Search

Layered materials play a crucial role in numerous essential structures, including adhesive connections, composite laminates, and various electronic components. This work focuses on proposing a novel framework of algorithms to improve the adaptability of element-free Galerkin method for modeling fracture in bimaterials exposed to thermoelastic loads. A bimaterial fracture problem is modeled as a combination of both weak and strong discontinuities — strong discontinuity owing to the presence of crack and weak discontinuity due to inherent material discontinuities. Initially, three distinct methods, comprising domain partitioning, lagrange multiplier, and jump function have been employed for interface crack modeling and error norm is used as an indicator to select the optimum one. Second, a novel interface enrichment algorithm has been introduced to effectively model the interface with limited computational costs with higher accuracy. Owing to the applicability of bimaterials in numerous applications under a combination of thermal/mechanical loads, the proposed formulation has been utilized for modeling and simulating a diverse bimaterial thermoelastic fracture problems using the proposed framework. The mixed mode (complex) stress intensity factors (SIFs) are numerically examined using modified domain form of interaction integral. A good agreement of results with available results from literature extends the computational prowess of the proposed framework in modeling a variety of thermoelastic bimaterial problems accurately and swiftly as compared to conventional EFGM. [ABSTRACT FROM AUTHOR]

The solution to the problem for the acoustic-emission field of displacements in an elastic bimaterial consisting of two half-spaces generated by a time-harmonic given displacement of opposite surfaces of an internal circular torsion crack parallel to the interfacial plane is obtained using the method of boundary integral equations. The effect on the parameters of displacement amplitudes of different types of contact conditions on the interface plane—perfect mechanical contact and contact through a thin compliant gap, which is modeled using effective spring boundary conditions—is investigated. The effect on the amplitudes of displacements in space, the frequency of displacements of the crack surfaces, the ratio of stiffnesses of the bimaterial components, and the location of the point of observation of displacements are analyzed numerically. The effect of shielding dynamic displacements by a layer in comparison with their analogs for half-spaces with perfect contact is determined. A decrease in the displacement amplitudes (relative to the case of a homogeneous body with a crack) in the defect-free component of the bimaterial is found with an increase in the ratio of stiffnesses of the contacting materials. [ABSTRACT FROM AUTHOR]

By using the method of integral Fourier transforms, the method of jump functions, and the method of conjugation of continua of different dimensions, we construct the solution of the basic problem of longitudinal shear of an anisotropic bimaterial containing a system of thin internal ribbon anisotropic inhomogeneities in each half space. By analyzing an example of reducing the problem of longitudinal shear of an anisotropic two-layer structure with thin inhomogeneities to the basic problem, we approve the previously developed method of direct cutting-out. We also investigate the influence of elastic moduli and specific geometric parameters of the problem on the generalized stress intensity factors. [ABSTRACT FROM AUTHOR]

We formulate the problem of thermoelasticity for a bimaterial with interface crack filled with a liquid with regard for the pressure and heat conductivity of the liquid. We consider the case of partial crack closure on the edges under the action of a compressive load and a heat flux. The problem is reduced to a system of nonlinear singular integrodifferential equations for a temperature jump between the crack faces and its opening displacement. The length of the contact zone is determined from the condition of smooth closure of crack faces at the points separating the open and closed parts of the crack. We analyze the changes in the crack length and height and in the pressure of liquid depending on the compressive loads, density of the heat flux, and its direction. We also determine the dependence of the mode-II stress intensity factor on the level of pressure and the thermal conductivity coefficient of liquid. [ABSTRACT FROM AUTHOR]

On the basis of the theory of functions of complex variable and the method of jump functions, we propose a procedure of taking into account the additional influence of surface stresses in the problem of thin interface inclusion in the bimaterial. In this problem, we take into account the possibility of imperfect contact between the inclusion and the matrix and, in particular, the possibility of contact with surface tension. This significantly extends the field of applicability of the results of simulation within the framework of the concept of representative volume element in micro- and macromechanics. We propose a generalized model of thin inclusion with arbitrary mechanical properties. The analysis of test problems reveals high accuracy and efficiency of the proposed approach. We present the results of numerical analyses of the stress fields in the case of interaction of the inclusion with concentrated forces and screw dislocations. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Green's functions of two-dimensional (2D) piezoelectric quasicrystal (PQC) in half-space and bimaterials. Based on the elastic theory of QCs, the Stroh formalism is used to derive the general solutions of displacements and stresses. Then, we obtain the analytical solutions of half-space and bimaterial Green's functions. Besides, the interfacial Green's function for bimaterials is also obtained in the analytical form. Before numerical studies, a comparative study is carried out to validate the present solutions. Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force, the line dislocation, the line charge, and the phason line force. As a result, the coupling effect among the phonon field, the phason field, and the electric field is prominent, and the butterfly-shaped contours are characteristic in 2D PQCs. In addition, the changes of material parameters cause variations in physical quantities to a certain degree. [ABSTRACT FROM AUTHOR]

The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier's law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method approach allowed us to estimate the thermophysical parameters sought. We validated the numerical procedure by using noiseless temperature fields at different time and space steps and two types of material: an homogeneous and a bimaterial one. To be close to real conditions, the influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results of this procedure show that the identified parameters are very less sensitive to the number of infra-red images varying from 40 to 80 and the number of elements ranging from 20 to 50 for a specimen size equals to 36.6 × 36.6 mm2. [ABSTRACT FROM AUTHOR]

Impact protection equipment typically relies on the material failure mechanism and is frequently discarded after the impact. A promising alternative emerges utilizing a foam-infilled lattice bimaterial with shape recovery trait and customizable impact protection capability. This study employs a numerical approach to elucidate the energy dissipation mechanism exhibited by the bimaterial under low-velocity impact condition. The experiment-based inverse method is used to characterize visco-hyperelastic models for two base materials. The investigation reveals that the interaction between the two base materials significantly amplifies the foam's energy dissipation capability, resulting in an overall higher energy dissipation for the bimaterial. Besides, the study establishes a close correlation between the bimaterial's effective viscoelastic properties and the enhancement in energy dissipation. Furthermore, the numerical design of experiments (DOE) analysis of base material properties indicates that there is an optimal region for selecting the critical foam material constants for a significant improvement of bimaterial energy dissipation. The results reveal that the combination effect of material interaction and material viscoelastic properties constitutes the fundamental elements of bimaterial energy dissipation mechanism. The insight derived from this study can inform the future design and material selection of a more complicated bimaterial across a wide range of impact protection applications. • Bimaterial is a promising impact protection gear compared with traditional materials. • Experiment-based inverse method contributes to representative model characterization. • Fundamental elements of bimaterial energy dissipation mechanism are revealed. • Material interactions enhance foam energy dissipation capabilities inside bimaterial. • Certain material constants combination can significantly improve energy dissipation. [ABSTRACT FROM AUTHOR]

We employ the Stroh octet formalism to develop a real-form expression of the Coulomb force acting on a line charge in an anisotropic piezoelectric bimaterial. The Coulomb force is derived using two different approaches and is expressed in terms of the generalized Barnett–Lothe tensors for the two piezoelectric half-spaces. Interestingly, we find that the Coulomb force is independent of the orientation of the bimaterial interface provided that the interface is parallel to the x 3 -axis and the distance between the charge and the interface remains unchanged. The Coulomb force on a line charge in a piezoelectric half-space with a rigid conducting surface or a traction-free insulating surface is deduced from the Coulomb force for two jointed piezoelectric half-spaces. In the case of a rigid conducting surface, we find that the Coulomb force always tends to attract the line charge to the surface. This is in contract to the case of a traction-free insulating surface for which we find that the Coulomb force can be either repulsive or attractive due to the piezoelectric effect. [ABSTRACT FROM AUTHOR]

A multimaterial strategy is adopted in combination with the structure innovation to achieve enhanced structural stiffness, and meanwhile, to retain the auxetic behavior for auxetic metamaterials. A bimaterial reentrant structure with additional soft arch-like beams and hinges is proposed, and then investigated using both experimental and simulation approaches. The results indicate that the buckling issue of the beam/wall can be significantly reduced if the strength of the hinge is kept small, and the reduction of auxetic behavior due to increased stiffness can also be minimized. Therefore, the strategy to enhance the design flexibility for auxetic metamaterials is verified. [ABSTRACT FROM AUTHOR]

In a private communication with D. M. Barnett, W. D. Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free surface of an isotropic elastic half-space. Nix drew a series of conclusions from his numerical computations including the independence of the net interaction force on the distance h. In seeking the extension of Nix's conclusions to half-spaces of arbitrary anisotropy, Barnett called Nix's original set of results 'Nix's Theorem'. In this paper, using the Stroh octet formalism, we derive new explicit and real form expressions for the net interaction force between two skew dislocations with generalized Burgers vectors, separated by a distance h, in an infinite anisotropic piezoelectric space, in a half-space and in a bimaterial. Each dislocation undergoes finite discontinuities in displacements and in electric potential across the slip plane. The net interaction force is yet again found independent of the separation distance. For an infinite space and half-space with a traction-free and charge-free surface, the net interaction force is found independent of the second component of each of the two generalized Burgers vectors and vanishes when only the second component of one generalized Burgers vector is nonzero and the remaining three components are zero. [ABSTRACT FROM AUTHOR]

We achieve elastic cloaking for a periodic distribution of an infinite number of parallel finite mode III cracks by means of the complex variable method and the theory of Cauchy singular integral equations. The cloaking bimaterial structure is composed of an undisturbed uniformly stressed left half-plane perfectly bonded via a wavy interface to the right half-plane which contains periodic cracks. The original design of the wavy interface and the positions of the periodic cracks are ultimately reduced to the solution of a Cauchy singular integral equation which can be solved numerically. [ABSTRACT FROM AUTHOR]

In this paper, primarily with the aid of analytic continuation, we derive analytic solutions for Eshelby's problem of a parabolic inclusion undergoing uniform anti‐plane and in‐plane eigenstrains located in one of two well‐bonded dissimilar elastic half‐planes. We obtain elementary expressions of the analytic functions defined in all three phases characterizing the elastic fields representing displacements, strains and stresses in the composite. [ABSTRACT FROM AUTHOR]

We experimentally and analytically explore supershear ruptures that are excited at the onset of frictional motion within "bimaterial interfaces," frictional interfaces formed by contacting bodies having different elastic (or geometric) properties. Our experiments on PMMA blocks sliding on polycarbonate show that the structure, transition sequence, and range of existence of such supershear ruptures are highly dependent on their propagation direction relative to the slip direction in the softer of the two materials. These properties are characterized for both the positive (parallel) and negative (antiparallel) propagation directions. An analytic, fracture‐mechanics based description of supershear ruptures is derived. The theory quantitatively predicts both supershear structure and the allowed propagation range of supershear ruptures. The latter compares well with both the experimentally observed supershear ruptures in the negative direction as well as localized slip pulses in the positive direction, whose propagation speed lies between the shear velocities of both materials. Supershear ruptures in the positive direction, which are composed of trains of propagating slip pulses, evade this theoretical description. Key Points: Supershear ruptures within bimaterial interfaces possess unique characteristic propertiesSupershear properties depend on their propagation directionA number of these properties are explained by our accompanying analytic solution [ABSTRACT FROM AUTHOR]

Summary: The eXtended hybridizable discontinuous Galerkin (X‐HDG) method is developed for the solution of Stokes problems with void or material interfaces. X‐HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high‐order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level‐set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two‐dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X‐HDG, with the freedom of computational meshes that do not fit the interfaces [ABSTRACT FROM AUTHOR]

Abstract Design of materials and structures with quite low coefficient of thermal expansion (CTE), even zero or negative CTE is important for industrial application where drastic temperature changes are encountered. In this paper, making use of the bending of bi-material beam and the unique deformation mechanism of chiral lattice structures, five sets of chiral lattice composite structures with tailorable CTEs are proposed, where synergic effects of rigid node rotation and bi-material ligament bending deformation are responsible for giant range of structural deformation due to temperature change, from positive CTE to negative CTE through adjusting the geometrical parameters of composite bi-material chiral unit cell, and the relationship between unit cell geometric parameters and CTEs of the structure are studied systematically through finite element analysis. Finally, design of bi-material cylindrical shells consisting of anti-tetra chiral unit cells are proposed, and its axial CTEs with different number of the unit cells along the circumferential are studied systematically, demonstrating the robust range of CTEs can be generated through adjusting the geometrical parameters of chiral bi-material unit cells. The proposed chiral structures demonstrated promising application potentials in industrial fields, such as: aerospace and microelectronics, where extremely high structural accuracy is required during harsh working temperature environment. [ABSTRACT FROM AUTHOR]

Highlights • Cylindrical system of vector functions. • Transversely isotropic diffusive bimaterials. • General concentrated dislocations and diffusive source. • Analytical Green's function solution. • Effect of diffusive coefficients on the dislocation field. Abstract While the fundamental solutions of concentrated forces and dislocations in purely elastic media are available for various applications, solutions in the corresponding diffusive materials have seldom been derived due to the involved complexity. In this paper, in terms of the cylindrical system of vector functions and under the assumption of steady-state deformation, we derive analytically the elastic and diffusive fields induced by the concentrated forces and dislocations which are located on the interface of a transversely isotropic and diffusive bimaterial space. Solution of the concentrated diffusive source has been also derived. These solutions can further be reduced to the corresponding isotropic bimaterial case and the transversely isotropic full-space case. Based on the newly derived solutions, field quantities induced by different concentrated dislocation sources are presented numerically to demonstrate the effect of the diffusive coefficients, material heterogeneity, and dislocation types on the induced fields. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel Brazilian bimaterial disc specimen with crack normal to and terminating at the interface subjected to varying mode mixities is studied using experimental method of photoelasticity. • Crack tip stress field equation for crack terminating at the bimaterial interface is revisited and incorporated in an in-house developed software PSIF for SIF evaluation. • The software is used to evaluate the SIFs with a non-linear least squares iterative procedure using data collected from experimental images of crack tip isochromatics. • Two bimaterial specimens, a polymer–polymer and a metal-polymer bimaterial pairs having two different bimaterial constant values are used for the study. • Mode-I and Mode-II SIFs and interfacial SIFs are evaluated at varying crack orientation angles with respect to the loading points. • The results provide an insight into the effect of mixed mode loading on the crack tip SIF in bimaterials with crack normal to the interface and subjected to similar loading conditions. SIFs for crack terminating perpendicular to the interface of a bimaterial subjected to varying mode mixities are evaluated with a novel bimaterial specimen using the experimental technique of photoelasticity. A simple form of multiparameter equation defining the stress field for the crack terminating at the interface at an arbitrary angle along with the details on interfacial SIF and combined SIF for a bimaterial problem are brought out. The stress field equation is incorporated in an in-house developed PSIF software as a separate problem module for the determination of crack tip stress field parameters using a non-linear least squares methodology. A compact bimaterial Brazilian disc specimen with crack in one of the material sides terminating perpendicular to the interface and at an arbitrary angle to the point of loading, is considered for the study. SIFs of two such specimens, a polymer–polymer pair, and a metal-polymer pair with two different bimaterial constants are determined. The normalized SIF values are evaluated as a function of crack orientation angles. The SIF values for the metal-polymer pair were found to be higher compared to the polymer–polymer interface. The peak values of SIFs are observed at a crack orientation angle of 30°. At orientation angles close to 0° and 90°, the SIF values were less pronounced. [ABSTRACT FROM AUTHOR]

• A bimaterial specimen subjected to bending with a crack terminating at an arbitrary angle to the interface is studied using photoelasticity technique. • Crack tip stress field equation for crack terminating at the bimaterial interface is revisited and incorporated in an in-house developed software PSIF for SIF evaluation. • The software is used to evaluate the SIFs with a non-linear least squares iterative procedure using data collected from experimental images of crack tip isochromatics. • SIFs are evaluated for varying crack inclination angels. • The results provide an insight into the effect of crack inclination angles on the crack tip SIFs. A bimaterial strip made of Aluminum-Epoxy pair with crack terminating at an arbitrary angle to the interface subjected to bending is studied using photoelasticity technique. When the crack terminates at an arbitrary angle to the interface, the stress singularity depends on the bimaterial elastic constants as well as the geometry of the crack. The shape of the photoelastic fringe patterns observed at the crack tip terminating at the interface varied based on the crack inclination angle. Complex crack tip stress field equation for crack terminating at an arbitrary angle to the interface along with an over deterministic non-linear least squares method incorporated in an in-house developed PSIF software is used for the evaluation of SIFs. The effect of the crack inclination angle on the SIF values is brought out. Mode-I and Mode-II SIFs, interfacial SIF, combined SIF, and phase angle are evaluated for the bimaterial pair considered. The corresponding normalized SIF values are calculated. It is observed that the SIF values increase with the crack inclination angle. Cracks at angles greater than 45° have significant SIF values, with highest SIF values occurring for 90° crack. [ABSTRACT FROM AUTHOR]

Abstract The partition of the energy release rate of beam-like geometries is analyzed here. Several methods for partitioning mode I and II energy release rates are presented and critically compared. A Timoshenko beam theory with Dugdale cohesive stress is applied and results show a mixed mode energy release rate dependence on the interface fracture toughness. A geometry is proposed that eliminates this dependence, offering a method to characterize the fracture properties of interfaces between dissimilar materials. [ABSTRACT FROM AUTHOR]

Abstract In this study, based on multipole expansion method an analytical treatment is presented for the anti-plane scattering of SH-waves by an arbitrarily oriented elliptic cavity/crack which is embedded near the interface between exponentially graded and homogeneous half-spaces. The cavity is embedded within the inhomogeneous half-space. The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy (i) the governing equation in each half-space, (ii) the continuity conditions across the interface between the two half-spaces, and (iii) the far-field radiation and regularity conditions. The analytical expressions for the scattered elastodynamic fields are derived and the dynamic stress concentration factor associated with the elliptic cavity as well as the dynamic stress intensity factor relevant to the case of a crack are calculated. In the given numerical examples, the effects of such parameters as the incident wave number, angle of the incident waves, the distance of the cavity to the bimaterial interface, and the aspect ratio and the orientation of the elliptic cavity/crack on the scattered field are addressed in detail. It is seen that such parameters have significant effect on the dynamic response of the medium. Highlights • SH-waves scattered by an arbitrarily oriented elliptic cavity/crack. • Multipole expansion of the scattered displacement field. • Exponentially graded half-space with an arbitrarily oriented elliptic cavity/crack. • Dynamic stress intensity factor at the crack-tip. • An arbitrarily oriented elliptic cavity/crack near the interface of a bimaterial. [ABSTRACT FROM AUTHOR]

We examine the plane strain deformations of a bimaterial system consisting of a line edge dislocation interacting with a flat interface between two dissimilar isotropic half-planes in which the additional effects of interface elasticity are incorporated into the model of deformation. The entire system is assumed to be free of any external loading. Despite the fact that it is generally accepted that the separate interface modulus describing interface elasticity is permitted to take negative values, we show that simple closed-form solutions for the dislocation-induced stress field and the image force acting on the dislocation are available only when the interface modulus is assumed to be positive; the corresponding system admits no valid solutions when the interface modulus is negative. We present several numerical examples to illustrate our solutions. Additionally, we show that the influence of interface elasticity on the dislocation-induced interfacial stress field decays with increasing hardness of the adjoining half-plane (free of the dislocation). Moreover, we find that for a given (positive) in-plane interface modulus, the corresponding interface effects on the image force (acting on the dislocation) can reach maximum or minimum values when the Burgers vector of the dislocation is either parallel or perpendicular to the interface. [ABSTRACT FROM AUTHOR]

Until now, the coupled stress and energy criterion has mainly been used in 2D applications, but it is possible to extend it to a 3D case. Herein the crack initiation in epoxy/aluminum bimaterial specimens under four point bending is predicted through a 3D numerical application of the coupled criterion. The stress and the energy conditions are computed by means of 3D finite element modeling of both undamaged and cracked specimens. The crack initiates at the epoxy/aluminum interface, meshes of the cracked specimens take into account the crack topology which is determined using the interface normal stress isocontours. By indirect confrontation to experimental tests on aluminum/epoxy bimaterial specimens of different width, the proposed approach allows determining the interface strength and fracture energy. The blind application of the proposed method to a crack initiation in aluminum/epoxy/aluminum specimens of different epoxy layer thickness under four point bending leads to a reasonable agreement with experimental data. [ABSTRACT FROM AUTHOR]

A novel strategy for the hybridizable discontinuous Galerkin (HDG) solution of heat bimaterial problems is proposed. It is based on eXtended finite element philosophy, together with a level set description of interfaces. Heaviside enrichment on cut elements and cut faces is used to represent discontinuities across the interface. A suitable weak form for the HDG local problem on cut elements is derived, accounting for the discontinuous enriched approximation, and weakly imposing continuity or jump conditions over the material interface. The computational mesh is not required to fit the interface, simplifying and reducing the cost of mesh generation and, in particular, avoiding continuous remeshing for evolving interfaces. Numerical experiments demonstrate that X-HDG keeps the accuracy of standard HDG methods in terms of optimal convergence and superconvergence. [ABSTRACT FROM AUTHOR]

We use the extended Stroh formalism and the theory of functions of complex variable to construct Somigliana-type integral relations and the corresponding equations for thermoelastic anisotropic bimaterial solids with imperfect thermal contact on the rectilinear interface between their components. Applying the mathematical model of thin deformable thermally insulated inclusion and the obtained integral relations, we solve the thermoelasticity problem for a finite anisotropic bimaterial solid containing a thin inhomogeneity with regard for the thermal resistance on the interface between the main components of the materials. [ABSTRACT FROM AUTHOR]

In this paper we derive explicit expressions for the Green’s functions in the case of an anisotropic elastic half-space and bimaterial subjected to a line force and a line dislocation. In contrast to previous studies in this area, our analysis includes the contributions of both anisotropic surface elasticity and surface van der Waals interaction forces. By means of the Stroh sextic formalism, analytical continuation and the state-space approach, the corresponding boundary value problem is reduced to a system of six (for a half-space) or 12 (for a bimaterial) coupled first-order differential equations. By employing the orthogonality relations among the corresponding eigenvectors, the coupled system of differential equations is further decoupled to six (for a half-space) or 12 (for a bimaterial) independent first-order differential equations. The latter is solved analytically using exponential integrals. In addition, we identify four and seven non-zero intrinsic material lengths for a half-space and a bimaterial, respectively, due entirely to the incorporation of the surface elasticity and surface van der Waal forces. We prove that these material lengths can be only either real and positive or complex conjugates with positive real parts. [ABSTRACT FROM AUTHOR]

The eXtended Finite Element Method (X-FEM) is a versatile tool to model cracks and interfaces where sharp gradients and even discontinuity of deformation across the interface may occur. The enrichment functions are introduced to depict possible discontinuity and singularity known from analytical solutions. For bimaterials, the gradients of the displacements are discontinuous across the interface, which can be modeled by ramp functions. In this work, we check the role of the enrichment strategies with and without ramp functions for the accuracy of enriching schemes, and also compare three different methods, i.e. the Interaction Integral Method (IIM), Contour Integration Method (CIM), and Displacement Correlation Method (DCM), to extract the Stress Intensity Factors (SIFs). Both planar and non-planar examples are employed to examine the enriching strategies and the three SIF extraction methods. We find that the enriched ramp functions can improve the accuracy in terms of strain energy, but do not significantly affect the SIFs. The IIM is the best choice to extract SIFs and the DCM can provide enough accuracy with a careful choice of extraction parameters. This work can help a reader when choose the enriching strategies and the extraction methods of the SIFs for interface cracks between dissimilar materials. • Cracks lying on the interface between bimaterials are modeled by the X-FEM. • The role of the enrichment strategies with and without ramp functions is examined for the accuracy of enriching schemes. • Three different methods to extract the stress intensity factors are intensively compared. • Both planar and non-planar examples are employed for the comparisons. [ABSTRACT FROM AUTHOR]

In this paper, a bimaterial composite consists of a stiff 3D printed frame and a soft viscoelastic foam is investigated for impact protection applications. Samples of the base materials, frames, and bimaterials with two different volume fractions were subjected to free fall impact at different impact velocities. The data from an accelerometer and a high-speed camera were analyzed to obtain the impact force, deformation, and energy dissipation. The experimental results showed that the impact force and deformation are inversely related, and the bimaterial composite can be a good compromise solution. The energy dissipation of the bimaterial, however, is reduced when compared with that of the base materials. The results also show that for the present lattice frame structure, increasing the volume fraction of the frame material can reduce displacement and energy dissipation but increase impact force. This phenomenon indicates the potential of tuning the attributes of bimaterial, such as the base material property and the 3D printed frame geometry, for improved impact protection performance. • 3D printed frame with viscoelastic foam is an effective composite for impact energy dissipation. • As the impact force and deformation are inversely related, the bimaterial is a good compromise. • Base material selection and 3D printed frame design can improve impact protection performance. [ABSTRACT FROM AUTHOR]

The present paper deals with an analytical description and FEM modeling of stress fields at the tip of a sharp rigid inclusion located on the bimaterial interface. In the asymptotic solutions obtained, modified stress intensity factors appear, which allow one to take into account the oscillatory singularity of occurring stress fields. Values of these factors are found using a FEM simulation combined with two probabilistic methods: extrapolation and approximation. Calculations are carried out for normal and shear loads. [ABSTRACT FROM AUTHOR]

The present work investigates the shape optimization of bimaterial structures. The problem is formulated using a level set description of the geometry and the extended finite element method (XFEM) to enable an easy treatment of complex geometries. A key issue comes from the sensitivity analysis of the structural responses with respect to the design parameters ruling the boundaries. Even if the approach does not imply any mesh modification, the study shows that shape modifications lead to difficulties when the perturbation of the level sets modifies the set of extended finite elements. To circumvent the problem, an analytical sensitivity analysis of the structural system is developed. Differences between the sensitivity analysis using FEM or XFEM are put in evidence. To conduct the sensitivity analysis, an efficient approach to evaluate the so-called velocity field is developed within the XFEM domain. The proposed approach determines a continuous velocity field in a boundary layer around the zero level set using a local finite element approximation. The analytical sensitivity analysis is validated against the finite differences and a semi-analytical approach. Finally, our shape optimization tool for bimaterial structures is illustrated by revisiting the classical problem of the shape of soft and stiff inclusions in plates. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Debonding fracture of a bimaterial strip with two interfaces is investigated subjected to concentrated forces and couples. In the previous paper (ZAMM, see below), closed form stress functions were derived for the bonded bimaterial planes with two interfaces. As a demonstration of geometry, semi-strips bonded at two places of the ends of strips subjected to concentrated forces and couples were analyzed. Using the stress function, the stress intensities of debonding (SID) are obtained. To investigate the accuracy of SID calculated by the stress function, a comparison with the results obtained by a boundary element analysis is carried out and it is confirmed that they agree well each other. It is stated that SID is the square root of the strain energy release rate and the same as the strain energy release rate for evaluating the strength of the fracture. Then the debonding extension behaviors are investigated for some initial debonding states and three loading conditions, concentrated forces, couples and both combined loadings, using SID. Expressions to calculate SID for arbitrary loading magnitudes are derived. Fatigue growth of debonding under cyclic loading is also investigated, using Paris law regarding fatigue. [ABSTRACT FROM AUTHOR]

A closed-form solution is derived for the bonded bimaterial planes at two interfaces subjected to different temperatures. The bonded planes with two interfaces are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann-Hilbert problem. The solution includes an integral term. This integral cannot be carried out. However, the first derivative of complex stress functions which does not include integral terms with regard to the variables of the mapping plane is achieved. Therefore, there is no need for numerical integration to calculate stress components and to determine unknown coefficients in a complex stress function. This is very beneficial. It is more difficult to derive the solution to the two-interface problem compared to the general solution. As a demonstration of geometry, semi-strips bonded in two places at the ends of strips are considered. Unbonded parts are a model of debonding. The solution for different geometrical shapes can be obtained by changing the mapping function. Some stress distributions are shown for different lengths of the interface. The stress intensity of debonding (SID) (corresponding to the root of strain energy release rate) is investigated for the debonding extension. SID is the same as the root of strain energy release rate for the evaluation of the strength at the debonding tip. [ABSTRACT FROM AUTHOR]

We study the anti-plane deformations of a linearly elastic bimaterial. One phase of the bimaterial is weakened by a finite crack with surface elasticity perpendicular to the interface and is also subjected to a screw dislocation. The surface elasticity is incorporated by using a version of the continuum-based surface/interface model of Gurtin and Murdoch. By considering a distribution of screw dislocations and line forces on the crack, the interaction problem is reduced to two decoupled first-order Cauchy singular integro-differential equations, which can be numerically solved by means of the Chebyshev polynomials and the collocation method. The associated problem of a mode III Zener-Stroh crack perpendicular to a bimaterial interface is also solved. [ABSTRACT FROM AUTHOR]

A representation theorem is obtained for an arbitrarily loaded elastic bimaterial solid consisting of an infinite plane containing a circular inhomogeneity. The elastic image method is used for the analysis. The theorem expresses the Airy stress functions that generate the elastic fields for the composite solid explicitly in terms of the Airy stress function for the corresponding homogeneous infinite solid. It shows that if the solution for the homogeneous infinite solid is available, then the solutions for the corresponding bimaterial solid can be deduced by the process of differentiation and integration. The result could provide the important advantage of economy of effort in the determination of the elastic fields for composite planes with circular interfaces. [ABSTRACT FROM AUTHOR]

A closed form solution is derived for the bonded bimaterial planes at two interfaces. The bonded planes with two interfaces are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann-Hilbert problem. Two interfaces problem to derive the general solution is more difficult than one interface problem. As a demonstration of geometry, semi-strips bonded at two parts at the ends of strips are considered. The solution of different geometrical shapes can be obtained by changing the mapping function. Concentrated forces and couples are applied to the each strip. The first derivative of complex stress functions which does not include integral terms with regard to variable of the mapping plane is achieved. Therefore, there is no need of numerical integration to calculate stress components and to determine unknown coefficients in complex stress function. This is very benefit. All elastic constants in complex stress functions are expressed by Dundurs' parameters. Stress distributions are shown for different lengths of the interface. [ABSTRACT FROM AUTHOR]

This work deals with the coupling interaction of a screw dislocation with a bimaterial interface and a nearby circular inclusion. Explicit series solutions are obtained by the complex potential and conformal mapping technique. Then the solutions are cast into new expressions with the coupling interaction effects separated. The new expressions converge rapidly and provide good first-order approximation formulae. The interaction energy and image force fields are formulated, evaluated, and shown graphically. It is found that the inclusion severely distorts the neighboring interaction energy contours and image force lines. There must be one unstable equilibrium point in Material 2 where the inclusion is located, whereas there may be zero, one or two equilibrium points (stable or unstable) in Material 1 without any inclusion, which depends on a combination of three material shear moduli and the nondimensional distance between the inclusion and bimaterial interface. It is interesting to notice that the direction of some local image forces in Material 1 may be inversed by a nearby inclusion in Material 2, and the inverse region is close to but not connected to the bimaterial interface. [ABSTRACT FROM AUTHOR]

The elastostatic bending of an arbitrarily loaded bimaterial plate with a circular interface is analysed. It is shown that the deflections in the composite solid are directly related to the deflection in the corresponding homogeneous material by integral and differential operators. It is further shown that, by a simple transformation of elastic constants, the Airy stress function induced in the composite by a stretching singularity can be deduced from the deflection induced by a bending singularity. This result is significant for reduction of mathematical labour and for systematic construction of solutions for more complex structures with circular geometry. [ABSTRACT FROM AUTHOR]

This paper presents the results of investigating a flat element of two-phase structure with sharp linear inclusion located at the interface. Analytical description of fields of stresses and displacements at the tip of a sharp rigid inclusion was obtained as an asymptotic. It was presented as a function of modified stress intensity factors. Relationship between the classically defined stress intensity factors KI, KII and modified coefficients ..., ... has been defined. Possibility of using different methods (e.g. the FEM) set on determining coefficients ... has been discussed, and thus these values have been calculated numerically and compared with the exact solution. [ABSTRACT FROM AUTHOR]

• A crack and an electrically charged electrode at the interface are considered. • Piezoelectric bimaterial with arbitrary direction of polarization is studied. • The combined Dirichlet-Riemann problem is formulated and solved analytically. • The impact of the electrode charge and the materials' polarization direction is shown. • The way of mitigating of the threat of crack propagation is suggested. A charged interface electrode and a conductive interface crack between different piezoelectric half-spaces with an arbitrary polarization direction under out-of-plane mechanical loading and in-plane electrical field are considered. An analytical method is used based upon the presentations of the electromechanical characteristics through sectionally-analytic vector-functions with the following formulation and solution of the combined Dirichlet-Riemann boundary value problem. Special attention is devoted to the formulation of the Gauss theorem for the electrode, which permits to take into account its charge. The expressions for stress, electric field, electric displacement jumps and the energy release rate (ERR) are found in a simple analytical form. The numerical results show the dependence of the ERR on the electrode charge, on the intensity of the electric field and on the directions of the polarization of the piezoelectric materials. It is particularly found that due to the appropriate choice of these parameters, the maximum value of the ERR for the crack can be substantially reduced, which mitigates the threat of crack propagation. [ABSTRACT FROM AUTHOR]

One attractive option to achieve real-time terahertz (THz) imaging is a microelectromechanical systems (MEMS) bimaterial sensor with embedded metamaterial absorbers. We have demonstrated that metamaterial films can be designed using standard MEMS materials such as silicon oxide (SiOx), silicon oxinitrate (SiOxNy), and aluminum (Al) to achieve nearly 100% resonant absorption matched to the illumination source, providing structural support, desired thermomechanical properties and access to external optical readout. The metamaterial structure absorbs the incident THz radiation and transfers the heat to bimaterial microcantilevers that are connected to the substrate, which acts as a heat sink via thermal insulating legs, allowing the overall structure to deform proportionally to the absorbed power. The amount of deformation can be probed by measuring the displacement of a laser beam reflected from the sensor's metallic ground plane. Several sensor configurations have been designed, fabricated, and characterized to optimize responsivity and speed of operation and to minimize structural residual stress. Measured responsivity values as high as 1.2 deg /µW and time constants as low as 20ms with detectable power on the order of 10 nW were obtained, indicating that the THz MEMS sensors have a great potential for real-time imaging. [ABSTRACT FROM AUTHOR]

Abstract: This work develops a series of Green’s functions for multi-phase Kirchhoff isotropic laminated plates. First, we derive the Green’s functions for a composite laminated plate composed of two bonded dissimilar isotropic laminated semi-infinite plates. Second, the obtained results for bimaterials are judiciously applied to obtain the Green’s function solution for a circular elastic inclusion embedded in an infinite isotropic laminated plate. Third, Green’s functions for a composite space composed of an arbitrary number of wedges of different isotropic laminated plates are derived. Finally, we derive Green’s functions for a laminated plate with an elliptical and a parabolic boundary, respectively. [Copyright &y& Elsevier]

Abstract: A new complex-variable formalism for the analysis of three-dimensional (3D) steady-state heat transfer problems in homogeneous solids with general anisotropic behaviour is proposed in this paper. The derived method is based on the adon transform, which is used in order to reduce the dimension of the problem to a two-dimensional (2D) adon space where a solution can be easily handled via a complex-variable method. Subsequently, the 3D solution is obtained by applying the inverse adon transform. Despite that the main goal of this work is to develop and illustrate the general methodology, the proposed formalism is further applied to derive new Green’s functions as application examples. Contributions include new forms for bimaterial and half-space Green’s functions for line, point, vortex and dipole heat sources. In particular Green’s functions due to heat vortex loop sources for infinite media, half-space and bimaterial systems are presented for the first time. The veracity and computability of the approach are demonstrated with some numerical examples. [Copyright &y& Elsevier]

In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials (e.g., BaTiO), piezomagnetic materials (e.g., CoFeO), and multiferroic composite materials (e.g., BaTiO-CoFeO composites) also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displacements, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional (3D) dislocation loops with a constant extended Burgers vector in transversely isotropic magneto-electro-elastic (MEE) bimaterials (i.e., joined half-spaces). The derived solutions can also be simply reduced to those expressions for piezoelectric, piezomagnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials. [ABSTRACT FROM AUTHOR]