Modelling of Rough Contact between Linear Viscoelastic Materials

Abstract

The important gradients of stress arising in rough mechanical contacts due to interaction at the asperity level are responsible for damage mechanisms like rolling contact fatigue, wear, or crack propagation. The deterministic approach to this process requires computationally effective numerical solutions, capable of handling very fine meshes that capture the particular features of the investigated contacting surface. The spatial discretization needs to be supported by temporal sampling of the simulation window when time-dependent viscoelastic constitutive laws are considered in the description of the material response. Moreover, when real surface microtopography is considered, steep slopes inevitably lead to localized plastic deformation at the tip of the asperities that are first brought into contact. A computer model for the rough contact of linear viscoelastic materials, capable of handling deterministic contact geometry, complex viscoelastic models, and arbitrary loading histories, is advanced in this paper. Plasticity is considered in a simplified manner that preserves the information regarding the contact area and the pressure distribution without computing the residual strains and stresses. The model is expected to predict the contact behavior of deterministic rough surfaces as resulting from practical engineering applications, thus assisting the design of durable machine elements using elastomers or rubbers.

Viscoelastic Contact Simulation under Harmonic Cyclic Load

“…The convergence of this quadratic optimization is guaranteed, but the method fails when adhesion-like tensile contact tractions are assumed. It should be noted that adhesion was not considered in either the classic or modern literature [3][4][5][6][7][8][9][10][11][12][13][14][15] of viscoelastic contact. The contact complementarity conditions imposed in the elastic contact model used in this paper match the boundary conditions employed in [7] and lead to a surface displacement compatible with the indenter profile within the contact area.…”

“…are coordinates of the center of the cell ( , ). Consequently, pressure is assumed to be uniform in any rectangular patch and therefore can be factored outside the integral operator in (15). The integral of the Green function ( ) ( 1 , 2 ), taken over the elementary patch of side lengths Δ 1 and Δ 2 along directions of → 1 and → 2 , respectively, yields the influence coefficient [28] for the elastic displacement ( ) :…”

“…As equations describing the purely elastic model are intrinsically time-independent, spatial discretization is adequate to circumvent the continuous integration in (15). The additional integration over the time span in which the body was loaded in (17) requires an additional temporal mesh capable of simulating the memory effect specific to viscoelastic materials (i.e., the property that the current state depends upon all previous states succeeded from the first loading).…”

“…A solution for the Cattaneo-Mindlin problem involving viscoelastic materials was advanced by Spinu and Cerlinca [13], based on the algorithm for the frictionless viscoelastic contact problem reported in [14]. More recently, the same authors studied [15] the rough contact of viscoelastic materials by imposing a simplified manner in which plasticity effects at the tip of the asperities are accounted for. While dealing with friction or with surface microtopography, these contact simulations employ simple loading programs consisting usually in step or ramped loadings.…”

Impact Fatigue of Viscoelastic Materials Subjected to Pounding

“…Therefore, an impact-fatigue study on the viscoelastic material of the PTMD is still necessary. Even though the impacts of the viscoelastic material have improved the vibration effectiveness and robustness of the PTMD, the repeated impacts may damage the material and deteriorate its long term performance [11][12][13]. Moreover, the PTMD is often applied to structures located in extreme environments (e.g., subsea jumpers and offshore platforms).…”