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Markov model of relaxation and aging processes fibrous materials


Markov model of relaxation and aging processes fibrous materials

Sevost'yanov P.A., Belevitin A.A., Burdin I.M.

Incoming article date: 23.11.2022

The concept of a fibrous material (hereinafter referred to as FM) as a soft structure formed by fiber elements surrounded by air and areas of fiber interaction on touch surfaces is proposed and substantiated. The fiber elements are in a deformed state. The deformation of the fibers is reversible, elastic-elastic. In the areas of interaction between the fibers, the forces of adhesion and dry friction act. The deformation of the fibers leads to the preservation of residual internal energy in the material. At low loads, the FM can change its state reversibly. At high loads, the structure of the interaction sites irreversibly changes. The processes of aging and degradation of FM are gradual irrevocable transitions from one group of states to others. The dynamics of these processes is statistical in nature. Therefore, a Markov model of state change has been developed in the form of several subsets of irrevocable subsets and one ergodic subset of states. At the qualitative level, the possibility of using the proposed model to describe the dynamics of FM aging processes and estimate the duration of this process, taking into account its probabilistic and statistical nature, is shown.

Keywords: fibrous material, aging, soft structure, elasto-elastic deformation, irreversible process, markov model, statistical dynamics