Implementation of fractional order viscoelastic models to finite element method

Download

index.pdf

Date

2019

Author

Hesammokri, Parnian

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

289
views

585
downloads

In the latest decades, fractional calculus has been commonly used to define the behavior of viscoelastic materials. Real viscoelastic materials such as rubbers, polymers, soft biological tissues, asphalt mixtures, soils, etc. represent power law creep and relaxation behaviors. In Scientific literature relaxation and creep of this type of material has been modelled, primarily through single and/or linear combinations of exponential functions, in an effort to capture the contributions of both solid and fluid phases. This strategy does not allow experimental findings to fit correctly. In this study, isotropic 3-D constitutive equations are evaluated using the fractional calculus by means of the concept of fading memory for a single spring pot, the fractional Kelvin-Voigt model, and the fractional standard linear solid model to reproduce the actual behavior of these materials. Using the UMAT subroutine in ABAQUS / Standard, a finite element code is developed for each model. To reach the strain and stress history of all fractional models, the Boltzmann superposition concept and the fractional derivatives evaluated by Grünwald-Letnikov were used. Relaxation and creep responses have been obtained for each fractional model and these computational results are compared to analytical results to demonstrate the correctness of the finite element codes. Access to the history of strain and stress at each Gauss point of each component is essential for the implementation of the model in a constructive way which is one of the most important aims of this study which has been reached by developing the finite element code using the Jacobian matrix not the strain energy density function which utilized widely in literature. These codes can describe the transition of the viscoelastic models’ behavior smoothly from rubbery to glassy just by changing the fractional coefficients. It has been shown that using this technique the process of extracting material parameters can be much easier as less coefficients are required compared to other techniques in constitutive models. This study demonstrates that 3D fractional viscoelastic models can be readily and effectively implemented in finite element software.

Subject Keywords

Viscoelasticity., Fractional Calculus, Viscoelasticity, Finite Element Method.

URI

http://etd.lib.metu.edu.tr/upload/12623925/index.pdf
https://hdl.handle.net/11511/44826

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation Demirci, Nagehan; Tönük, Ergin (2014-01-01) Purpose: During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non...
Assessment and improvement of elementary force computations for cold forward rod extrusion Ocal, M; Egemen, N; Tekkaya, AE (2005-06-01) Two commonly used analytical force computation methods for cold forward rod extrusion are evaluated by means of precise finite element computations. The upperbound model by Avitzur based on the spherical velocity field and the model by Siebel based on a quasi-upper-bound solution are considered. It has been found that the pure deformation forces obtained by summing the ideal force and shear force terms deviate between +25% and -20% from the finite element solutions. Larger deviations, however, occur for the...
Modeling and simulation of viscous electro-active polymers Vogel, Franziska; Göktepe, Serdar; Steinmann, Paul; Kuhl, Ellen (2014-11-01) Electro-active materials are capable of undergoing large deformation when stimulated by an electric field. They can be divided into electronic and ionic electro-active polymers (EAPs) depending on their actuation mechanism based on their composition. We consider electronic EAPs, for which attractive Coulomb forces or local re-orientation of polar groups cause a bulk deformation. Many of these materials exhibit pronounced visco-elastic behavior. Here we show the development and implementation (o)f a constitu...
Investigation of nanoantennas using surface integral equations and the multilevel fast multipole algorithm Karaosmanoglu, Barıscan; Gur, Ugur Merıc; Ergül, Özgür Salih (2015-07-09) A rigorous analysis of nanoantennas using surface integral equations and the multilevel fast multipole algorithm (MLFMA) is presented. Plasmonic properties of materials at optical frequencies are considered by using the Lorentz-Drude models and employing surface formulations for penetrable objects. The electric and magnetic current combined-field integral equation is preferred for fast and accurate solutions, which are further accelerated by an MLFMA implementation that is modified for plasmonic structures....
Investigation of fluid rheology effects on ultrasound propagation Özkök, Ozan; Uludağ, Yusuf; Department of Chemical Engineering (2012) In this study, a mathematical model is developed for investigating the discrete sound propagation in viscoelastic medium to identify its viscoelastic properties. The outcome of the model suggests that pulse repetition frequency is a very important parameter for the determination of relaxation time. Adjusting the order of magnitude of the pulse repetition frequency, the corresponding relaxation time which has similar magnitude with pulse repetition frequency is filtered while the others in the spectrum are d...

Citation Formats

P. Hesammokri, “Implementation of fractional order viscoelastic models to finite element method,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Mechanical Engineering., Middle East Technical University, 2019.