An Incremental Adaptive Procedure for Viscoelastic Contact Problems

Mahmoud, F.F.; El-Shafei, Ahmed G.; Attia, Mohamed A.

doi:10.1115/ijtc2006-12073

Cited by 9 publications

(11 citation statements)

References 25 publications

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“…In the context of contact mechanics, and in addition to the classical boundary conditions given by equations (4), the following contact constraints should be imposed throughout the indentation interface Γc 43–49 …”

Section: The Mathematical Formulation Of the Problemmentioning

confidence: 99%

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Attia

El-Shafei

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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In tribological and thermo-electro-mechanical applications with an appropriate gradation of properties, functionally graded materials provide superior performance for damage and wear resistance of contact systems and thermal and mechanical responses for other mechanical devices. This paper presents a nonlinear mixed variational-based computational model for the analysis of nonlinear plane indentation problems of elastic functionally graded layered elastic solids. The functionally graded elastic layer is perfectly bonded to the elastic substrate and is normally loaded by a cylindrical rigid punch. In addition to nonlinearity inherent to the contact problem, the developed model accounts for the geometric nonlinearity in the sense of larger displacements and rotations, but smaller strains. The modulus of elasticity as well as Poisson's ratio of the graded layer are varying along the thickness of the layer according to both exponential and power laws. On the contrary, in the conventional homogeneous finite element formulation the isoparametric graded finite element formulation is adopted on the level of Gaussian integration points to realize the gradation in material properties. The friction at the contact interface is modeled using Coulomb's friction law. Moreover, the inequality contact constraints are exactly satisfied throughout the contact interface by employing the Lagrange multiplier method, where the indentation force and the displacement fields are treated as independent variables. The obtained results of contact pressure, tangential contact stress, stress distribution, and indentation force show a significant influence of the material distribution, gradation law, gradient index, and thickness of the functionally graded layer.

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Section: The Mathematical Formulation Of the Problemmentioning

confidence: 99%

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Attia

El-Shafei

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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“…Extension to contact problems utilizing the energetic approach in BEM Visco-elastic frictionless contact problems are numerically handled usually by utilizing FEM, cf. [24,25,26,27,28,29]. To our best knowledge, except for the specific case of rolling contact [30], it is the first time that a BEM formulation for contact problems of visco-elastic solids is presented and fully explored, although it has been also used in [21] and originally proposed in [20].…”

Section: Extension To Multi-domain Problemsmentioning

confidence: 99%

A simple and efficient BEM implementation of quasistatic linear visco-elasticity

Panagiotopoulos

Mantič

Roubíček

2014

International Journal of Solids and Structures

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a b s t r a c tA simple yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced. This procedure is based on the implicit discretisation in time (the so-called Rothe method) combined with a simple ''algebraic'' transformation of variables, leading to a numerically stable procedure (proved explicitly by discrete energy estimates), which can be easily implemented in a BEM code to solve initial-boundary value visco-elastic problems by using the Kelvin elastostatic fundamental solution only. It is worth mentioning that no inverse Laplace transform is required here. The formulation is straightforward for both 2D and 3D problems involving unilateral frictionless contact. Although the focus is to the simplest Kelvin-Voigt rheology, a generalization to Maxwell, Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and implemented in the BEM code too. A few 2D and 3D initial-boundary value problems, one of them with unilateral frictionless contact, are solved numerically.

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“…Based on the LVE Wiechert model and the NVE Schapery's model, Mahmoud et al. 31–34 accounted for quasi-static frictionless and frictional contact problems in LVE and NVE solids.…”

Section: Introductionmentioning

confidence: 99%

“…The results support a theoretical model formulated based on the principles of contact mechanics. Based on the LVE Wiechert model and the NVE Schapery's model, Mahmoud et al [31][32][33][34] accounted for quasi-static frictionless and frictional contact problems in LVE and NVE solids. This paper presents a computational FE model to solve and analyze steady-state frictional rolling contact problems in NVE solids.…”

Section: Introductionmentioning

confidence: 99%

Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity

Abdelrahman

El-Shafei

Mahmoud

2018

Proceedings of the Institution of Mechanical Engineers, Part J:

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In the context of an updated Lagrangian formulation, a computational model is developed for analyzing the steady-state frictional rolling contact problems in nonlinear viscoelastic solids. Schapery's nonlinear viscoelastic model is adopted to simulate the viscoelastic behavior. In addition to the material nonlinearity, the model accounts for geometrical nonlinearities, large displacements, and rotations with small strains. To satisfy the steady-state rolling contact condition, a spatially dependent incremental form of the viscoelastic constitutive equations is derived. Consequently, the dependence on the past history of the strain rate in the stress–strain law is expressed in terms of the spatial variation of the strain. The contact conditions are exactly satisfied by employing the Lagrange multiplier approach to enforce the contact constraints. The classical Coulomb's friction law is used to simulate friction. The developed model is verified and compared and good agreement is obtained. The applicability of the developed model is demonstrated by analyzing the steady-state rolling contact response of viscoelastically walled-wheel over rigid foundation. Moreover, the obtained results show remarkable effects of the rotational velocity and the viscoelastic material parameters on the mechanical response of steady-state frictional rolling contact.

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An Incremental Adaptive Procedure for Viscoelastic Contact Problems

Cited by 9 publications

References 25 publications

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

A simple and efficient BEM implementation of quasistatic linear visco-elasticity

Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity

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