Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

A Multi-Layered Model for Heat Conduction Analysis of Thermoelectric Material Strip

A multi-layered model for heat conduction analysis of a thermoelectric material strip(TEMs)with a Griffith crack under the electric flux and energy flux load has been developed.The materials parameters of the TEMs vary continuously in an arbitrary manner.To derive the solution,the TEMs is divided into several sub-layers with different material properties.The mixed boundary problem is reduced to a system of singular integral equations,which are solved numerically.The effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied.

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

The contact problem for thermoelectric materials with functionally graded properties is considered.The material properties,such as the electric conductivity,the thermal conductivity,the shear modulus,and the thermal expansion coefficient,vary in an exponential function.Using the Fourier transform technique,the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density,the normal energy flux,and the contact pressure.Meanwhile,the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula.After addressing the non-linearity excited by thermoelectric effects,the particular solutions of the displacement fields can be assessed.The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented.The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials(FGTEMs).

Heat Conduction in Multilayered Thermoelectric Materials with Multiple Cracks

Multilayer thin-film thermoelectric materials are of technological importance. This paper describes a method to analyze the heat conduction in a multilayered thermoelectric plate containing some non-collinear cracks. The material properties in one layer may be different from those in another even though each layer may still be homogeneous. Using the Fourier integral transforms, the boundary value problem is reduced to a system of general singular integral equations. The model is sufficiently general to account for any number of layers and any number of cracks. As a numerical illustration, the electric flux intensity factor, energy flux intensity factor and thermal flux intensity factor for a three-layer plate specimen with two cracks are presented. The effects of strip width on the electric flux intensity factor and thermal flux intensity factor are studied.

Two Kinds of Contact Problems in Dodecagonal Quasicrystals of Point Group 12 mm

In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.

Surface effects on the indentation of a soft layer on a rigid substrate with an elliptical cylinder indenter

Surface effects often play a significant role in the mechanical properties of soft materials such as hydrogels and biological tissues.In this paper,we investigate the plane-strain indentation of a soft elastic layer bonded to a rigid substrate.The surface effects on the indentation behavior of the elastic layer-substrate system are theoretically analyzed.Indentation tests using indenters with different elliptical shapes are compared.Analytical expressions are derived for the indentation force-displacement relation using the Kerr model with the effect of surface tension.The theoretical solution is verified by finite element simulations.The dependence of surface effects on the ratio of the indenter’s major and minor elliptical axes is also examined.This work helps understand the size effects on the indentation behaviors of soft materials and guides the design of corresponding measurement tests.

Frictionless Multi-field Coupling Contact Problem for a Thermoelectric Layer Loaded by Two Rigid Punches

In this paper,the thermo-electro-mechanical coupling contact problem of thermoelectric material with double punches is analyzed accurately.Using the Fourier cosine transform technique,the thermo-electro-elastic problem is transformed into three sets of singular integral equations,which are numerically solved by the Gauss–Chebyshev integral formula according to the unknown normal electric current density,normal energy flux and normal contact stress.For a rigid flat indenter,the results can be covered by the degradation results of two rigid flat indenters.The numerical results reveal the interaction between two punches and the effect of thermoelectric load on the indentation behaviors.The interaction between the two punches reduces the contact pressure at the inner edge of the indenter as the thermoelectric load increases while increasing the stress singularity at the outer edge.The change of punches’spacing makes the singularity of normal stress at the inner and outer edges asymmetric.The results provide an in-depth understanding of the multi-region contact damage mechanism of thermoelectric material.