1. Multiscale techniques
The effect of surface roughness in the fretting wear profile can be significant and must, therefore, be considered. However, most of the finite element (FE) models that are used to predict fretting wear do not take it into consideration.
Adding all small surfaces features in a macro FE model is very computationally demanding and another approaches that allow the roughness information to be analysed are of great interest. In this regard, multiscale modelling offers the advantage to efficiently connect results from different scales and being thus a powerful tool to deal with roughness in fretting.
Introduction
Multiscale techniques
Homogenization
Semi-concurrent approach
Concurrent technique
Micro and macro models are independent (one-way coupling)
Models are coupled in a parallel way (two-way coupling)
All scales are handled at once in the same numerical model
Atomistic region (modelled with MD)
Continuum region (modelled with FEM)
Bridge region
Analysis of a nanocomposite done by Talebi et al. [1]
Contact model done by Anciaux and Molinari [2]
Homogenization for contact problems
Homogenization is used in contact as a tool to derive macroscopic constitutive equations for the contact stiffness based on microscopic simulations. These equations would have information regarding the effect of the roughness and then could be used on the macro-model.
The macroscopic constitutive equation for normal frictionless contact can be written as (Wriggers and Nettingsmeier [3]):
p=cn d m
p is the average normal pressure, d the normal approach between the two bodies and cn and m are contact stiffness parameters.
Conclusions and Future Work
The homogenization procedure may be used in fretting models to take into account the effect of roughness in contact problems.
As future work, we intend to apply the discussed methodology in fretting simulations and validate the results with experimental (or literature) data.
References
[1] H. Talebi, M. Silani, S. P. A. Bordas, P. Kerfriden, and T. Rabczuk. A computational library for multiscale modeling of material failure. Computational Mechanics, 53:1047–1071, 2014
[2] G. Anciaux and J. F. Molinari. Sliding of rough surfaces and energy dissipation with a 3d multiscale approach. International Journal for Numerical Methods in Engineering, 83(8-9):1255–1271, 2010.
[3] P. Wriggers and J. Nettingsmeier. Computational Contact Mechanics - CISM courses and lectures. Springer, 2007.
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