Abstract
The paper addresses the methods of description of friction-induced self-healing at the interface between two solid bodies. A macroscopic description of self-healing is based on a Turing system for the transfer of matter that leads to self-organization at the interface in the case of an unstable state. A microscopic description deals with a kinetic model of the process and entropy production during self-organization. The paper provides a brief overview of the Turing system approach and statistical kinetic models. The relation between these methods and the description of the self-healing surfaces is discussed, as well as results of their application. The analytical considerations are illustrated by numerical simulations.
Highlights
Self-healing of surfaces is one of the most surprising and complex phenomena of biological systems
It is demonstrated that known entropy methods of self-organization analysis naturally correspond to the models based on Turing systems
In the case of distributed systems, Turing system can be considered as a suitable model both for dynamics of reagent concentrations and for dynamics of matter distribution
Summary
Self-healing of surfaces is one of the most surprising and complex phenomena of biological systems. Gershman and Bushe [10] considered the surfaces with self-healing induced by friction, and suggested to apply the methods that are commonly used for analysis of a self-organization phenomenon (see e.g., [11,12]) They studied self-healing by the use of thermodynamics of non-linear dynamical systems and applied the entropy principles to self-healing [13]. Further progress in this direction was achieved by Nosonovsky and Bhushan [6,7], who considered self-healing as a hierarchical phenomenon Analysis of this phenomenon by the methods of non-linear dynamical systems theory led to consideration of self-organization that occurs on different hierarchical levels of the material: from nanoscale via microscale to macroscale. Analytical considerations of the models are illustrated by numerical simulations
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