Analysis of quasistatic frictional contact problems in nonlinear viscoelasticity with large deformations

F. F. Mahmoud, A. G. El-Shafei, M. A. Attia, A. A.Abdel Rahman

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


A numerical model for the analysis of frictional contact problems in viscoelastic structures, undergoing both material and geometrical nonlinearities is presented. The nonlinear Schapery constitutive viscoelastic model is used for the stress, strain, and time relationships. The constitutive equations are expressed in an incremental form assuming a constant strain rate within each time increment. The hereditary integral is updated at the end of time increment by recursive procedure. The normal contact forces are treated as independent variables. In addition, the regularized Coulomb's friction model is adopted to model the friction throughout the contact interface. The friction resistance is represented by tangential contact stiffness. The Updated Lagrangian approach is adopted to derive the equilibrium equations for the contact systems. The Newton-Raphson iterative scheme is utilized to obtain the converged solution at the end of each time increment. The developed model is verified and compared with the available analytical methods and benchmarks. The applicability of the developed computational incremental iterative scheme is demonstrated by solving two different cases of contact problems with different geometry, loading, and boundary conditions. Numerical results show that material nonlinearity and friction have great effects on viscoelastic contact behavior.

Original languageEnglish
Pages (from-to)109-119
Number of pages11
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - Jan 2013


  • Finite element method (FEM)
  • Frictional contact
  • Large deformation
  • Nonlinear viscoelasticity
  • Schapery's model
  • Updated Lagrangian formulation (U.L.)

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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