Imperfect Contact Conditions Research Articles

Analysis of mechanical and electrical imperfect contacts in piezoelectric composites

The problem of a heterogeneous piezoelectric composite with mechanical and electrical imperfect contact conditions is studied by means of the asymptotic homogenization method. As an illustrative example, in order to provide a benchmark for the numerical validation of theoretical models, a one-dimensional two-phase periodic laminate piezoelectric composite is considered with imperfect adhesion. Numerical examples show the effect of interface imperfections on the effective properties. Reductions in the effective Young’s modulus, the piezoelectric coupling and the dielectric permittivity under the effect of the imperfect contact conditions are reported herein.

Effective Elastic Properties of Stochastic Granular Composites with Interfacial Defects

The problem of effective elastic properties of a matrix composite material with imperfect contact conditions between the matrix and quasi-spherical inclusions in the form of porous interfacial layers between the matrix and quasi-spherical inclusions, which are considered as the third component, is considered. It is based on the stochastic equations of elasticity for a multi-component material. An approach, where three-component material is reduced to two-component material by replacing the inclusions with interfacial layer by composite inclusions with equivalent or effective elastic properties is used. Composite inclusions are modeled using two-component matrix material, where inclusions and matrix have elastic moduli and volume fractions of corresponding real inclusions and interfacial layers. The dependence of bulk compression and shear efficient moduli on the volume fractions of inclusions and porosity of interfacial layers is investigated.

Study of guided wave propagation on a plate between two solid bodies with imperfect contact conditions

In this work, fundamental symmetric Lamb wave S0 mode is characterized in terms of its velocity variation as function of the interfacial conditions between solid bodies in contact. Imperfect contact conditions are numerically and experimentally determined by using ultrasonic Lamb wave propagation parameters. For the study, an experimental system was used, formed by two solid aluminum rods (25.4mm in diameter) axially loading a thin aluminum plate to control contact interfacial stiffness. The axially applied load on the aluminum plate was varied from 0MPa to 10MPa. Experimental Lamb wave signals were excited on the plate through two longitudinal contact transducers (1MHz of central frequency) using a pitch-catch configuration. Numerical simulations of contact conditions and Lamb wave propagation were performed through Finite Element Analysis (FEA) in commercial software, ANSYS 15®. Simulated Lamb wave signals were generated by means of a 5 cycles tone burst signals with different frequency values. Results indicate a velocity change in both, experimental and simulated Lamb wave signals as function of the applied load. Finally, a comparison between numerical results and experimental measurements was performed obtaining a good agreement.

Forced vibration of the elastic system consisting of the hollow cylinder and surrounding elastic medium under perfect and imperfect contact

The bi-material elastic system consisting of the circular hollow cylinder and the infinite elastic medium surrounding this cylinder is considered and it is assumed that on the inner free face of the cylinder a point-located axisymmetric time harmonic force, with respect to the cylinder\'s axis and which is uniformly distributed in the circumferential direction, acts. The shear-spring type imperfect contact conditions on the interface between the constituents are satisfied. The mathematical formulation of the problem is made within the scope of the exact equations of linear elastodynamics. The focus is on the frequency-response of the interface normal and shear stresses and the influence of the problem parameters, such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfectness, on these responses. Corresponding numerical results are presented and discussed. In particular, it is established that the character of the influence of the contact imperfection on the frequency response of the interface stresses depends on the values of the vibration frequency of the external forces.

Near-surface waves in a system consisting of a covering layer and a half-space with imperfect interface under two-axial initial stresses

The influence of shear-spring + normal-spring type imperfect interface conditions on the dispersion of the generalized Rayleigh waves in a system consisting of a covering layer and a half-space with two-axial homogeneous initial stresses is investigated. The three-dimensional linearized theory of elastic waves in initially stressed bodies is employed and the plane-strain state is considered. The elasticity relations of the materials of the constituents are described through the Murnaghan potential and the influence of the third order elastic constants which enter the expression of this potential is taken into consideration. The corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the action of the parameters, which enter the formulation of the imperfect contact conditions, on the wave dispersion curves are presented and discussed. The results of these investigations can be successfully used for estimation of the degree of the bonded defects between the covering layer and the half-space.

Investigation of Wave Processes in Inhomogeneous Media with Imperfect Contact Conditions

The author considers the problem of numerical modeling and optimization of wave processes in inhomogeneous domains with imperfect contact conditions on the basis of Schrodinger parabolic wave equation. The optimality criterion is formulated. The differential properties of the optimization problem are investigated. The numerical method is proposed for modeling and optimization of acoustic fields in inhomogeneous domains.

Determination of dynamic elastic modulus of polymeric materials using vertical split Hopkinson pressure bar

This paper is focused on the determination of dynamic elastic modulus of polymer materials under high strain rate loading using the split Hopkinson pressure bar (SHPB) technique. Experiments conducted on the epoxy specimen by the traditional SHPB and the proposed vertical SHPB equipment demonstrates that the vertical SHPB can give more accurate measurements. The related factors, namely, the effect of stress inequilibrium in specimen, indentation in bars due to specimen and the tilt between specimen and bars, are extensively studied. It is concluded through theoretical analysis and numerical calculations that the influence of stress inequilibrium becomes negligible after two characteristic times. The numerical study on the indentation effect shows that the bar to specimen specific elastic modulus ratio and specific diameter ratio are critical to the level of influence on indentation. However, polymers with low elastic modulus values can still be accurately measured regardless of the indentation displayed. The numerical investigation on tilt effect indicates that the imperfect contact condition severely affects the accuracy of measured elastic modulus. This issue can be rectified by the newly proposed vertical SHPB. It can improve the contact conditions between bars and specimen significantly and offer acceptable accurate measurements for the dynamic elastic modulus of polymeric materials.

Effect of Conjugated Heat Transfer Conditions on the Crystallization of the Composite Coating

This paper presents the thermophysical model of crystallization of the coating at the conditions of imperfect contact between the coating and sunstrate. The model takes into account the heat exchange of coating with the environment and with the substrate. The influence of thermal resistance of the interface and concentration of filler in the coating on the change of temperature during cooling is investigated.

Effect of Imperfect Contact on the Dispersion of Generalized Rayleigh Waves in a System Consisting of a Prestressed Layer and a Prestressed Half-Plane

The effect of shear-spring + normal-spring-type imperfect contact conditions on the dispersion of generalized Rayleigh waves in a system consisting of a two-axially prestressed covering layer and a two-axially prestressed half-plane is investigated. A three-dimensional linearized theory of elastic waves in initially stressed bodies is utilized, and a plane strain state is considered. The elasticity relations for materials of the constituents are described by the Murnaghan potential. Numerical results obtained for the effect of the parameters entering in the imperfect contact conditions on wave dispersion curves are presented and discussed.

Axisymmetric Contact Problem of Thermoelasticity for a Three-Layer Elastic Cylinder with Rigid Nonuniformly Heated Core

We consider an axisymmetric contact problem for a finite three-layer elastic cylinder with rigid nonuniformly heated core under the conditions of external convective heat transfer. The conditions of perfect unilateral mechanical contact and imperfect thermal contact are given on the surfaces of possible contact of the cylinder with the core and between the layers. The variational formulation of the problem is obtained. Finally, we propose an iterative numerical algorithm in each iteration of which it is necessary to solve the uncoupled elasticity and heat-conduction problems and the finite-element method is used for their discretization.

Influence of an Imperfection of Interfacial Contact on the Dispersion of Flexural Waves in a Compound Cylinder

Dispersion of flexural waves in a compound solid cylinder containing a shear-spring-type imperfection between its constituents is investigated utilizing the three-dimensional equations and relations of the linear theory of elastodynamics. Attention is focused on the influence of the imperfection on dispersion curves. By using an analytical solution of corresponding field equations, dispersion equations for the cases considered are obtained. Based on numerical solutions of the equations, dispersion curves are constructed for a biomaterial cylinder, consisting of steel and aluminum cylinders, for the first fundamental vibration mode. In particular, it is established that the type of imperfect contact conditions considered can give rise to additional branches of dispersion curve related to the fundamental mode. One of these branches approaches the dispersion curve obtained for a perfect interfacial contact, but the other disappears as the values shear-spring parameters decrease.

Effective conductivity of a composite material with stiff imperfect contact conditions

We present an analytic and numerical analysis of several properties of a composite material with stiff imperfect interface conditions. Spaces of functions are identified wherewe can guarantee existence and uniqueness of solutions. In particular, formulas for the temperature distribution and flux are exhibited. Numerical calculations of the material characteristics such as temperature, flux and the effective conductivity are also performed and interpreted. Copyright © 2015 John Wiley & Sons, Ltd.

Effective properties evaluation for smart composite materials with imperfect fiber–matrix adhesion

A numerical approach is proposed to evaluate the effective properties of piezoelectric fibers embedded in a nonpiezoelectric matrix, considering imperfect contact between fiber and matrix. Firstly, a Representative Volume Element is analyzed via Finite Element Method for different loadings with suitable boundary conditions applied in a unique way. Transversely, isotropic piezoelectric materials with circular and square cross-section fibers are analyzed for square arrangements with different fiber volume fractions as well as with perfect and imperfect contact conditions. The results for circular and square cross-section fibers with perfect contact are compared to the literature data in order to verify the consistency of proposed numerical approach. After that, the results with imperfect contact are discussed, observing the influence of the fiber volume fraction and the level of the imperfection in the fiber–matrix adhesion. Results show that the imperfect contact not only influences the elastic constants, but also the piezoelectric effective values.

Сдвиговые волны флоке в магнитоэлектроупругих средах с периодическими поверхностями неполного контакт.

This paper aims at investigating the shear waves propagation in magneto-electro-elastic piezo active homogeneous solid of the one-dimensional periodic structure of imperfect contact interfaces. In the framework of the Floquet theory the dispersion equations are obtained defining shear wave frequency pass and gap band structure. For three kinds of imperfect contact conditions the analysis of dispersion relations is presented.

Mathematical Modeling of the Steady-State Processes of Convective Diffusion in Regular Structures Under Mixed Boundary Conditions

We study steady-state processes of the mass transfer of admixtures in two-phase regular structures with regard for the periodic character of convective phenomena under mixed boundary conditions. To construct the exact analytic solutions of contact boundary-value problems of this kind, we adapt the method based on the use of different integral transformations in different contacting domains. A relation between these integral transformations is established by using the conditions of imperfect contact. We obtain the analytic solution of the diffusion problem for a two-phase layer of regular structure with regard for convective transfer in one of the phases with preservation of a constant concentration on the surface of this phase and a constant diffusion flow on the boundary of the other phase. The mass flows through the internal interface contact surface are investigated and numerical analysis of the concentration of migrating particles in structural elements of the body is performed. The interpretation of the results of experimental investigations of the processes of mass transfer in polycrystalline bodies and capillary-porous media is based on the solution of the corresponding boundary-value problems of mathematical physics, which take into account the influence of internal structures [9, 15, 16, 18]. In particular, the exact solutions of specific contact boundary-value problems of mass transfer for piecewise homogeneous systems, e.g., spatially regular, are of a certain interest. These media may consist of domains characterized by different diffusion coefficients and the presence or absence of the convective transfer of particles. The mass transfer is realized between these domains. Since the construction of exact solutions of this problems even for the simplest geometric regions is connected with significant difficulties, the researchers, as a rule, apply the approximate analytic [2, 6, 13, 14] or numerical [4, 8, 10, 17] methods. A new method for the construction of the exact solutions of contact boundary-value diffusion problems in bodies with regular structures based on the integral transformations with respect to spatial variables (separate in different contacting domains) was proposed in [12] and then developed in [11]. The analytic solution of the diffusion problem was found for a horizontal layer in the form of a periodic structure formed by two physically different vertical sublayers. On this basis, the transitions to the continuum limits corresponding to the approximations of single inclusion [13] and continual heterodiffusion [7] were investigated. In the present work, this method is generalized to the case where convective transfer is realized in the sublayers of one of the components of periodic structure and constant values of concentration are preserved on the external boundaries and a constant mass flow is specified on one of the boundaries of domains of the other component. For the steady-state mode, we obtain analytic expressions for the concentration of admixtures and mass flows through the internal contact surface.

A heat conduction problem of 2D unbounded composites with imperfect contact conditions

We consider a steady-state heat conduction problem in 2D unbounded doubly periodic composite materials with temperature independent conductivities of their components. Imperfect contact conditions are assumed on the boundaries between the matrix and inclusions. By introducing complex potentials, the corresponding boundary value problem for the Laplace equation is transformed into a special R-linear boundary value problem for doubly periodic analytic functions. The method of functional equations is used for obtaining a solution. Thus, the R-linear boundary value problem is transformed into a system of functional equations which is analysed afterwards. A new improved algorithm for solving this system is proposed. It allows to compute the average property and reconstruct the temperature and the flux at an arbitrary point of the composite. Computational examples are presented.

Numerical investigations of effective properties of fiber reinforced composites with parallelogram arrangements and imperfect interface

In this paper unidirectional fiber composites with imperfect interface conditions between the reinforcement and the filler are considered. The microstructure is periodic and the phases have isotropic properties. The periodicity of the microstructure is characterized by a parallelogram. Using the concept of a representative volume element (RVE) a finite element model is developed, in which the distribution of fibers and imperfect contact conditions between interfaces of phases can vary. Applying appropriate periodic boundary conditions to the chosen RVE effective material properties are derived, where those are related to a predefined coordinate system. The homogenization technique is validated by comparing results to literature as far as possible.

Micromechanical analysis of fibrous piezoelectric composites with imperfectly bonded adherence

In this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Mechanical imperfect contact at the interface of the piezoelectric composites is studied via linear spring model. The statement of the problem for two-phase piezoelectric composites with mechanical imperfect contact is given. The local problems are formulated by means of the asymptotic homogenization method, and their solutions are found using complex variable theory. Analytical formulae are obtained for the effective properties of the composites with spring imperfect type of contact and different rhombic cells. Using the concept of a representative volume element (RVE), a finite element model is created, which combines the angular distribution of fibers and imperfect contact conditions (spring type) between the phases. Periodic boundary conditions are applied to the RVE, so that effective material properties can be derived. The fibers are distributed in such a way that the microstructure is characterized by a rhombic cell. The presented numerical homogenization technique is validated by comparing results with theoretical approach reported in the literature. Some studies of particular cases, numerical examples, and comparisons between the two aforementioned methods with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of rhombic cells and the aforementioned imperfect contact.

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.

Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphases

We obtain a limit model for a thin curved anisotropic interphase adherent to two elastic media. Our method is based on asymptotic expansions and energy minimization procedures. The model of perfect interface is obtained at the first order, while an imperfect interface model is obtained at the next order. The conditions of imperfect contact, given in a parallel orthogonal curvilinear coordinate system, involve the interphase material properties, the first order displacement and traction vectors, and their derivatives. An example of implementation of the imperfect interface condition is given for a composite sphere assemblage.