scholarly journals Melnikov analysis of the nonlocal nanobeam resting on fractional-order softening nonlinear viscoelastic foundations

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Guy Joseph Eyebe ◽  
◽  
Betchewe Gambo ◽  
Alidou Mohamadou ◽  
Timoleon Crepin Kofane ◽  
...  
Keyword(s):  
Fractional Order ◽  
Nonlinear Viscoelastic ◽  
Melnikov Analysis

scholarly journals Nonlinear Viscoelastic-Plastic Creep Model of Rock Based on Fractional Calculus

2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Erjian Wei ◽  
Bin Hu ◽  
Jing Li ◽  
Kai Cui ◽  
Zhen Zhang ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Engineering Application ◽  
Creep Model ◽  
Nonlinear Viscoelastic ◽  
Rock Creep ◽  
Order Change ◽  
Creep Constitutive Model ◽  
Plastic Creep

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long-term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic-plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user-defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic-plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic-plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long-term engineering stability research.

A Nonlinear Viscoelastic Rheological Model of Soft Soil Based on Fractional Order Derivative

2013 ◽  
Vol 438-439 ◽  
pp. 1056-1059
Author(s):  
Rui Duo Li ◽  
Jin Chao Yue ◽  
Cun Zhen Zhu ◽  
Zhen Yang Sun
Keyword(s):  
Fractional Order ◽  
Soft Soil ◽  
Classical Model ◽  
Order Derivative ◽  
Solid Model ◽  
Kelvin Model ◽  
Fractional Order Derivative ◽  
Nonlinear Viscoelastic ◽  
Generalized Kelvin Model ◽  
Three Components

In order to overcome the defects of the classical model in the description of the rheological properties of soft soil, an Abel glue pot was defined based on the fractional derivative theory by the fractional calculus of Riemann-Liouville. Three components fractional order derivative solid model was built with Abel glue pot. Then the experimental data was fit using the new model. The simulation results show that the three components fractional order derivative solid model is more accurately than the generalized Kelvin model or Burgers model and that it has few parameters.

Numerical Techniques to Model Fractional-Order Nonlinear Viscoelasticity in Soft Elastomers

2018 ◽  
Author(s):  
Paul Miles ◽  
Graham Pash ◽  
William Oates ◽  
Ralph C. Smith
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Nonlinear Viscoelasticity ◽  
Nonlinear Modeling ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Accurate Approximation ◽  
Modeling Framework ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Dielectric elastomers are employed on a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many instances a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. In this paper, we demonstrate the effectiveness of using quadrature techniques in approximating the Riemann-Liouville definition for fractional derivatives in the context of developing a nonlinear viscoelastic model.

Rheological characterization of tack and viscoelasticity of compositions of crepe coating used in the Yankee dryer

TAPPI Journal ◽  
2019 ◽  
Vol 18 (11) ◽  
pp. 641-649
Author(s):  
JOSHUA OMAMBALA ◽  
CARL MCINTYRE
Keyword(s):  
Normal Force ◽  
Weight Ratio ◽  
Good Combination ◽  
Rheological Characterization ◽  
Nonlinear Viscoelastic ◽  
Coating Composition ◽  
Linear And Nonlinear ◽  
Work Done ◽  
Tissue Production

The vast majority of tissue production uses creping to achieve the required set of properties on the base sheet. The Yankee coating helps to develop the desired crepe that in turn determines properties such as bulk and softness. The adhesion of the sheet to the Yankee surface is a very important characteristic to consider in achieving the desired crepe. The coating mix usually consists of the adhesive, modifier, and release. A good combination of these components is essential to achieving the desired properties of the tissue or towel, which often are determined by trials on the machine that can be time consuming and lead to costly rejects. In this paper, five compositions of an industrial Yankee coating adhesive, modifier, and release were examined rheologically. The weight ratio of the adhesive was kept constant at 30% in all five compositions and the modifier and release ratios were varied. The normal force and work done by the different compositions have been shown at various temperatures simulating that of the Yankee surface, and the oscillatory test was carried out to explain the linear and nonlinear viscoelastic characteristic of the optimal coating composition.

Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

1988 ◽  
Vol 16 (3) ◽  
pp. 146-170 ◽  
Author(s):  
S. Roy ◽  
J. N. Reddy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Viscoelastic Behavior ◽  
Bonded Joints ◽  
Adhesively Bonded ◽  
Element Analysis ◽  
Adhesively Bonded Joints ◽  
Nonlinear Viscoelastic ◽  
Structural Failures ◽  
Updated Lagrangian

Abstract A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

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