Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties

An algorithm for calculating the force of friction between a fractal rough solid surface and a model elastomer with arbitrary linear rheological properties has been developed based on the method of dimensionality reduction with application of a hierarchically organized memory. Using this method, it is possible to calculate the friction force between an elastomer and a solid surface with experimentally determined topography, taking into account both the broad spectrum of wave vectors (ranging from nanometers to centimeters) for real surfaces and the wide range of relaxation times (from nanoseconds to seconds).