Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements

Deepak S. Ramrakhyani, George A. Lesieutre, Edward Smith

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

A model of the one-dimensional dynamic behavior of elastomeric materials is developed based on a previously existing model. An initial model consisted of nonlinear multiple anelastic displacement fields in parallel with discrete friction elements. The motivation for the development of a new model is reduction of the number of parameters needed to accurately capture material behavior. A new element, a "continuously yielding element," is developed, which conceptually represents a distribution of parallel friction elements. This element replaces the entire collection of discrete friction elements used in the initial model. In addition, a linear fractional derivative anelastic displacement field element replaces the multiple linear anelastic displacement field elements used in the older model. Finally, nonlinearity is introduced into the fractional derivative anelastic displacement field element, in an attempt to capture observed amplitude dependence of storage and loss moduli at higher amplitudes. The different parts of the new model are first compared individually to those of the initial model then combined and compared as an integrated whole. The new model captures the frequency and amplitude variation of the storage and loss moduli of the material better than the initial model, while the total number of parameters is reduced to seven from sixteen.

Original languageEnglish (US)
Pages (from-to)3929-3948
Number of pages20
JournalInternational Journal of Solids and Structures
Volume41
Issue number14
DOIs
StatePublished - Jul 1 2004

Fingerprint

Fractional Derivative
Friction
friction
Derivatives
Modeling
Model
Modulus
elastomeric
Dynamic Behavior
nonlinearity
Entire
Nonlinearity

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

@article{b5105547558e432fbad343d3df5918df,
title = "Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements",
abstract = "A model of the one-dimensional dynamic behavior of elastomeric materials is developed based on a previously existing model. An initial model consisted of nonlinear multiple anelastic displacement fields in parallel with discrete friction elements. The motivation for the development of a new model is reduction of the number of parameters needed to accurately capture material behavior. A new element, a {"}continuously yielding element,{"} is developed, which conceptually represents a distribution of parallel friction elements. This element replaces the entire collection of discrete friction elements used in the initial model. In addition, a linear fractional derivative anelastic displacement field element replaces the multiple linear anelastic displacement field elements used in the older model. Finally, nonlinearity is introduced into the fractional derivative anelastic displacement field element, in an attempt to capture observed amplitude dependence of storage and loss moduli at higher amplitudes. The different parts of the new model are first compared individually to those of the initial model then combined and compared as an integrated whole. The new model captures the frequency and amplitude variation of the storage and loss moduli of the material better than the initial model, while the total number of parameters is reduced to seven from sixteen.",
author = "Ramrakhyani, {Deepak S.} and Lesieutre, {George A.} and Edward Smith",
year = "2004",
month = "7",
day = "1",
doi = "10.1016/j.ijsolstr.2004.02.034",
language = "English (US)",
volume = "41",
pages = "3929--3948",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "14",

}

TY - JOUR

T1 - Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements

AU - Ramrakhyani, Deepak S.

AU - Lesieutre, George A.

AU - Smith, Edward

PY - 2004/7/1

Y1 - 2004/7/1

N2 - A model of the one-dimensional dynamic behavior of elastomeric materials is developed based on a previously existing model. An initial model consisted of nonlinear multiple anelastic displacement fields in parallel with discrete friction elements. The motivation for the development of a new model is reduction of the number of parameters needed to accurately capture material behavior. A new element, a "continuously yielding element," is developed, which conceptually represents a distribution of parallel friction elements. This element replaces the entire collection of discrete friction elements used in the initial model. In addition, a linear fractional derivative anelastic displacement field element replaces the multiple linear anelastic displacement field elements used in the older model. Finally, nonlinearity is introduced into the fractional derivative anelastic displacement field element, in an attempt to capture observed amplitude dependence of storage and loss moduli at higher amplitudes. The different parts of the new model are first compared individually to those of the initial model then combined and compared as an integrated whole. The new model captures the frequency and amplitude variation of the storage and loss moduli of the material better than the initial model, while the total number of parameters is reduced to seven from sixteen.

AB - A model of the one-dimensional dynamic behavior of elastomeric materials is developed based on a previously existing model. An initial model consisted of nonlinear multiple anelastic displacement fields in parallel with discrete friction elements. The motivation for the development of a new model is reduction of the number of parameters needed to accurately capture material behavior. A new element, a "continuously yielding element," is developed, which conceptually represents a distribution of parallel friction elements. This element replaces the entire collection of discrete friction elements used in the initial model. In addition, a linear fractional derivative anelastic displacement field element replaces the multiple linear anelastic displacement field elements used in the older model. Finally, nonlinearity is introduced into the fractional derivative anelastic displacement field element, in an attempt to capture observed amplitude dependence of storage and loss moduli at higher amplitudes. The different parts of the new model are first compared individually to those of the initial model then combined and compared as an integrated whole. The new model captures the frequency and amplitude variation of the storage and loss moduli of the material better than the initial model, while the total number of parameters is reduced to seven from sixteen.

UR - http://www.scopus.com/inward/record.url?scp=2442659366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442659366&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2004.02.034

DO - 10.1016/j.ijsolstr.2004.02.034

M3 - Article

VL - 41

SP - 3929

EP - 3948

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 14

ER -