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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]

[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]

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]

• 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]