Penetration of self-affine fractal rough rigid bodies into a model elastomer having a linear viscous rheology.

The penetration of a rigid body with a randomly rough, self-affine surface in a half space filled with a linearly viscous elastomer is studied numerically using the method of boundary elements. Using Radok's principle of functional equations, it is shown analytically that this problem is closely related to the recently investigated problem of contact of self-affine surfaces with an elastic half space. We show that the penetration velocity occurs to be a power function of the applied force and time, the corresponding exponents depending only on the Hurst exponent. For comparison, the same problem is solved using the method of reduction of dimensionality. Both three-dimensional numerical results and the method of reduction of dimensionality support the analytical predictions provided by general scaling arguments.