Our core competence here at Multiscale Consulting is the Persson contact mechanics theory which has contributed to the scientific progress in many fields. The basic theory with its submodules to different applications is a unique and powerful tool which we offer to our customers. After more than 15 years of cutting edge theory and software development, the original codes of Persson are ready for being shared. Most of the calculations in our publications are direct results of this software package.
The software is used to calculate the contact between two elastic solids with randomly rough surfaces. Here the most important results are the real area of contact as a function of the nominal pressure or the magnification, the corresponding stress distribution at the interface and the interfacial separation between the two solids in the non-contact regions. All these results are of huge importance for many problems in mechanical engineering.

Below we show the latest user interface of the windows version of the multiscale contact mechanics software:


Windows Version of the multiscale contact mechanics software


Note that the program is a powerful tool which not only solves elastic contact mechanics. It can also be applied to related problems such as:

  • Elastic Contact Mechanics
  • Viscoelastic Contact Mechanics
  • Elastoplastic Contact Mechanics
  • Contact Mechanics with Plastic Yielding
  • Contact Mechanics with Layered Materials
  • Adhesion | Capillary Adhesion
  • Elastohydrodynamics
  • Fluid Squeeze-Out between Rough Elastic Surfaces
  • Leak-Rate of Seals

The heat transfer module describes the heat current from one solid to another via the contacting interface. It takes into account the heat flow through the real area of contact and the non-contact area (via convective processes, radiative heat transfer or the propagating electromagnetic waves). Please see this publication for more information.

Squeeze-out of a fluid from the contacting interface is another important topic which is addressed by our software, especially in lubrication or when a tyre is rolling on a wet road. The program can calculate the squeeze-out as a function of time, nominal pressure and viscosity (see publication for more information).

The submodule mixed lubrication is of special interest in many engineering applications involving lubricated systems in relative motion. When a system is accelerated from zero to a finite velocity, it undergoes first dry friction as the surfaces are not yet separated by a lubricating layer of fluid. Before reaching hydrodynamic lubrication where the two interfaces are separated by a thick layer of fluid, a situation comparable to water skiing, the system is in the mixed lubrication regime. Here the two solids are partly separated by the fluid, however, because of the low velocities involved, the fluid can partly be expelled or squeezed-out of the contact. In these dry regions the friction can be calculated by our software. This topic is for example important for dynamic seals or wiper blades. With the software one can calculate the friction for all these different regimes and estimate the total friction coefficient (see publication for more information).

Also note that most of the submodules have been tested both numerically and experimentally. A numerical test is for example to compare the theory predictions to results exact numerical results obtained for small system sized FEM simulations for example. As contact mechanics involve surface roughness on a large number of length scales, numerical simulation would have to take into account too many degrees of freedom for the computer today. Even with the latest supercomputer it would not be possible to solve these systems within a sufficient time period.

More information on the validation of the theory we refer you to our validation section. Here we show how we have performed specially designed experiments and numerical simulations to test the Multiscale Consulting approach on contact mechanics and rubber friction. Below are shown some results obtained with the multiscale contact mechanics software.

In the figure on the left is shown the real area of contact between an elastic solid squeezed into contact with a hard and randomly rough solid. The plot shows how the contact area increases with increasing nominal force. On the right you see the real area of contact as a function of the logarithm (with 10 as basis) of the magnification. The lower the magnification under which the system under investigation is observed the less roughness components can be resolved. At magnification 1 there are no surface roughness asperities and hence the real area of contact A1 divided by the nominal contact area A0 is 1 or 100%. When increasing the magnification, and hence improving the resolution, more and more roughness can be observed and the contact area consequently decreases. The true area of contact can be written of this graph at the magnification where atomic resolution is reached.


A plot of the real area of contact at the highest magnification as a function of the nominal pressure
The real area of contact and its dependency on the applied magnification


Below are shown the pressure distribution on the left and the calculated leak rate of a static seal on the right. The pressure distribution gives information on the acting contact pressures in the regions of contact. Here is shown the relative probability as a function of pressure. The curve has to start at 0, exhibits a maximum at a finite pressure and extends with a tail to higher pressures. The integral of the curve shown in the graph gives the applied nominal pressure.

On the right is the logarithm (with 10 as basis) of the leak-rate as a function of the normal pressure applied on the seal. One can see that the leakage depends very strongly on the contact pressure in the beginning of the graph at low pressures. Note that the y-axis is on a logarithmic scale! By doubling the contact pressure the leakage can be changed by orders of magnitude. For high contact pressure a dramatic decrease in the leak-rate can be observed until a very small, finite value is reached. Basically the pressure applied is here large enough to seal off the small leak channels through which the fluid moves. The percolation threshold of the seal is reached and no fluid can flow from the high to the low pressure side. The finite value which is reached is basically a numerical 0.


The pressure distribution function in the contact regions The leak rate of a static seal (with log10 as basis) as a function of


The multiscale contact mechanics program needs as input only the power spectrum (characterizing the surface roughness) and some information about the elasticity of the material (Young's modulus, Poisson's ratio or the full complex modulus). Depending on which submodule is used additional information may be needed.


For further information on the contact mechanics software please consider the following information:

The manual of the contact mechanics software for the Windows version. Coming Soon
The Data.Out file is a summary of the different options chosen for a particular calculation. The options are briefly explained and the most important results summarized. The Data.Out file is always created after the calculation is finished. Download Data.Out
An example contact mechanics output file. Contact area as a function of nominal pressure. Download Example Contact Mechanics Results
An example contact mechanics output file. Contact area as a function of magnification. Download Example Contact Mechanics Results
An example contact mechanics output file. Pressure distribution at the interface. Download Example Contact Mechanics Results


In case you are interested in using the contact mechanics program or you have further questions concerning the software please feel free to contact us.