Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method
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Mechanical Department, University of Technology- Baghdad, Iraq
Technical Engineering, Al-Farahidi University, Iraq
Mechanical department, University of Baghdad
Mechanical Engineering Department, Gulf University
Automated Manufacturing Engineering Department, University of Baghdad
Energy Department, University of Baghdad, Iraq
Submission date: 2023-10-22
Final revision date: 2024-01-06
Acceptance date: 2024-02-15
Online publication date: 2024-03-26
Publication date: 2024-03-27
Corresponding author
Oday Abdullah   

Energy Department, University of Baghdad, Iraq
International Journal of Applied Mechanics and Engineering 2024;29(1):142-158
This research paper applies the finite element method as a methodology to evaluate the structural performance of nonlinear viscoelastic solids. A finite element algorithm was built and developed to simulate the mathematical nonlinear viscoelastic material behavior based on incremental constitutive equations. The derived Equation of the incremental constitutive included the complete strain and stress histories. The Schapery’s nonlinear viscoelastic material model was integrated within the displacement-based finite element environment to perform the analysis. A modified Newton-Raphson technique was used to solve the nonlinear part in the resultant equations. In this work, the deviatoric and volumetric strain–stress relations were decoupled, and the hereditary strains were updated at the end of each time increment. It is worth mentioning that the developed algorithm can be effectively employed for all the permissible values of Poisson’s ratio by using a selective integration procedure. The algorithm was tested for a number of applications, and the results were compared with some previously published experimental results. A small percentage error of (1%) was observed comparing the published experimental results. The developed algorithm can be considered a promising numerical tool that overcomes convergence issues, enhancing equilibrium with high-accuracy results.
Bažant Z.P. (1972): Matrix differential equation and higher‐order numerical methods for problems of non‐linear creep, viscoelasticity and elasto‐plasticity.– International Journal for Numerical Methods in Engineering, vol.4, No.1, pp.11-15.
Yadagiri S. and Reddy C.P. (1985): Viscoelastic analysis of nearly incompressible solids.– Computers & Structures, vol.20, No.5, pp.817-825.
Tressou B., Vaziri R. and Nadot-Martin C. (2018): Application of the incremental variational approach (EIV model) to the linear viscoelastic homogenization of different types of microstructures: long fiber- particle-reinforced and strand-based composites.– European Journal of Mechanics-A/Solids, vol.68, pp.104-116.
Henriksen M. (1984): Nonlinear viscoelastic stress analysis-a finite element approach.– Computers & structures, vol.18, No.1, pp.133-139.
Haj‐Ali R.M. and Muliana A.H. (2004): Numerical finite element formulation of the Schapery non‐linear viscoelastic material model.– International Journal for Numerical Methods in Engineering, vol.59,No.1, pp.25-45.
Lai J. and Bakker A. (1996): 3-D Schapery representation for non-linear viscoelasticity and finite element implementation.– Computational mechanics, vol.18, No.3, pp.182-191.
Haj-Ali R. M. and Muliana A.H. (2003): A micromechanical constitutive framework for the nonlinear viscoelastic behavior of pultruded composite materials.– International Journal of Solids and Structures, vol.40, No.5, pp.1037-1057.
Muliana A., Nair A., Khan K.A. and Wagner S. (2006): Characterization of thermo-mechanical and long-term behaviors of multi-layered composite materials.– Composites Science and Technology, vol.66, No.15, pp.2907-2924.
Muliana A.H.and Haj-Ali R. (2008): A multi-scale framework for layered composites with thermo-rheologically complex behaviors.– International Journal of Solids and Structures, vol.45, No.10, pp.2937-2963.
Jabbar N.A., Hussain I.Y. Abdullah O.I. and Mohammed M.N. (2023). An experimental investigation and numerical analysis of the thermal behavior of a clutch system using the frictional facing of functionally graded materials.– Designs, vol.7, No.6, pp.125.
Zobeiry N., Malek S., Vaziri R. and Poursartip A. (2016): A differential approach to finite element modelling of isotropic and transversely isotropic viscoelastic materials.– Mechanics of Materials, vol.97, pp.76-91.
Schapery R. A. (1969): On the characterization of nonlinear viscoelastic materials.– Polymer Engineering & Science, vol.9, No.4, pp.295-310.
Haj-Ali, R.M. Muliana A.H. (2004). A multi-scale constitutive formulation for the nonlinear viscoelastic analysis of laminated composite materials and structures.– International Journal of Solids and Structures, vol.41, No.13, pp.3461-3490.
Muliana A.H. and Haj-Ali R.M. (2006): Analysis for creep behavior and collapse of thick-section composite structures.– Composite Structures, vol.73, No.3, pp.331-341.
Huang C.W., Abu Al-Rub R.K., Masad E.A. and Little D.N. (2011): Three-dimensional simulations of asphalt pavement permanent deformation using a nonlinear viscoelastic and viscoplastic model.– Journal of materials in civil engineering, vol.23, No.1, pp.56-68.
Rahmani E., Darabi M.K., Al-Rub R.K.A., Kassem E., Masad E.A. and Little D.N. (2013): Effect of confinement pressure on the nonlinear-viscoelastic response of asphalt concrete at high temperatures.– Construction and Building Materials, vol.47, pp.779-788.
Peña J.A., Martínez M.A. and Peña E. (2011): A formulation to model the nonlinear viscoelastic properties of the vascular tissue.– Acta Mechanica, vol.217, pp.63-74.
Feng H., Zhou J., Gao S. and Jiang L. (2021): Finite element simulation of the viscoelastic behavior of elastomers under finite deformation with consideration of nonlinear material viscosity.– Acta Mechanica, vol.232, pp.4111-4132.
Takaoka H. and Sakaue K. (2020): Evaluation of viscoelastic-viscoplastic characteristics and finite element analyses for thermoplastics.– Advanced Composite Materials, vol.29, No.3, pp.273-284.
Assie A.E., Eltaher M.A. and Mahmoud F.F. (2010): The response of viscoelastic-frictionless bodies under normal impact.– International Journal of Mechanical Sciences, vol.52, No.3, pp.446-454.
Assie A.E., Eltaher M.A. and Mahmoud F.F. (2011): Behavior of a viscoelastic composite plates under transient load.– Journal of Mechanical Science and Technology, vol.25, pp.1129-1140.
Ali I.A., Alazwari M.A., Eltaher M.A. and Abdelrahman A.A. (2022): Effects of viscoelastic bonding layer on performance of piezoelectric actuator attached to elastic structure.– Materials Research Express, vol.9, No.4, pp.045701.
Abdelrahman A.A., Nabawy A.E. Abdelhaleem A.M., Alieldin S.S. Eltaher M.A. (2020): Nonlinear dynamics of viscoelastic flexible structural systems by finite element method.– Engineering with Computers, vol.38, pp.169-190.
Akbaş Ş.D., Fageehi Y.A., Assie A.E. and Eltaher M.A. (2022): Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load.– Engineering with Computers, vol.38, pp.365-377.
Ghandourah E.E., Daikh A.A., Khatir S., Alhawsawi A.M., Banoqitah E.M. and Eltaher M.A. (2023): A dynamic analysis of porous coated functionally graded nanoshells rested on viscoelastic medium.– Mathematics, vol.11, No.10, pp.2407.
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