Fractional order derivative approach of viscoelastic behavior of tropical wood

TL;DR

This paper models the viscoelastic behavior of tropical wood using fractional calculus, achieving high accuracy in predicting creep and recovery, and introduces nonlinear modifications for better stress-level adaptability.

Contribution

It applies fractional calculus to model wood's viscoelasticity and develops nonlinear fractional models for improved predictive accuracy across stress levels.

Findings

Model fits creep data with 96% reliability

Model fits recovery data with 99% reliability

Nonlinear fractional models enhance stress-level prediction

Abstract

For some time now, wood has offered itself as an alternative to other modern construction materials, and has become the material of choice for structures, mainly because of its renewable nature, durability and ease of shaping. However, once in service, even at room temperature and under low stresses, it deforms and faces the problems of creep and recovery. The aims of this work is to model and predict the viscoelastic deformations of tropical wood by a rheological approach based on fractional calculus theory. Frist, Zener fractional model was used to elucidate these phenomena. The simulations show that the proposed model fit the creep experimental data with an average reliability of 96% and the recovery process with a reliability of 99%. The optimal parameters of this model, determined through an optimization algorithm, exhibit sensitivity to the stress level. To address this issue and enhance the predictive capability of the model, nonlinearities are incorporated into the fractional model, resulting in modified versions that remain applicable across various stress levels.