Modeling concrete and polymer creep using fractional calculus

Abstract

Although the strains on a given material depend on its properties and, in general, on the stresses, on the temperature and on the time under load, they may be modeled as a function of the stresses alone in most practical structural analyses at low service-to-fusion temperature ratios. Most metallic and ceramic alloys can be modeled in such a simplified way at room temperatures, but some important materials, among them polymers and concretes, can creep significantly even at room temperatures. Under relatively low stresses, they can usually be modeled as linear viscoelastic using simple rheological models based on springs and dashpots. However, in many practical cases such models cannot fit well experimental data unless many of those elements are used, a problem that can much impair their use in structural analyses. Fractional rheological elements based on fractional calculus techniques have been recently proposed as a promising modeling technique to avoid this problem, and in this work their performance is evaluated by comparing their fitting behavior with traditional modeling techniques, using representative creep data from polypropylene and from a medium strength concrete.

Keywords

• Concrete
• Creep
• Fractional calculus
• Fractional Kelvin-VoigtScot-Blair elements