On the convexity of anelastic and viscoelastic relaxation functions

Abstract

The creep and stress relaxation functions for anelastic and linear viscoelastic materials with discrete relaxation spectra are shown to be convex upwards and convex downwards, respectively, for all times t > 0. (Linearity arises in simple limiting cases.) The analysis is based on the electrical → mechanical analogy and uses certain standard theorems on the synthesis of discrete electrical networks. The results should provide useful guidelines and constraints in the phenomenological modelling of experimental data in terms of equivalent networks.