This paper examines the interfacial behavior of an electrode imperfectly bonded to a thermoelectric substrate, either with or without an adhesive interlayer. The governing integro-differential equations for the interface problem under consideration are formulated based on the equilibrium and deformation compatibility conditions. The integral equations are solved by utilizing the Gauss-Chebyshev discretization method. The effects of the debonding length, the debonding position, the thermoelectric load, the geometry, and the shear modulus of the electrode and the adhesive interlayer on the interfacial response are comprehensively studied. The singularities of the current density, the energy flux, and the shear stress at the debonding edges are analyzed in detail. It is found that a more reliable interface can be achieved if the electrode has a lower modulus. A thicker adhesive interlayer is demonstrated to effectively mitigate interfacial stress concentration. The results provide important references for the design of electrode-thermoelectric substrate systems in advanced flexible and stretchable thermoelectric devices.

Abstract The multifield coupled mechanical behavior at the contact interface of thermoelectric devices is a key scientific issue restricting their service performance and structural reliability, so relevant theoretical investigations possess important engineering and academic significance. This article addresses the thermo-electro-mechanical coupled contact problem between a rigid periodic wavy surface and functionally graded thermoelectric materials. A singular integral equation with a cotangent kernel is established, in which the kernel function involves an infinite series summation and material gradient parameters, enabling simultaneous characterization of the spatially inhomogeneous distributions of electrical conductivity, shear modulus, and thermal expansion coefficient. The Chebyshev collocation method is adopted to achieve highly accurate numerical solutions, with emphasis on the regulation mechanisms of surface morphology, material gradients, electric current load, and energy flux load on contact stress. Results show that surface period, gradient parameters, and energy flux load can significantly modify the contact stress level and the distribution profile. Proper gradient matching and energy flux input can effectively alleviate contact stress and realize active control of the contact state. The multifield coupled contact model constructed in this work provides direct theoretical support and numerical references for stress optimization and structural design of contact interfaces in thermoelectric devices.

Unlike conventional piezoelectric materials, quasicrystals (QCs) exhibit piezoelectric properties governed by both phason and phonon fields. As smart parts shrink to the micro-nano scale, surface adhesion becomes significant. To examine the difference of piezoelectric QCs in adhesive behavior compared with conventional piezoelectric materials, this study firstly establishes frictionless Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models for a two-dimensional hexagonal piezoelectric quasicrystal (2D HPQC) half-space indented by a rigid conical indenter (electrically conducting or insulating). Using the superposition principle and Griffith’s energy balance, key adhesive contact parameters are derived analytically. The results of this study are verified by reducing the models to classical piezoelectricity cases reported in the literature. Numerical results demonstrate that adjusting the cone angle and electrical potential influences the adhesive contact behavior of 2D HPQC. Most significantly, the analysis indicates that the adhesive behavior of 2D HPQC shows little difference compared to corresponding results from the conventional piezoelectric framework, as modeled by extended JKR and M-D theories. This work demonstrates that conventional piezoelectric contact theories are sufficient for modeling the adhesion behavior of 2D HPQC for given the specified material coefficients, thereby offering a critical simplification for the design and analysis of QCs-based devices.

With the advancement of micro-nano manufacturing technology, piezoelectric semiconductors(PS) devices are trending toward miniaturization, integration, and low power consumption. The core of regulating their interfaces and designing for high reliability lies in uncovering the mechanoelectric coupling mechanisms between interfacial stress transfer and carrier transport in three-dimensional adhesive contacts(TDAC), thereby enabling precise control over device performance. Based on the Maugin-Dugdale adhesion theory, this paper investigates the TDAC problem between a PS half-space and a rigid spherical indenter. A 3D multi-field coupled contact mechanical model considering the influence of carrier concentration is established. The pressure distribution, electric potential field, electric displacement, and stress field in the contact region are efficiently solved using the discrete convolution-fast Fourier transform (DC-FFT) algorithm. Numerical results show that an increase in carrier concentration enhances the internal screening effect of PS coupling, resulting in a slight increase in the contact radius. The contact pressure exhibits a centrally symmetric distribution, and the peak von Mises stress is concentrated at the contact edge, where this geometric discontinuity serves as a potential failure source. An increase in adhesion energy significantly strengthens the interfacial bonding strength and effectively suppresses contact damage, especially under low-load conditions. Increasing the adhesion parameter not only intensifies the edge stress concentration but also improves the uniformity of the electric potential field by optimizing the charge distribution and reduces the interfacial electric potential gradient, thereby enhancing the mechanoelectric reliability of the device.

The research of the contact vibration characteristics of piezoelectric semiconductors is crucial for the realization and optimization of functions such as energy conversion and signal sensing. This investigation analyzes the axisymmetric dynamic response of a semi-infinite piezoelectric semiconductor medium under localized loading from a spherical rigid indenter. Through the use of perturbation techniques and Hankel integral transformations, the dynamic contact pressure distribution and contact displacement are derived. Additionally, the dynamic contact stiffness (DCS) is obtained based on displacement boundary conditions. The numerical analysis section explores the effects of factors such as vibration frequency, contact displacement, internal friction coefficient, piezoelectric effect, semiconductor effect, and material constants on the DCS factor. The results show that the presence of the piezoelectric and semiconductor effects increases the contact stiffness of piezoelectric semiconductor materials and accelerates energy dissipation. Compared to the piezoelectric constant and carrier concentration, the elastic constant has a more significant impact on the DCS factor. The findings provide a theoretical foundation for the mechanical response of piezoelectric semiconductor materials in practical contact and vibration environments and offer valuable references for optimizing their performance and applications.

This paper presents a bond-based peridynamic (BBPD) model with rotational effects, accounting for the phonon-phason coupling to simulate damage evolution in one-dimensional hexagonal quasicrystals (1DHQCs) thin plate with a central crack. The expressions of the microscopic bond potential energy and the pairwise force are derived, from which the micromodulus functions are obtained. Based on these, a bond-based methodology is designed to simulate dynamic crack propagation while mitigating mesh sensitivity. The details are as follows: (i) the equations of motion are discretized; (ii) an explicit time-integration algorithm based on the central difference method is developed; (iii) a mesh adaptive strategy is introduced. Numerical results indicate that the phason field dissipates energy at the crack tip, thereby preventing local energy concentrations and delaying both crack initiation and branching. Furthermore, the reduction of shear stress in the phonon field alters the crack propagation mode from multidirectional branching to a straight path along the loading direction. These findings demonstrate the regulatory role of shear stress on crack morphology. The proposed BBPD method provides a novel pathway for investigating fracture in 1DHQCs, as it naturally captures crack propagation through bond-breaking without requiring a predefined path.

For evaluating material performance and ensuring structural integrity, we need to understand how the crack geometry and material property modulate wave-scattering phenomena. This task becomes a challenge when intricate geometric configurations and multi-physics coupling are involved. According to the Gurtin-Murdoch (G-M) surface/interface theory and the wave function expansion method, the present study addresses the scattering of SH waves induced by an arbitrary shaped nanohole on the boundary of a half-plane of one-dimensional hexagonal (1DH) quasicrystals (QCs). By applying Huygens principle and the orthogonality of trigonometric functions, an infinite set of algebraic equations for the scattering problem is derived, from which the solutions of the dynamic stress concentration factors (DSCFs) are obtained. The present study explores the impact of surface effects, incident angles and other factors on the DSCFs for three typical boundary nanohole shapes. The results show that the surface effect can suppress the dynamic stress concentration around the nanohole. The shape of the nanohole plays a key role in the variation trend of the DSCFs around the hole. When the shape of the nanohole changes, the DSCFs exhibit dramatic differences with changes in elastic constants. These findings offer valuable insights for nondestructive testing and reliability assessment of QCs, especially for crack inversion.

Exploring the interfacial adhesion mechanism between piezoelectric semiconductors (PESC) and other materials plays a pivotal role in enhancing devices reliability and prolonging its lifespan. This paper focuses on the mechanical behavior of axisymmetric adhesive contact in PESC materials and uncovers novel multi-physics contact mechanisms. The adhesive contact problem is converted into a singular integral equation with a Cauchy kernel by means of integral transform and transfer matrix method, and then numerically solved to obtain the multi-physics field distribution on the contact surface. An iterative algorithm is successfully developed to address the mechanical behavior of adhesive contact in PESC. The results demonstrate that under pressure loading, elevated adhesion stress inhibits the development of indentation depth (requiring a larger load) but enhances the expansion of the contact area (demanding a smaller load). An increase in initial carrier concentration weakens the adhesion effect, inducing a decrease in the critical pull-off force. These findings contribute to more accurate prediction and control of adhesion strength, thereby facilitating the optimization of PESC device design.

The wave scattering caused by the quasicrystals (QCs) inclusion directly affects the overall wave behaviors of the QCs. Using the Gurtin-Murdoch (G-M) surface/interface theory and the complex function theory, this paper explores the scattering problem of SH wave by a cylindrical nano inclusion in the 1D hexagonal QCs. The scattered wave is expressed as a series of wave functions by applying the wave function expansion method. Then, the boundary conditions at the nanoscale, extrapolated from the generalized Young-Laplace equations, are used to establish an infinite system of algebraic equations for solving the scattered wave functions with unknown coefficients. The analytical stress field solutions are derived from the orthogonal characteristics of the trigonometric functions, which provide a new idea and solution for wave propagation problems in QCs. The effects of the surface effect parameters, the elastic constants, the coupling coefficients, and the wave numbers on the dimensionless hoop and radial stresses of the phonon and phason fields (DHRSPP) around the nano inclusion are analyzed in numerical examples. The results show that the dimensionless hoop stress (DHS) around the nano inclusion gradually decreases, and the dimensionless radial stress (DRS) increases with the increase of the surface effect parameters as well as the ratio of the phonon field's elastic constants. The distribution of dimensionless radial and hoop stress around the nano inclusion becomes more complex with the increase in wave number. The coupling coefficients have a considerably small effect on the DHRSPP around the nano inclusion. The research here contributes to the optimization and improvement of acoustic imaging, non-destructive testing, and material evaluation methods for QCs.

When quasicrystal coatings are attached to substrates and subjected to local loads, the separation of the contact region edges is a common mechanical phenomenon, which makes receding contact a typical scenario that must be considered in the design and analysis of such structures. The frictionless receding contact problem between a one-dimensional hexagonal quasicrystal (QC) layer and an elastic substrate is investigated in this paper. By applying the Fourier integral transform, the plane problem is transformed into the first-kind Cauchy singular integral equation, where the unknowns are contact stress and half-length. By employing the Gauss–Chebyshev integration formula, the singular integral equation is discretized into a system of algebraic equations. An iterative algorithm is constructed to obtain contact length and stress that satisfy the force equilibrium condition. The numerical results discuss the influence of surface load length, phonon elastic constants, phason elastic constants, phonon–phason coupling coefficients, and substrate shear modulus on the contact behavior. The study demonstrates that reducing the phonon–phason coupling coefficient and the shear modulus of substrate can lower the peak contact stress, thereby helping to minimize contact damage to the greatest extent possible.

Using the integral transformation method, this study investigates the dynamic propagation problem of a moving crack in a functionally graded one-dimensional hexagonal quasicrystal strip. A Yoffe-type constant-velocity crack model was adopted. The boundary value problem of the partial differential equation was transformed into two pairs of dual integral equations through Fourier cosine transform, which are then solved by the Copson method. The stress field distribution near the crack tip was obtained. Expressions for the dynamic stress intensity factors (DSIFs) and the dynamic energy release rate of the phonon and phason fields were further derived. A numerical simulation was conducted to analyze the influences of material gradient parameters, crack velocity, crack length, strip thickness, phonon–phason coupling coefficient, and external load on the fracture behavior. The research results are expected to provide a theoretical basis for the fracture performance evaluation and gradient optimization design of functionally graded quasicrystals under dynamic loading.

The dynamic stability and durability of quasicrystal materials (QCMs) hinge on their corresponding contact vibration analysis. This study examines the axisymmetric vibrational characteristics induced by a one-dimensional hexagonal quasicrystal semi-infinite medium subjected to a rigid spherical indenter. By employing perturbation techniques combined with the Hankel transforms, this study determines the pressure distribution and displacement field during dynamic contact and establishes the dynamic contact stiffness (DCS) formulation under two different displacement boundary conditions. The numerical section presents the effects of various factors, including vibration frequency, displacement constraints, internal friction coefficient, phason field, and material elastic properties on the DCS behavior. The findings demonstrate that the phason field significantly decreases the stiffness characteristics of the one-dimensional hexagonal quasicrystal material and accelerates energy dissipation. The phonon field's elastic properties exert a greater influence on dynamic contact behavior compared to those associated with the phason field. The results obtained from this investigation make contributions towards unveiling the mechanisms of vibration transmission and energy dissipation at the contact interface of quasicrystal structures.

It is difficult to analytically solve the contact problem of one-dimensional hexagonal quasicrystal (1DHQ) coating considering the coupling effects of adhesion, friction force and frictional heat in the contact region, especially considering both the frictional heat and adhesion simultaneously. The thermally frictional adhesive contact problem of 1DHQ coating is investigated using a discrete convolution-fast Fourier transform-based (DC-FFT-based) semi-analytical method. The adhesive behavior is described based on the Maugis-Dugdale model, which was used to investigate the influence of adhesive force on the thermoelastic field. It is a continuum-mechanics model with all microscopic features subsumed in the elastic constants, covers only elastic behavior, omitting all other physical characteristics of quasicrystals. By developing an adhesion-driven conjugate gradient method (AD-CGM), the contact process is numerically implemented, and the DC-FFT method is applied to solve the contact displacement. The numerical results indicate that the contact area under the consideration of adhesive force is much larger than that without. For a given external force, the contact radius and adhesive radius increase with increasing parameters. And each physical quantity exhibits different changing trends with the variation of adhesive parameters, with 0.5 as the dividing line. The research results may provide theoretical guidance for the practical application of quasicrystals as thermal barrier coating materials, nanodevice materials, and intelligent robot coating materials.

The scattering characteristics of SH waves enable a deeper understanding of wave propagation, thereby improving the accuracy and reliability of non-destructive testing. By combining with the generalized Young–Laplace equation and the wave function expansion method, the anti-plane problem of SH wave scattering by a circular arc-shaped nano-hole within one-dimensional hexagonal (1DH) quasicrystal (QC) half-plane boundary is studied. Based on the Huygens principle, the Graf’s addition formula and the orthogonal characteristic of trigonometric functions, the analytical solutions for the dynamic stress concentration factors (DSCFs) are obtained. Numerical examples discuss the effects of the surface effects, the wave numbers, and the incident angle on DSCFs with different circular arc-shaped nano-holes. The results indicate that the DSCF of the phonon field decreases gradually with the increasing of the surface effect factors or the incident angle at low frequencies (LFs). The influence of the incident angle and surface effect factors on the DSCFs is irregular at high frequencies (HFs). The arc shape significantly affects the DSCFs as the surface effect factors change. This research enhances understanding of disruption caused by nano-holes to the internal stress field in QCs and provides theoretical support for analyzing their mechanical properties and structural health.

The thermoelectric effect is a general term for the electrical effects that arise from a temperature difference, as well as the reversible thermal effects induced by electric current, commonly including the Seebeck effect, Peltier effect, and Thomson effect. Thermoelectric devices based on the advantageous thermoelectric effect are increasing used in practical engineering, such as the temperature measurement and thermoelectric power generation. The periodic wavy contact behavior is crucial for the long-term stability and energy conversion efficiency improvement of thermoelectric devices. This paper investigates the two-dimensional periodic MaugisDugdale (MD) adhesion contact behavior of thermoelectric half-plane using the integral equation method. The contact problem is transformed into a singular integral equation (SIE) with the Hilbert kernel, in which the size of cohesive zone becomes the key unknown parameter. Through theoretical analysis and numerical calculation, the relationships between normal load, contact zone and adhesion zone under two dimensionless parameters including classical Tabor parameter and the ratio of the surface energy of the grooved surface to the elastic strain energy when the grooved surface is smoothed-out are analyzed, and their curve distributions during loading and unloading are discussed. The results show that rougher surfaces cause more energy loss due to adhesion hysteresis. As the total current and energy flow increase, the normal load necessary to achieve the same contact halfwidth also rises. This enables us to adjust the surface contact behavior by varying the thermoelectric loads, thereby altering the stress distribution on the contact surface.

The interaction between cracks is the main cause of material failure when the material contains multiple cracks. Using the classical Kachanov method and Fourier integral transformation, the thermoelastic behavior of one-dimensional hexagonal (1DH) quasicrystals (QCs) containing two asymmetric collinear cracks in a non-periodic plane is studied. Considering the interaction between cracks, the solutions of the thermal stress intensity factors (TSIFs), and strain energy density factors (SEDFs) are determined. Numerical results analyze the influence of the coupling coefficients, external loads, thermal conductivity and crack interaction coefficients on the temperature, TSIFs and SEDFs. The results show that when the spacing between cracks is smaller than the length of each crack, the collinear cracks will influence each other more. The propagation of cracks can be suppressed by selecting QCs with appropriate coupling coefficients. These results enhance the understanding of crack interaction mechanisms in QCs and the impact of micro- cracks on the main crack, with a novel contribution being the comprehensive consideration of both crack interaction in QCs using the Kachanov method.

Based on the principles of continuum mechanics and the Gurtin-Murdoch (GM) surface/interface theoretical model, the mechanical behavior characteristics of a nanoscale lip-shaped orifice with two asymmetric nano-cracks in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) is studied, taking into account surface effects. By employing conformal mapping techniques, the electro-elastic field distribution is obtained. Under partially electrically permeable boundary conditions, the precise analytical solutions are derived for the intensity factors of electro-elastic fields and the energy release rate (ERR) at the crack tips. The obtained solutions can be reduced to existing results to verify the effectiveness of the method. Meanwhile, the effects of surface effects on stress intensity factors (SIFs), electric displacement factor (EDIF), and ERR are analyzed in detail through numerical examples, and the physical mechanism is also explained. The results indicate that the electro-elastic field intensity factors exhibit significant size dependence. The surface effect usually acts as a "shield" and attenuates the intensity of the crack tip field. Appropriately increasing the electrical conductivity can effectively inhibit crack propagation. The findings of this study provide invaluable theoretical guidance for the design of smart devices in micro-electromechanical systems and nano-electromechanical systems.

Prestrains and residual stresses have certain impacts on the characteristics and functions of soft materials and tissues. Consequently, prestrains and residual stresses also influence the indentation test of soft materials. This paper focuses on the indentation contact of a compressible rubber polymer with prestretching conditions. It derives the semi-analytical expressions for the ratio of the indentation force to the indentation depth and the stress distribution. Subsequently, these semi-analytical expressions can be simplified into analytical expressions in the equiaxial prestretching case. Based on the deduced results, the influences of prestrain, ambient temperature, and indenter parameters on indentation force, indentation depth, and stress distribution parameters are further analyzed. The results indicate that the compressibility of the material makes the surface stiffness of the material increase under the condition of prestretching, resulting in a smaller indentation force or indentation depth during the indentation test. The analytical expressions obtained here in the equiaxial prestretching situation provides a theoretical reference for the indentation test of some soft materials.

Based on the complex potential theory and the Gurtin-Murdoch surface/interface elasticity theory, the crack propagation behavior and microfracture mechanism of a nanoscale lip-shaped orifice with four nano-cracks in an infinite one-dimensional (1D) hexagonal piezoelectric quasicrystal (PEQC) material with surface effect are investigated, which is subjected to far-field anti-plane mechanical loads and in-plane electrical loads. By using the analytic function conformal mapping technique, the analytical solutions of the electro-elastic field intensity factors and the energy release rate (ERR) at the crack tip are obtained for partially electrically permeable boundary conditions. The obtained solutions can be reduced to the existing results. Then numerical examples are used to analyze the effects of the geometrical parameters of defects, the crack length, mechanic loadings, electric loading, dielectric constant, and phonon-phason coupling coefficient on the mechanical behavior. The results show that the surface effect has a greater effect on the stress intensity factor than the electric field intensity factor at the nanometer scale. An increase in the length of the lip orifice and the length of the transverse crack at the orifice’s edge tends to accelerate crack growth. Conversely, an increase in the ratio of lip orifice height to crack length can delay crack growth. The research provides novel ideas and methodologies for studying the mechanical and electrical properties of materials at the nanoscale.

The study of sliding adhesive contact problem can reveal the mechanisms of interface friction, energy dissipation, and electric force coupling, and solve the problem of device performance degradation caused by contact failure. Based on the three-dimensional (3D) general solution of one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), the sliding adhesion contact problem of 1D hexagonal PEQCs under a 1D hexagonal PEQCs spherical indenter was studied. The frequency response function of 1D hexagonal PEQCs half-space was analytically deduced and transformed into the corresponding influence coefficient. The numerical solution method composed of adhesion-driven conjugate gradient method (AD-CGM) and discrete convolution-Fourier transform (DC-FFT) is used to calculate phonon and phason displacements and stresses, potential and electric displacement. Numerical analysis provides insights into the effects of the friction coefficient, the total charge and adhesion parameters on the adhesion contact of 1D hexagonal PEQCs on half-space. The research results indicate that the influence of adhesion on surface stress and phason displacement is more pronounced, and the influence on other physical quantities can be ignored. The research results obtained here contribute to the optimization of interface design for quasicrystal materials and the improvement of device reliability.