THE MATRIX FORM OF DIFFERENTIAL CONSTITUTIVE EQUATION FOR VISCOELASTIC MODEL¹⁾

This paper derived the general matrix form for the linear viscoelastic model for arbitrarily linked springs and dampers. Firstly, the underlying linear viscoelastic problem is modeled through the standard model composed of basic Maxwell units. Then the standard model is transformed into a directed graph, and the basic stress equation and strain equation are expressed in the form of independent path and closed enclosure. And then the general matrix form of a differential constitutive equation for an arbitrary viscoelastic model is derived. Finally, a universal paradigm suitable for computer programming is developed, and the relevant algorithm is realized with the Python language along with numerical results.