# Fractional Burgers models in creep and stress relaxation tests

## TL;DR

This paper investigates fractional Burgers models in creep and stress relaxation tests, deriving conditions for physically consistent behavior and analyzing their asymptotic properties.

## Contribution

It provides a thermodynamically consistent analysis of fractional Burgers models, identifying parameter ranges for physically meaningful creep and relaxation behaviors.

## Key findings

- Creep compliance is a Bernstein function within certain parameters.
- Relaxation modulus can be oscillatory with decreasing amplitude.
- Asymptotic behaviors are characterized near initial and large times.

## Abstract

Classical and thermodynamically consistent fractional Burgers models are examined in creep and stress relaxation tests. Using the Laplace transform method, the creep compliance and relaxation modulus are obtained in integral form, that yielded, when compared to the thermodynamical requirements, the narrower range of model parameters in which the creep compliance is a Bernstein function while the relaxation modulus is completely monotonic. Moreover, the relaxation modulus may even be oscillatory function with decreasing amplitude. The asymptotic analysis of the creep compliance and relaxation modulus is performed near the initial time-instant and for large time as well.