Abstract
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.
Highlights
Important engineering applications involving products like automotive belts and tires, seals, or biomedical devices require accurate prediction of tribological processes between viscoelastic materials such as elastomers or rubbers
Noted that whereas Ting’s framework requires the punch to be axisymmetric and leads to tedious algebraic manipulations due to the five possible algorithm branches when the contact area does not vary monotonically with time, the algorithm proposed in this paper can readily handle irregular contact geometry, generalized boundary conditions, and complex material properties
A robust algorithm for the resolution of linear viscoelastic contact scenarios is advanced in this paper by generalizing an existing well-known numerical solution for the contact of linear elastic bodies
Summary
Important engineering applications involving products like automotive belts and tires, seals, or biomedical devices require accurate prediction of tribological processes between viscoelastic materials such as elastomers or rubbers. The classic method for solving the linear viscoelastic problems of stress analysis is based on the concept of associated elastic problem [1, 2] This approach involves removal of time dimension via Laplace transform, reducing the viscoelastic problem to a formally identical elastic problem whose solution is easier to achieve. Chen et al [10] developed a new semi-analytical method (SAM) for contact modeling of polymer-based materials with complicated properties and surface topography. These authors [11] studied the multi-indentation of a viscoelastic half-space by rigid bodies using a two-scale iterative method (TIM). The algorithmic computational efficiency is optimized by employing state-of-the-art numerical techniques: (1) the conjugate gradient method (CGM), with its superlinear rate of convergence, is used for the resolution of the emerging linear system of equations, whereas (2) the Discrete Convolution Fast Fourier Transform (DCFFT) technique [17] is engaged in the rapid computation of discrete convolution products
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