Transient and steady-state viscoelastic contact responses of layer-substrate systems with interfacial imperfections

Zhang, Xin; Wang, Q. Jane; He, Tao

doi:10.1016/j.jmps.2020.104170

Cited by 51 publications

(20 citation statements)

References 58 publications

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“…In many cases of technology developments, the mechanical effects, such as power transmission and contact of various material systems [5,6], have been studied in great detail, for example, indentation mechanics of layered [7][8][9] and functionally graded [10,11] materials using analytical or numerical methods, micromechanics of materials involving inhomogeneities or inclusions [12][13][14][15] by the phase-field model or the equivalent inclusion method, and nanomechanics of thin films and nano/microstructures [16][17][18][19][20][21] by the theories of strain-gradient plasticity or couple-stress elasticity. In heat transfer, a great deal of work has been focused on capturing the thermal behaviors of different material systems, among them are the development of the theories of heat transfer [22] and the studies of heat conduction in layered [23][24][25] and functionally graded [26,27] materials, as well as in materials involving inhomogeneities or inclusions [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

Zhang

Wang

2022

ASME Open Journal of Engineering

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This paper reports a unified analogy-based computation methodology, together with a concept of multifield, multifunctional sensing, from elasticity to electromagnetic-chemical-thermal fields, via utilizing the similarities of mechanical-electromagnetic-chemical-thermal (MEMCT) field variables, governing equations, and the material properties pertaining to each individual field. Two equivalences are systemized, which are the field-formulation equivalence and surface-value equivalence. Due to similarity, a number of thermal, electromagnetic, or chemical solutions can be obtained from the direct degeneration of existing mechanical solutions by making specified equivalences of 2G↔k0↔ϖ0↔μ0↔β0 with G for shear modulus, k0 for heat conductivity, ϖ0 for dielectric permittivity, μ0 for magnetic permeability, and β0 for chemical diffusivity, as well as by setting Poisson’s ratio ν → 0.5. These specified equivalences enable quick solutions to other fields directly from mechanics formulations, such as those in the forms of the Galerkin vectors and Papkovich-Neuber potentials, and field coupling, by means of analogy. Several examples are given, one is used to demonstrate that the field solutions of a layered half-space with imperfect thermal, electromagnetic, or chemical interfaces can be readily obtained from the elastic solutions involving interfacial imperfections via the obtained formulation equivalence. A set of simple equations are derived to relate surface behaviors of different fields via the obtained surface-value equivalence, on which a concept of multifield sensing is proposed.

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Section: Introductionmentioning

confidence: 99%

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

Zhang

Wang

2022

ASME Open Journal of Engineering

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“…The semi-analytical models (SAMs), supported by the conjugate gradient method (CGM) and the fast Fourier transform (FFT) [25][26][27], appear to be efficient in solving 3D contact problems involving multifield coupling [28][29][30][31]. This paper reports the development of the frictional contact of 1D-hexagonal PEQCs layer, based on the SAMs, by the first mathematical derivation of the closed-form FRFs for 1D-hexagonal PEQCs layer and creative extension of the numerical DC-FFT framework.…”

Section: Introductionmentioning

confidence: 99%

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

et al. 2021

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Based on three-dimensional (3D) general solutions for one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), this paper studied the frictional contact problem of 1D-hexagonal PEQCs layer. The frequency response functions (FRFs) for 1D-hexagonal PEQCs layer are analytically derived by applying double Fourier integral transforms to the general solutions and boundary conditions, which are consequently converted to the corresponding influence coefficients (ICs). The conjugate gradient method (CGM) is used to obtain the unknown pressure distribution, while the discrete convolution-fast Fourier transform technique (DC-FFT) is applied to calculate the displacements and stresses of phonon and phason, electric potentials and electric displacements.Numerical results are given to reveal the influences of material parameters and loading conditions on the contact behavior. The obtained 3D contact solutions are not only helpful further analysis and understanding of the coupling characteristics of phonon, phason and electric field, but also provide a reference basis for experimental analysis and material development.

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“…This is especially true for the contact of nominally flat surfaces, which involves a large nominal contact area. Numerous research efforts in computational contact mechanics [10][11][12][13][14][15][16][17][18][19][20][21][22][23] were focussed on improving the algorithmic efficiency by Fourier analysis, supported by the fast Fourier transform (FFT) algorithm for the calculation of the discrete Fourier transform. This paper advances an FFT-assisted numerical solution to the contact of nominally flat surfaces, by using a surface area as a representative domain that is periodically extended laterally to mimic a periodic contact problem.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Approach to the Contact of Nominally Flat Surfaces

Cerlinca¹,

Spinu²

2021

IJMMT

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Machined surfaces can be described by heights and wavelengths of the surface asperities that show a statistical variation. Considering that a regular wavy surface with a sinusoidal profile is the crudest model for a rough surface, studying the contact of regular wavy surfaces is a good approximation for the contact of nominally flat surfaces. Such contact problems exhibit periodicity that can be simulated with the aid of computational techniques derived for contact mechanics in the frequency domain. The displacement calculation, which is a necessary step in the resolution of the contact problem, is mathematically a convolution product that can be calculated in the frequency domain with increased computational efficiency. The displacement induced by a unit surface load can be expressed in the frequency domain by the frequency response functions, which are counterparts of the space domain solutions to half-space fundamental problems such as the Boussinesq problem. The displacement induced by a periodic pressure distribution can be computed by executing the convolution product between the frequency response function and pressure on a single period. It should be noted that the convolution calculation in the spectral domain implies that the contributions of all neighbouring pressure periods are accounted for. The need to treat numerically only a single period results in remarkable computational efficiency, allowing for high density meshes that can capture the essential features of any textured real surface. The displacement calculation promotes the solution of the contact problem by an iterative approach. The advanced method is benchmarked against existing analytical solutions for the 3D contact of surfaces possessing two-dimensional waviness. This essentially deterministic model, supported by a direct numerical solution that can be obtained for samples of real rough surfaces, presents itself as a worthy alternative to the existing statistical models for rough contact interaction.

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Transient and steady-state viscoelastic contact responses of layer-substrate systems with interfacial imperfections

Cited by 51 publications

References 58 publications

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

A Unified Analogy-Based Computation Methodology From Elasticity to Electromagnetic-Chemical-Thermal Fields and a Concept of Multifield Sensing

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

A Numerical Approach to the Contact of Nominally Flat Surfaces

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