roughness and geometrical nonlinearity are included into the general framework of the matched-asymptotic-expansion theory. The elastic equilibrium problem of a three-composite body comprising two elastic adherents and an adhesive interphase is investigated. Higher order interface models are derived within the cases of soft and hard interphase materials. Simple FEM-based numerical applications are also presented.

On modelling brick/mortar interface via a St. Venant-Kirchhoff orthotropic soft interface. Part II: in silico analysis

A new strategy for the numerical modelling of brick/mortar interfaces at the macro-scale taking into account finite strains and evolving microcracking phenomena is introduced. A numerical validation of the non-linear-imperfect interface model formulated in Part I of the present paper, is proposed. Well-established experimental data concerning diagonal compression of masonry walls are simulated within the finite element method. The localisation zones of highest displacement jumps and stresses obtained through the numerical simulations are in good agreement with the experimental findings. The proposed non-linear interface model is also compared with a linear interface model for masonry structures.

On modelling brick/mortar interface via a St. Venant-Kirchhoff orthotropic soft interface. Part II: in silico analysis

A new strategy for the numerical modelling of brick/mortar interfaces at the macro-scale taking into account finite strains and evolving microcracking phenomena is introduced. A numerical validation of the non-linear-imperfect interface model formulated in Part I of the present paper, is proposed. Well-established experimental data concerning diagonal compression of masonry walls are simulated within the finite element method. The localisation zones of highest displacement jumps and stresses obtained through the numerical simulations are in good agreement with the experimental findings. The proposed non-linear interface model is also compared with a linear interface model for masonry structures.

Scaling of Electrode-Electrolyte Interface Model Parameters In Phosphate Buffered Saline.

We report how the impedance presented by a platinum electrode scales with the concentration of phosphate buffered saline (PBS). We measure the response in various dilutions of PBS with an electrode array as is commonly used in spinal cord stimulator (SCS) implants. We match the parameters of a non-linear electrode-electrolyte interface model to these measurements. We find that the constant phase element of the model scales with approximately the log of concentration, whereas the resistivity is inversely proportional. Using a novel DC measurement technique we show that the onset of Faradaic conduction for a platinum electrode, and thus the safe exposure limit, does not scale with concentration. We compare objective measurements made in saline to those made in the spinal cavity of live sheep. We comment upon the appropriateness of using PBS as a substitute for in-vivo measurements.

Modeling of Flexural Wave Propagation in a Plate with Contacting Interfaces

Propagation characteristics of a flexural wave in a thin plate which surfaces are in imperfect contact with solid bodies are examined theoretically as well as numerically. To this purpose, a nonlinear interface model of solid-solid contact is incorporated in the Mindlin plate theory. The governing differential equations are derived for a plate in contact with rigid bodies on both surfaces, and the dispersion relation for infinitesimal amplitudes is obtained theoretically. The derived equations are solved by the finite difference method to examine the propagation of a flexural wave packet. The numerical results show that the interfacial stiffnesses influence the velocity and the broadening of the propagating wave packet, and the contact nonlinearity brings about harmonic generation. It is discussed how these features are influenced by the linear and nonlinear interface parameters, the wave amplitude and the propagation distance.

Pressure-Dependent Stiffnesses and Nonlinear Ultrasonic Response of Contacting Surfaces

An experimental study of the pressure dependence of the interfacial stiffnesses of contacting solid-solid surfaces and their nonlinear ultrasonic responses is presented. To this purpose, the contact-pressure dependence of the reflection coefficients of longitudinal and transverse waves were measured at normal incidence to three types of contacting interfaces of aluminum blocks with different surface conditions, namely, polished surfaces, roughened surfaces and fractured surfaces. The results show remarkable influence of the surface condition on the pressure-dependent variation of the normal and tangential stiffnesses as well as their ratio. Based on the obtained stiffness-pressure relations, the second harmonic generation behavior for normal-incidence longitudinal wave is examined theoretically according to the foregoing theoretical results by a nonlinear interface model, and it is shown that smoother surfaces exhibit harmonic generation more significantly than rougher ones. Relevant experimental results are demonstrated for polished surfaces and discussed in comparison to the theoretical predictions.

Experimental and theoretical study of harmonic generation at contacting interface

The second harmonic generation behavior of a contacting interface has been evaluated experimentally and discussed theoretically in the light of a nonlinear interface model. Two aluminum blocks were mated together to constitute a contact interface and subjected to normal compressive loading. A 5 MHz longitudinal toneburst wave was sent to the interface in the normal direction and the transmitted wave was recorded, from which the fundamental and the second harmonic components were extracted. A nonlinearity parameter was obtained as the ratio of the second harmonic amplitude to the squared fundamental amplitude. From the measured contact pressure dependence of the transmitted fundamental amplitude, the linear and the second-order interfacial stiffness parameters were identified, which enabled the evaluation of the nonlinearity parameter based on the theoretical model. The theoretical contact pressure dependence of the nonlinearity parameter was found to be in good qualitative agreement with the experimental results.

An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites

Linear spring interface model and interphase model are often used to simulate the interface behaviour of particle-reinforced composite materials. However, the former may give rise to nonphysical interpenetration at the interface between a particle and the surrounding material. In this paper, first, a model is presented to prevent the interpenetration phenomenon at the interface. This model can be used together with a given linear or nonlinear interface model to calculate the stress field in particle-reinforced composites with imperfect interface bonding condition, or with debonding damage. Second, the connections between the thin interphase model and interface models are studied for spherical particle-reinforced composites. It is found that while a relatively thin and compliant interphase can be well approximated by the equivalent linear spring interface model, a relatively thin and stiff interphase can be well approximated by the equivalent interface stress model. For the latter, the relations between the equivalent interface moduli and the interphase stiffness and thickness are presented.

Application of damage model for soil–structure interface

The constitutive modeling of soil–structure interfaces plays a major role in numerical simulation of soil–structure interaction problems. The interface shear tests showed that the failure of a rough soil–structure interface was accompanied with strong strain-softening and normal dilatancy during shearing. In this paper, the general framework of a damage model is developed to characterize such behavior of a rough interface with nine parameters. The relation matrix between stress and strain increments in the interface is derived and the damage model was incorporated into a FEM program. Back-predictions for the interface tests demonstrate that the proposed damage model is capable of capturing most of the rough interface behavior, such as hardening, softening, and shear dilatancy. Numerical modeling of soil–structure interaction problems is conducted, and the comparative studies between the proposed model and a conventional nonlinear interface model show that more realistic calculation results can be obtained by adopting a damage model.

Properties of large-amplitude internal waves

Properties of solitary waves propagating in a two-layer fluid are investigated comparing experiments and theory. In the experiments the velocity field induced by the waves, the propagation speed and the wave shape are quite accurately measured using particle tracking velocimetry (PTV) and image analysis. The experiments are calibrated with a layer of fresh water above a layer of brine. The depth of the brine is 4.13 times the depth of the fresh water. Theoretical results are given for this depth ratio, and, in addition, in a few examples for larger ratios, up to 100[ratio ]1. The wave amplitudes in the experiments range from a small value up to almost maximal amplitude. The thickness of the pycnocline is in the range of approximately 0.13–0.26 times the depth of the thinner layer. Solitary waves are generated by releasing a volume of fresh water trapped behind a gate. By careful adjustment of the length and depth of the initial volume we always generate a single solitary wave, even for very large volumes. The experiments are very repeatable and the recording technique is very accurate. The error in the measured velocities non-dimensionalized by the linear long wave speed is less than about 7–8% in all cases. The experiments are compared with a fully nonlinear interface model and weakly nonlinear Korteweg–de Vries (KdV) theory. The fully nonlinear model compares excellently with the experiments for all quantities measured. This is true for the whole amplitude range, even for a pycnocline which is not very sharp. The KdV theory is relevant for small wave amplitude but exhibit a systematic deviation from the experiments and the fully nonlinear theory for wave amplitudes exceeding about 0.4 times the depth of the thinner layer. In the experiments with the largest waves, rolls develop behind the maximal displacement of the wave due to the Kelvin–Helmholtz instability. The recordings enable evaluation of the local Richardson number due to the flow in the pycnocline. We find that stability or instability of the flow occurs in approximate agreement with the theorem of Miles and Howard.