Мodulus of Elasticity as a Function of a Process in Hereditary Mechanics

Abstract

The article considers the problem of determining the modulus of elasticity for polymer materials. The measurement process of these materials is considerably complex, mainly due to the fact that they comply with the laws of viscoelasticity. The Boltzmann — Volterra method is applied to the consideration of the behavior of a hereditarily elastic body, namely, to synthetic threads. We revealed that the elastic modulus for polymer materials is not a constant value and depends on the frequency of exposure during the deformation of the material. It is particularly noted that the modulus of elasticity is not a function of the state, but a function of the process. In this regard, it is necessary to consider various modes of deformation, namely static, acoustic, and dynamic modes. The Boltzmann heredity principle is utilized to provide a clear understanding of the concepts of static, dynamic, and acoustic modulus of elasticity. Furthermore, the applicability of the Boltzmann equation to dynamic mechanical processes is analyzed using two methods — the hierarchy of relaxation times and the method of linearization. In addition, the concept of the interaction core of static and dynamic parts of deformation is introduced. This concept helps to explain the relationship between the static and dynamic moduli of elasticity and their impact on material properties.