Mathematical Modelling of Materials Behavior Under Creep Conditions

Abstract

This article will provide a short survey of some recent advances in the mathematical modelling of materials behavior under creep conditions. The mechanical behavior of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behavior. This article presents certain principles, methods, and recent successful applications of tensor functions in creep mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. Finally, we have carried out our own experiments to examine the validity of the mathematical modelling. Furthermore, an overview of some important experimental investigations in creep mechanics of other scientists has been provided. There are 243 references cited in this review article.