Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T11:53:23.558Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Viscoelastic Incremental-Layerwise Finite Element Method for Multilayered Structure Analysis Based on the Relaxation Approach

Published online by Cambridge University Press:  12 August 2014

M. Malakouti ,
M. Ameri  and
P. Malekzadeh
M. Malakouti*
Affiliation:
Department of Civil Engineering, Persian Gulf University, Bushehr, Iran
M. Ameri
Affiliation:
Mahmoud Ameri, Professor and Director of Center of Excellence for PMS, Transportation and Safety, Iran University of Science & Technology
P. Malekzadeh
Affiliation:
Department of Mechanical Engineering, Persian Gulf University, Bushehr, Iran
*
*[email protected]
Get access

Abstract

This paper presents an axisymmetric layerwise finite element formulation for dynamic analysis of laminated structures with embedded viscoelastic material whose constitutive behavior is represented by the Prony-generalized Maxwell series. To account the time dependence of the constitutive relations of linear viscoelastic materials, the incremental formulation in the temporal domain is used. Layerwise finite element has been shown to provide an efficient and accurate tool for the simulation of laminated structure. Most of the previous work on numerical simulation of laminated structures has been limited to elastic material behavior. Thus, the current work focuses on layerwise finite element analysis of laminated structures with embedded viscoelastic material. A computer code based on the presented formulation has been developed to provide the numerical results. The present approach is verified by studying its convergence behavior and comparing the numerical results with those obtained using the ABAQUS software. Finally, and as an application of the presented formulation, the effects of load duration on the dynamic structural responses of multilayered pavements are studied.

Keywords

Layerwise finite elementViscoelastic behaviorIncremental formulationDynamic responseProny series
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 6 , December 2014 , pp. 593 - 602
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Jianlin, W. and Bjorn, B., “A Time Domain Boundary Element Method for Modeling the Quasi-Static Viscoelastic Behavior of Asphalt Pavements,” Engineering Analysis with Boundary Elements, 31, pp. 226–240 (2007).Google Scholar
2.Al-Huniti, N., Al-Faqs, F. and Abu Zaid, O., “Finite Element Dynamic Analysis of Laminated Viscoelastic Structures,” Applied Composite Materials, 17, pp. 489–498 (2010).Google Scholar
3.Jaeseung, K., “General Viscoelastic Solutions for Multilayered Systems Subjected to Static and Moving Loads,” Journal of Materials in Civil Engineering, 23, pp. 1007–1016 (2011).Google Scholar
4.Chen, E. Y. G., Pan, E., Norfolk, T. S. and Wang, Q., “Surface Loading of a Multilayered Viscoelastic Pavement: Moving Dynamic Load,” Road Materials and Pavement Design, 12, pp. 849–874 (2011).Google Scholar
5.Ameri, M., Malakouti, M. and Malekzadeh, P., “Quasi-Static Analysis of Multilayered Domains with Viscoelastic Layer Using Incremental-Layerwise Finite Element Method,” Mechanics of Time-Dependent Materials, 18, pp. 275–291 (2014).Google Scholar
6.Bozza, A. and Gentili, G., “Inversion and Quasi-Static Problems in Linear Viscoelasticity,” Meccanica, 30, pp. 321–335 (1995).CrossRefGoogle Scholar
7.Drozdov, A. D. and Dorfmann, A., “A Constitutive Model in Finite Viscoelasticity of Particle-Reinforced Rubbers,” Meccanica, 39, pp. 245–270 (2004).Google Scholar
8.Ghazlan, G., Caperaa, S. and Petit, C., “An Incremental Formulation for the Linear Analysis of Thin Viscoelastic Structures Using Generalized Variables,” International Journal for Numerical Methods in Engineering, 38, pp. 3315–3333 (1995).Google Scholar
9.Zocher, M. A., Groves, S. E. and Aellen, D. H., “A Three-Dimensional Finite Element Formulation for Thermoviscoelastic Orthotropic Media,” International Journal for Numerical Methods in Engineering, 40, pp. 2267–2288 (1997).Google Scholar
10.Kim, K. S. and Sung Lee, H., “An Incremental Formulation for the Prediction of Two-Dimensional Fatigue Crack Growth with Curved Paths,” International Journal for Numerical Methods in Engineering, 72, pp. 697–721 (2007).Google Scholar
11.Theocaris, P. S., “Creep and Relaxation Contraction Ratio of Linear Viscoelastic Materials,” Journal of the Mechanics and Physics of Solids, 12, pp. 125–138 (1964).Google Scholar
12.Chazal, C. and Pitti, R. M., “An Incremental Constitutive Law for Ageing Viscoelastic Materials, a Three Dimensional Approach,” Comptes Rendus Mecanique, 337, pp. 30–33 (2009).Google Scholar
13.Dubois, F., Chazal, C. and Petit, C., “A Finite Element Analysis of Creep-Crack Growth in Viscoelastic Media,” Mechanics of Time-Dependent Materials, 2, pp. 269–286 (1999).Google Scholar
14.Chen, W. H. and Lin, T. C., “Dynamic Analysis of Viscoelastic Structures Using Incremental Finite Element Method,” Engineering Structures, 4, pp. 271–276 (1982).Google Scholar
15.Chen, E., Pan, E. and Green, R., “Surface Loading of a Multilayered Viscoelastic Pavement: Semi Analytical Solution,” Journal of Engineering Mechanics, 35, pp. 517–528 (2009).Google Scholar
16.Gibson, N. H., Schwartz, C. W., Schapery, R. A. and Witczak, M. W., “Viscoelastic, Viscoplastic, and Damage Modeling of Asphalt Concrete in Uncon-fined Compression,” Transport Research Record, 1860, pp. 3–15 (2003).Google Scholar
17.Elseifi, M. A., Al-Qadi, I. L. and Yoo, P. J., “Viscoe-lastic Modeling and Field Validation of Flexible Pavement,” Journal of Engineering Mechanics, 132, pp. 172–178 (2006).Google Scholar
18.Ghoreishy, M. H. R., “Determination of the Parameters of the Prony Series in Hyper-Viscoelastic Material Models Using the Finite Element Method,” Materials and Design, 35, pp. 791–797 (2012).Google Scholar
19.Mulungye, R. M., Owende, P. M. O. and Mellon, K., “Finite Element Modelling of Flexible Pavements on Soft Soil Subgrades,” Materials and Design, 28, pp. 739–756 (2007).Google Scholar
20.Pellinen, T. K. and Witczak, M. W., “Use of Stiffness of Hot-Mix Asphalt as a Simple Performance Test,” Transport Research Record, 1789, pp. 80–90 (2002).Google Scholar
21.Olard, F., Benedetto, H. D., Dony, A. and Vaniscote, J. C., “Properties of Bituminous Mixtures at Low Temperatures and Relations with Binder Characteristics,” Material and Structure, 38, pp. 121–126 (2005).Google Scholar
22.Chupin, O., Chabot, A., Piau, J. M. and Duhamel, D., “Influence of Sliding Interfaces on the Response of a Layered Viscoelastic Medium Under a Moving Load,” International Journal of Solids and Structures, 47, pp. 3435–3446 (2010).Google Scholar
23.Bahia, H. U. and Anderson, D. A., “The Development of the Bending Beam Rheometer, Basics and Critical Evaluation of the Rheometer,” ASTM Physical Properties of Asphalt Cement Binders Conference, 1241, pp. 28–50 (1995).Google Scholar
24.Reddy, J. N., “A Generalization of Two-Dimensional Theories of Laminated Composite Plates,” Communications in Applied Numerical Methods, 3, pp. 173–180 (1987).Google Scholar
25.Tahani, M. and Nosier, A., “Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates,” Mechanics of Advanced Materials and Structures, 11, pp. 67–92 (2004).Google Scholar
26.Malekzadeh, P., Setoodeh, A. R. and Barmshouri, E., “A Hybrid Layerwise and Differential Quadrature Method for In-Plane Free Vibration of Laminated Thick Circular Arches,” Journal of Sound and Vibration, 315, pp. 212–225 (2008).Google Scholar
27.Shakeri, M. and Mirzaeifar, R., “Static and Dynamic Analysis of Thick Functionally Graded Plates with Piezoelectric Layers Using Layerwise Finite Element Model,” Mechanics of Advanced Materials and Structures, 16, pp. 561–575 (2009).Google Scholar
28.Setoodeh, A. R., Malekzadeh, P. and Nikbin, K., “Low Velocity Impact Analysis of Laminated Composite Plates Using a 3D Elasticity Based Layerwise FEM,” Materials and Design, 30, pp. 3795–3801 (2009).Google Scholar
29.Setoodeh, A. R. and Karami, G., “Static Free Vibration and Buckling Analysis of Anisotropic Thick Laminated Composite Plates on Distributed and Point Elastic Supports Using a 3-D Layer-Wise FEM,” Journal of Engineering Structures, 26, pp. 211–220 (2004).Google Scholar
30.Tahani, M., “Analysis of Laminated Composite Beams Using Layerwise Displacement Theories,” Composite Structure, 79, pp. 535–547 (2007).Google Scholar
31.Malekzadeh, P., “A Two-Dimensional Layerwise-Differential Quadrature Static Analysis of Thick Laminated Composite Circular Arches,” Applied Mathematical Modelling, 33, pp. 1850–1861 (2009).Google Scholar
32.Boltzmann, L., “Zur Theorie Der Elastischen Nachwirkung Sitzungsber,” Mat Naturwiss Kl Kaiser Akad Wiss, pp. 70–275 (1878).Google Scholar
33.Picoux, B., ElAyadi, A. and Petit, C., “Dynamic Response of a Flexible Pavement Submitted by Impulsive Loading,” Soil Dynamics and Earthquake Engineering, 29, pp. 845–854 (2009).Google Scholar
34.Dave Eshan, V., Paulino Glaucio, H. and Buttlar William, G., “Viscoelastic Functionally Graded Finite-Element Method Using Correspondence Principle,” Journal of Materials in Civil Engineering, 23, pp. 39–48 (2011).Google Scholar
35.Kim, J., Roque, R. and Byron, T., “Viscoelastic Analysis of Flexible Pavements and Its Effects on Top-Down Cracking,” Journal of Materials in Civil Engineering, 21, pp. 324–332 (2009).Google Scholar
36.Bathe, K. J., Finite Element Procedures, 2rd Edition, New Jersey: Prentice-Hall (1996).Google Scholar
37.Lee, H. J., “Uniaxial Constitutive Modeling of Asphalt Concrete Using Viscoelasticity and Continuum Damage Theory,” PhD Dissertation, North Carolina State University, Raleigh, NC (1996).Google Scholar
38.Huang, Y. H., Pavement Analysis and Design, 2rd Edition, Pearson Prentice Hall, Upper Saddle River, NJ (2004).Google Scholar