Semi-Analytical Viscoelastic Contact Modeling of Polymer-Based Materials

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
W. Wayne Chen ◽  
Q. Jane Wang ◽  
Z. Huan ◽  
X. Luo
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Contact Pressure ◽  
Contact Process ◽  
Indentation Test ◽  
Surface Displacement ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Viscoelastic Materials ◽  
Viscoelastic Contact

Contact of viscoelastic materials with complicated properties and surface topography require numerical solution approaches. This paper presents a 3-D semianalytical contact model for viscoelastic materials. With the hereditary integral operator and elastic-viscoelastic correspondence principle, surface displacement is expressed in terms of viscoelastic creep compliance and contact pressure distribution history in the course of a contact process. Through discretizing the contact equations in both spatial and temporal dimensions, a numerical algorithm based on the robust Conjugate Gradient method and Fast Fourier transform has been developed to solve the normal approach, contact pressure, and real contact area simultaneously. The transient contact analysis in the time domain is computationally expensive. The fast Fourier transform algorithm can help reduce the computation cost significantly. The comparisons of the new numerical results with an analytical viscoelastic contact solution for Maxwell materials and with an indentation test measurement reported in the literature has validated and demonstrated the accuracy of the proposed model. Moreover, the present model has been used to simulate the contact between a polymethyl methacrylate (PMMA) substrate and a rigid sphere driven by step, ramped, and harmonic normal loads. The validated model and numerical method can successfully compute the viscoelastic contact responses of polymer-based materials with time-dependent properties and surface roughness subjected to complicated loading profiles.

A Rough Surface Contact Model for General Anisotropic Materials

2004 ◽  
Vol 126 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Rough Surface ◽  
Half Space ◽  
Contact Pressure ◽  
Surface Displacement ◽  
Anisotropic Materials ◽  
Elastic Half Space ◽  
Iteration Scheme ◽  
Real Contact Area ◽  
Surface Contact ◽  
Rough Surface Contact

A method for solving the two-dimensional (2-D) isothermal rough surface contact problem of general anisotropic materials with friction is presented. By using Stroh’s formalism, the surface displacements of an elastic half-space due to uniform distributions of traction over a strip are derived from the surface Green’s function. The surface displacement and subsurface stresses of the anisotropic half-space due to the distributed contact pressure may then be calculated by superposition. The real contact area and the contact pressure are determined via an iteration scheme using the conjugate gradient method.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2005 ◽  
Vol 127 (2) ◽  
pp. 325-330 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.

Contact Calculation for Rolling Bearings in Quarter-Spaces

2015 ◽  
Vol 642 ◽  
pp. 333-336
Author(s):  
Zhi Jian Wang ◽  
Xue Jin Shen ◽  
Xiao Yang Chen
Keyword(s):  
Fourier Transform ◽  
Free Surface ◽  
Fast Fourier Transform ◽  
Contact Pressure ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Analytical Method ◽  
Elastic Contact ◽  
Rolling Bearings ◽  
Modified Conjugate Gradient Method

An elastic contact solution considering the effect of free surface and code are developed using Hetenyi’s approach and semi-analytical method. Discrete convolution-fast Fourier transform (DC-FFT) is used to calculate elastic deformation. The modified conjugate gradient method is applied to solve surface contact pressure. By comparing with other literatures’ results, the program made by authors is proved valid.

scholarly journals Viscoelastic Contact Simulation under Harmonic Cyclic Load

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Sergiu Spinu
Keyword(s):  
Energy Dissipation ◽  
Internal Energy ◽  
Viscoelastic Material ◽  
Cyclic Load ◽  
Complex Modulus ◽  
Contact Process ◽  
Contact Radius ◽  
Viscoelastic Materials ◽  
Rheological Models ◽  
Viscoelastic Contact

Characterization of viscoelastic materials from a mechanical point of view is often performed via dynamic mechanical analysis (DMA), consisting in the arousal of a steady-state undulated response in a uniaxial bar specimen, allowing for the experimental measurement of the so-called complex modulus, assessing both the elastic energy storage and the internal energy dissipation in the viscoelastic material. The existing theoretical investigations of the complex modulus’ influence on the contact behavior feature severe limitations due to the employed contact solution inferring a nondecreasing contact radius during the loading program. In case of a harmonic cyclic load, this assumption is verified only if the oscillation indentation depth is negligible compared to that due to the step load. This limitation is released in the present numerical model, which is capable of contact simulation under arbitrary loading profiles, irregular contact geometry, and complicated rheological models of linear viscoelastic materials, featuring more than one relaxation time. The classical method of deriving viscoelastic solutions for the problems of stress analysis, based on the elastic-viscoelastic correspondence principle, is applied here to derive the displacement response of the viscoelastic material under an arbitrary distribution of surface tractions. The latter solution is further used to construct a sequence of contact problems with boundary conditions that match the ones of the original viscoelastic contact problem at specific time intervals, assuring accurate reproduction of the contact process history. The developed computer code is validated against classical contact solutions for universal rheological models and then employed in the simulation of a harmonic cyclic indentation of a polymethyl methacrylate half-space by a rigid sphere. The contact process stabilization after the first cycles is demonstrated and the energy loss per cycle is calculated under an extended spectrum of harmonic load frequencies, highlighting the frequency for which the internal energy dissipation reaches its maximum.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2004 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

Impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β ≤ 1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β ≤ 1, and increases gradually for β > 1. Based on finite element results for the subsurface stress, strain, and velocity fields, and simple theoretical model that yields approximated closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β ≤ 1), and its validity was confirmed by favor comparisons with finite element results.

Thermo-Electro-Mechanical Simulation of Aluminum-Steel Imperfect Electrical Contact With Extremely High Interfacial Temperature

2005 ◽  
Author(s):  
Wan-Sik Kim ◽  
Shuangbiao Liu ◽  
Q. Jane Wang ◽  
Leon M. Keer
Keyword(s):  
Boundary Condition ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Electrical Contact ◽  
Surface Displacement ◽  
Influence Coefficient ◽  
Pressure Surface ◽  
Large Contact Area

This paper introduces the frequency response function (FRF)-based continuous convolution and fast Fourier transform (CC-FFT) algorithm to simulate a periodically large contact area rather than the influence coefficient (IC)-based discrete convolution fast Fourier transform (DC-FFT). The former and the latter may be called as a periodic boundary condition (PBC) and a non-periodic boundary condition (nPBC) based on their periodicity. In the calculation, the contact pressure, surface displacement, and surface temperature are analyzed and compared by means of PBC CC-FFT and nPBC DC-FFT.

Sign in / Sign up

Export Citation Format

Share Document