Application of variable-order fractional calculus in solid mechanics

Authors

• Behrouz Parsa Moghaddam, Islamic Azad University, Lahijan Branch
• Arman Dabiri, Eastern Michigan University
• Jose Antonio Tenreiro Machado, Instituto Superior de Engenharia do Porto

Document Type

Book Chapter

Publication Date

2019

Department/School

Engineering Technology

Publication Title

Applications in Engineering, Life and Social Sciences, Part A

Abstract

This chapter discusses the adoption of fractional derivative operators in modeling viscoelastic materials and their creep behavior. The damper elements in three conventional rheological models are replaced by fractional-order dashpots that include fixed- and variable-order fractional derivative operators. It is shown that the creep response of the presented fractional rheological models can be realistic if and only if they have monotonically decreasing variable-order functions. Finally, the presented rheological models are used to model the creep behavior of an epoxy by using experimental isothermal creep tests.

Comments

A. Dabiri is a faculty member in EMU's School of Engineering.

Recommended Citation

Moghaddam, B., Dabiri, A., & Tenreiro Machado, J. A. (2019). Application of variable-order fractional calculus in solid mechanics. In D. Bǎleanu & A. Mendes Lopes (Eds.), Applications in engineering, life and social sciences, part A (pp. 207–224). De Gruyter. https://doi.org/10.1515/9783110571905-011