Imperfect Contact Conditions Research Articles

Effective properties of centro-symmetric micropolar composites with non-uniform imperfect contact conditions

In this work, the homogenization theory is addressed within the framework of three-dimensional linear micropolar composite materials with centro-symmetric constituents and non-uniform imperfect interface conditions. The imperfect contact conditions are modeled like a generalization of the spring model, where tractions and coupled stresses are continuous, but displacements and microrotations are discontinuous across the interface. The jumps in displacement and microrotation components are proportional to the interface traction and coupled stress components in terms of a partition of different spring-factor-type interface parameters, respectively. The two-scale asymptotic homogenization method (AHM) is developed, through series expansions for displacements and micro-rotations, to find the analytical statement of the local problems on the periodic cell and the corresponding effective coefficients. In particular, centro-symmetric multi-laminated micropolar composites with non-uniform imperfect contact conditions are studied, and their corresponding effective properties are explicitly declared. Numerical results show the effects of the interface partition lengths, the non-uniform imperfection values, and the constituent’s fraction volumes on the effective properties of centro-symmetric bi-laminated composite with isotropic constituent materials. We also analyze and discuss the effective behaviors illustrated in the results. In general, the effective properties are always affected by a non-uniform imperfect interface, and they are bounded between those achieved when the contact conditions are perfect and imperfect uniform. The reported formulas and data may be helpful as benchmarks for checking other experimental and numerical results.

Effect of imperfect interface on the effective properties of elastic micropolar multilaminated nanostructures

AbstractIn this paper, the problem of a heterogeneous elastic micropolar nanostructure with a periodic structure subject to imperfect contact conditions is analyzed through the two‐scale asymptotic homogenization method (AHM). The imperfect interface is modeled as a generalization of the well‐known spring model; that is, the homogeneous imperfect interface is described by the following conditions: tractions and coupled stress are continuous, but displacements and microrotations are discontinuous across the imperfect interface. The jumps in displacements and microrotations are proportional to the interface traction and coupled stress components, respectively. In particular, micropolar multilaminated nanocomposites with centro‐symmetric isotropic constituents and imperfect contact conditions are studied. From AHM, the solutions for the displacement and microrotation fields are found by means of two‐scale series expansions depending on a local (microscopic) variable and a global (macroscopic) variable. The local problem statements and the corresponding effective properties are explicitly described. The formulation depends on the constituent physical properties, the imperfection parameters, the cell length in the y3‐direction, and the phase's volume fractions. Numerical results are illustrated and discussed. We concluded that the effective moduli are affected by the imperfections and the cell length in the y3‐direction.

The influence of imperfect contact conditions on the natural frequencies of a three-layer hollow sphere for high-order harmonics

The influence of imperfect contact conditions on the natural frequencies of a three-layer hollow sphere for high-order harmonics

Dispersion of torsional surface waves in a threefold concentric compounded cylinder with imperfect interface

The present paper investigates the torsional wave propagation in a threefold concentric pre-stressed compounded cylinder with imperfect contact conditions. The three-dimensional linearized theory of elastic waves and the piecewise homogeneous body model has been employed to formulate the problem. The mathematical modeling has been carried out in two independent cases. In the first case, a solid cylinder encased in a hollow cylinder embedded in an infinite elastic medium has been considered. Whereas the second case comprises a hollow cylinder of finite thickness in place of a solid cylinder. By means of Murnaghan potential, the mechanical characteristics of the three materials have been used. Further, the dispersion relations for both the cases have been obtained in terms of the Bessel and modified Bessel functions. In order to validate the present findings, two particular cases have been derived that matches with the previous works. The first case is obtained by removing the outermost cylinder, while the second case has been derived by removing the imperfection in addition to that. To summarize the computations, a complete numerical simulation has been carried out, and graphical illustrations have been shown to aid the mathematical analyses.

Asymptotic analysis for non-local problems in composites with different imperfect contact conditions

We consider a composite material made up of a hosting medium containing an ε-periodic array of perfect thermal conductors. Comparing with the previous contributions in the literature, in the present paper, the inclusions are completely disconnected and form two families with dissimilar physical behaviour. More specifically, the imperfect contact between the hosting medium and the inclusions obeys two different laws, according to the two different types of inclusions. The contact conditions involve the small parameter ε and two positive constants . We investigate the homogenization limit and the limits for going to 0 or , taken in any order, with the aim to find out the cases in which the two limits commute.

Time domain numerical modeling of wave propagation in poroelastic media with Chebyshev rational approximation of the fractional attenuation

In this work, we investigate the poroelastic waves by solving the time‐domain Biot‐JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson‐Koplik‐Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time‐domain Biot‐JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative Chebyshev approximation of the square‐root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge‐Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach.

Prediction of effective properties for multilayered laminated composite with delamination: A multiscale methodology proposal

In the manuscript, piezoelectric composites with non-uniform imperfect contact at the interface are studied. For this, the two-scales asymptotic homogenization method is used to determine the effective properties of said piezocomposite. First, a theoretical framework is offered to determine the effective properties of piezoelectric materials with generalized periodicity. In addition, a method to solve the local problems for the particular case of stratified media with imperfect contact conditions is described. In the second part, the above-described methodology is used to study different numerical examples and compare the results taking into account distinct contact conditions at the interfaces. Examples include wavy composites with uniform imperfect contact, laminate composite with cracks at the interface, and non-uniform imperfect contact conditions elastic and piezoelectric composites. Also, the influence on the average properties of the small geometrical parameter related to the size of the periodic cell in the homogenization is illustrated. To validate the model, some of the results are compared with the values obtained by the finite elements method (FEM).

Higher order interface conditions for piezoelectric spherical hollow composites: asymptotic approach and transfer matrix homogenization method

The paper describes the mechanical behavior of composites made of piezoelectric spheres in perfect or imperfect contact. The imperfect contact is achieved by interposing piezoelectric thin adhesive layers between the spheres. First, using asymptotic analysis, transmission conditions of imperfect interface equivalent to the behavior of piezoelectric adhesive layers are obtained at order 0 and 1. These transmission conditions are calculated for ”hard” adhesives, i.e. adhesive materials whose electromechanical constants do not rescale with their thickness. Next, under the assumption of spherical symmetry, the transmission conditions are condensed to a general law of imperfect contact, able to simultaneously describe different contact regimes: piezoelectric hard (order 0 and 1) and soft (or spring-type, order 0 and 1) interface conditions, the perfect continuity conditions, and the piezoelectric rigid (Gurtin–Murdoch or membrane-type) conditions. Lastly, following Bufler’s approach, the homogenization problem of a spherical hollow piezoelectric assembly is solved, extending the classical transfer matrix method to take into account the presence of thin adhesive layers described using the proposed transmission conditions of imperfect contact. A simple numerical example is provided, illustrating the correctness and effectiveness of the homogenization approach in describing the electromechanical behavior of spherical piezoelectric assemblies.

Shear vertical waves in laminated coupled electro-mechanic materials with imperfect contact conditions at the interfaces

Shear vertical waves in laminated coupled electro-mechanic materials with imperfect contact conditions at the interfaces

A methodology for hygrothermal modelling of imperfect masonry interfaces

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

The Influence of Imperfect Contact Conditions between Layers of a Hollow Sandwich Sphere on its Natural Frequencies

The influence of imperfect contact conditions between layers of a hollow sandwich sphere on its natural frequencies is studied. It is assumed that the materials of face layers are the same, but different from the core layer material. Each layer is made of a homogeneous isotropic material and has a constant thickness. Investigations are performed using a piecewise homogeneous body model with the use of exact three-dimensional equations and relations of elastodynamics. The solution of the corresponding equations of motion of the hollow sandwich sphere is presented through the Helmholtz potentials in spherical coordinates. Numerical results for the influence of imperfect contact conditions between layers on the natural frequencies of the sphere are presented and discussed. It is established that an imperfect contact between sphere layers can decrease its natural frequencies significantly.

Numerical Validation of Multiphysic Imperfect Interfaces Models

We investigate some mathematical and numerical methods based on asymptotic expansions for the modeling of bonding interfaces in the presence of linear coupled multiphysics phenomena. After reviewing new recently proposed imperfect contact conditions Serpilli et al. (2019), we present some numerical examples designed to show the efficiency of the proposed methodology. The examples are framed within two different multiphysics theories, piezoelectricity and thermo- mechanical coupling. The numerical investigations are based on a finite element approach generalizing to multiphysics problems the procedure developed in Dumont et al. (2018a)

Behavior of piezoelectric layered composites with mechanical and electrical non-uniform imperfect contacts

In this work, the two scales asymptotic homogenization method (AHM) is applied for determining the effective coefficients of laminated piezoelectric composite with periodic structure under non-uniform electrical and mechanical imperfect contact conditions. The analytical expressions of the local problems and the effective coefficients as result of the AHM are explicitly described. The constituent materials have properties belonging to 2 mm symmetry point group. Numerical values of the effective coefficients are reported and compared with limit cases, where perfect and uniform imperfect contact conditions are considered. Good agreements are found for these comparisons. Hence, the effect of the non-uniform imperfect contact conditions on the effective coefficients can be analyzed.

Simulations on Current Distribution in Railgun Under Imperfect Contact Conditions

In the process of electromagnetic launch, the initial contact pressure distribution of armature/rail (A/R) contacts interface is uneven, and the actual contact area is obviously different from the perfect contact. The uneven contact pressure leads to uneven contact resistance distribution, affecting the magnetic diffusion process and changing the A/R interface current distribution. Therefore, it is necessary to consider the influence of contact pressure on the current distribution. In the past, the simulation studies usually considered the contact between rails and armature as the perfect contact, and the result obtained may be different from the actual situation. This paper uses the finite element software COMSOL to perform coupling simulation analysis on the electromagnetic module and solid mechanics module in the initial stage of electromagnetic launch. At the initial stage of electromagnetic launch, the contact pressure is mainly provided by the prepressure generated by the interference fit. In this paper, the influence of contact pressure on current distribution and the influence of magnitude of interference on contact position, contact pressure, and current distribution are analyzed.

Analysis of Viscoelastic Mechanical Response of Asphalt Mixture Pavement on Steel Deck under Imperfect Contact Conditions

Abstract For long-span steel bridges, the contact states between the pavement and the steel decks change significantly during the operation stage. Different interlayer contact states have different effects on the viscoelastic mechanical properties of the pavement. Here, the modified SMA10 mixture and the epoxy–asphalt mixture are compared in terms of the transverse tensile strain, the transverse tensile stress, and the deflection at the bottom of the asphalt layer under different contact conditions. The main curve clusters of the relaxation modulus were obtained using the creep test data, and the effects of four different contact conditions on the viscoelastic mechanical response of the asphalt mixture pavement of the Huangpu Suspension Bridge in China were analyzed accordingly. It was found that the delayed deformation capacity of the epoxy–asphalt mixture is better than that of the modified SMA10 mixture. The change of the interlayer contact condition has an impact on the viscoelastic mechanical response of the asphalt mixture pavement; for the modified SMA10 asphalt mixture pavement, the transverse tensile stress and the transverse tensile strain at the bottom of the pavement are more sensitive to the contact condition than the deflection. For the epoxy–asphalt mixture pavement, the deflection is more sensitive to the contact condition.

Antiplane Shear of an Elastic Body with Elliptic Inclusions Under the Conditions of Imperfect Contact on the Interfaces

We study the problem of аntiplane shear of an elastic body containing a finite array of arbitrarily located and oriented elliptic inclusions under the conditions of imperfect mechanical contact on the interfaces. The analytic solution of the problem is obtained by the method of multipole expansions with the use of the technique of complex potentials. By expanding the disturbances of the field of displacements caused by inclusions in a series in the system of elliptic harmonics and using the formulas for their reexpansion and exact validity of all contact conditions, we reduce the boundary-value problem of the theory of elasticity to an infinite system of linear algebraic equations. It is also proved that the reduction method is applicable to the indicated system, the rate of convergence of the solution is investigated, and the accumulated results are compared with the data available from the literature. The presented numerical results of parametric investigations reveal the presence of a strong dependence of stress concentration on the conditions of contact on the interfaces, as well as on the sizes, shapes, and relative positions of the inclusions.

Nonlinear Second Harmonics of Localized Shear Waves in an Anisotropic Layer Between Anisotropic Half Spaces Under the Conditions of Imperfect Contact

We construct a numerical-analytic solution of the problem of generation of the nonlinear second harmonics in the course of propagation of elastic symmetric localized shear waves in the crystalline layer of cubic system of the m3m class located between the crystalline half spaces of the same type and the same class of anisotropy under the conditions of imperfect sliding contact of components of the waveguide. We determine the analytic form of the functions of wave motions for nonlinear anharmonic perturbations in the form of longitudinal-shear-type waves. We also perform the numerical investigations of the amplitude-frequency characteristics of the second harmonics for monochromatic localized waves in a layer of a single crystal of germanium between the half spaces from the single crystal of silicon.

Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

A family of one-dimensional (1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method (RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

Tape surface characterization and classification in automated tape placement processability: Modeling and numerical analysis

Many composite forming processes are based on the consolidation of preimpregnated preforms of different types, e.g., sheets, tapes, .... Composite plies are put in contact using different technologies and consolidation is performed by supplying heat and pressure, the first to promote molecular diffusion at the plies interface and both (heat and pressure) to facilitate the intimate contact by squeezing surface asperities. Optimal processing requires an intimate contact as large as possible between the surfaces put in contact, for different reasons: (i) first, a perfect contact becomes compulsory to make possible molecular diffusion at the interface level in order to ensure bulk properties at interfaces; (ii) second, imperfect contact conditions result in micro and meso pores located at the interface, weakening it from the mechanical point of view, where macro defects (cracks, plies delamination, etc.) are susceptible of appearing. As just indicated, the main process parameters are the applied heat and pressure, as well as the process time (associated with the laying head velocity). These parameters should be adjusted to ensure optimal consolidation, avoiding imperfect bonding or thermal degradation. However, experiments evidence that the consolidation degree is strongly dependent on the surface characteristics (roughness). The same process parameters applied to different surfaces produce very different degrees of intimate contact. The present study aims at identifying the main surface descriptors able to describe the evolution of the degree of intimate contact during processing. That knowledge is crucial for online process control in order to maximize both productivity and part quality.

Domain decomposition algorithms for problems of thermomechanical contact between several elastic bodies

We consider a thermoelastic multibody contact problem for finite bodies with unilateral mechanical and imperfect thermal contact conditions. Using a penalty method, we obtain a weak formulation of this problem in the form of a system of linear and nonlinear variational equations in Hilbert space. To solve this variational system, we propose a class of iterative Robin type domain decomposition algorithms. In each iterative step of these algorithms one have to solve two linear variational equations for each of the bodies, which correspond to heat conduction problem with Newton boundary conditions on the possible contact areas and linear elasticity problem with additional volume forces and Robin boundary conditions respectively. The program implementation of proposed algorithms is made for plane thermoelastic contact problems with the use of linear and quadratic finite element approximations on triangles. The numerical analysis is performed for one-body and two-body thermoelastic contact problems.