A method for the orthotropic coating-substrate system: Green׳s function for a normal line force on the surface

Hou, Pengfei; Jiang, Haiyang; Li, Ji-Ran

doi:10.1016/j.ijmecsci.2015.03.005

Cited by 15 publications

(6 citation statements)

References 44 publications

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“…They used closed form solutions and an iterative algorithm to obtain the solutions and to explain the behavior of the contact pressure distributions on the layers resulting from the changes in material property mismatches and coefficient of friction. A new method based on the Green's function for orthotropic coating‐substrate system loaded by a normal line force is explained in []. By assuming the coating and the substrate as infinite and semi‐infinite layers respectively and perfectly bonded to each other, they studied the coating tensile failure and the effect of material property changes on the contact distributions.…”

Section: Introductionmentioning

confidence: 99%

Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system

et al. 2019

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In this study, the contact problem for a homogeneous orthotropic coating‐isotropic substrate system is considered. The rigid stamp slides over the orthotropic coating whose bottom surface is bonded to a homogeneous isotropic substrate. The bottom surface of the substrate is fixed to the ground. By using Fourier integral transforms, the partial differential equations are converted to ordinary differential equations (ODEs). The displacement components for coating and substrate are obtained by solving the corresponding ODEs. A numerical study based on finite element analysis (FEA) is also conducted. The results from the analytical formulation are directly compared with the FEA results. The effects of orthotropic and isotropic material properties, coefficient of friction between the sliding surfaces, geometrical properties on the contact stresses and contact widths are presented. The results of this study may help tribology engineers to understand the deformation characteristics of the coating‐substrate systems and enhance their knowledge on friction and wear mechanisms of sliding surfaces.

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Section: Introductionmentioning

confidence: 99%

Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system

et al. 2019

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“…By virtue of Equation (34), the selection of the optimum thickness of the piezoelectric device will get twice the result with half the effort. For an example, when one designs the piezoelectric sensor or piezoelectric energy harvester under a cylindrical distributed force P(j) in Equation (31), the relationships between peak values of stresses t §j , s § , s j and non-dimensional thickness H are as plotted in Figure 29, and the relationships between the peak values of electric displacement D § D j and non-dimensional thickness H are as plotted in Figure 30.…”

Section: The Coupled Field In the Piezoelectric Plate With Different mentioning

confidence: 99%

“…Toward this aim, a series of investigations has been carried out in this article and the main procedures are as follows. In Section 2, the general solution of the orthotropic piezoelectric material is listed [34]. The Green's function solution of an orthotropic piezoelectric plate subjected to a line charge and a normal line force is derived in Section 3.…”

Section: Introductionmentioning

confidence: 99%

A method for the coupled field of an orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load

Shang¹,

Hou

Tong

2020

Mathematics and Mechanics of Solids

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There are a number of plate-type piezoelectric devices in engineering, hence it is crucial to search for a method that can accurately acquire the electro-mechanical coupled field of a piezoelectric plate. A method for calculating the coupled field of an orthotropic piezoelectric plate with arbitrary thickness under an arbitrary electro-mechanical load is put forward in this article. First, the Green’s function solution of an orthotropic piezoelectric plate subjected to a line charge and a normal line force is derived based on the general solution of the orthotropic piezoelectric material. All stress and electric components of the orthotropic piezoelectric plate are derived when the general solution is substituted into suitable harmonic functions containing undetermined constants. Once the boundary conditions and electro-mechanical equilibrium conditions are satisfied, those constants can be solved. In addition, according to the obtained Green’s function solution and superposition principle, the coupled field of the orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load can be solved. Numerical results indicate that the convergence and precision of the method are quite good. A concise skill without repeated calculations is also presented for acquiring the coupled fields in the orthotropic piezoelectric plates with various thickness, which facilitates the effective design of plate thickness in plate-type piezoelectric devices. Finally, some valuable conclusions for the fine design of plate-type piezoelectric sensors, energy harvesters and actuators are presented based on the numerical results.

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“…The general solution (Hou et al

\begin{matrix} true \\ right u & = & left \sum_{i = 1}^{2} \frac{\partial ψ_{i}}{\partial x}, w = \sum_{i = 1}^{2} s_{i} k_{i} \frac{\partial ψ_{i}}{\partial z_{i}}, \\ right σ_{x} & = & left - \sum_{i = 1}^{2} s_{i}^{2} ω_{i} \frac{\partial^{2} ψ_{i}}{\partial z_{i}^{2}}, σ_{z} = \sum_{i = 1}^{2} ω_{i} \frac{\partial^{2} ψ_{i}}{\partial z_{i}^{2}}, τ_{z x} = \sum_{i = 1}^{2} s_{i} ω_{i} \frac{\partial^{2} ψ_{i}}{\partial x \partial z_{i}}, \end{matrix}

where

ψ_{i}

in Equation are harmonic functions and satisfy the Laplace's equation:

\begin{matrix} true \\ right ((), \frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial z_{i}^{2}}) ψ_{i} = 0, ((), i = 1, 2), \end{matrix}

and

\begin{matrix} true \\ right z_{i} = s_{i} z . \end{matrix}

s_{i} false(i = 1, 2 false)

, which satisfy

Re (s_{i}) > 0

, are two eigenvalues of following polynomial: …”

Section: General Solutions For the Orthotropic Piezoelectric Materialmentioning

confidence: 99%

Two‐dimensional Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure

et al. 2019

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Piezoelectric materials, as functional material, are widely used in electronic devices, such as piezoelectric sensors, piezoelectric energy harvester and piezoelectric actuators. In some electronic devices, piezoelectric materials are placed between two substrates in the form of thin sheet. Therefore, this kind of piezoelectric structure is simplified into a three‐phase orthotropic piezoelectric structure which consists of an infinite piezoelectric plate and two semi‐infinite bodies in this paper. In this case, the Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure is deduced. Based on this solution, the accurate electro‐elastic fields of the three‐phase orthotropic piezoelectric structure are given. And some numerical examples are designed to investigate the effects of various material properties of the piezoelectric plate or the substrates on the stresses at interfaces and the electric potential difference between interfaces of piezoelectric plate.

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A method for the orthotropic coating-substrate system: Green׳s function for a normal line force on the surface

Cited by 15 publications

References 44 publications

Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system

Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system

A method for the coupled field of an orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load

Two‐dimensional Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure

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