A numerical algorithm and a computer system for the analysis of rheological schemes

Abstract

We construct an algorithm for computing the material stress and strain diagrams on the basis of rheological schemes with an arbitrary level of complexity. In the case of simple schemes, including elastic and viscous elements, the corresponding system of linear ordinary differential equations is solved by an implicit method. If the scheme contains nonlinear elements (plastic hinges or rigid contacts), then iterative processes of numerical solution of variational inequalities with one-sided constraints are applied. The algorithm is numerically realized in the form of a computer system with a convenient input and output graphical interface. As an example illustrating the application of this algorithm, some results of computation of the creep and stress relaxation diagrams are discussed for rheological schemes with elements of all possible types.