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

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

doi:10.1016/j.ijmecsci.2012.11.001

Cited by 16 publications

(8 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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:

View full text Add to dashboard Cite

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.

show abstract

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:

View full text Add to dashboard Cite

show abstract

“…Equation 15 16works as nip mechanics model for rolling calenders (NMMR) used in textile industry. This equation can be applied to linear, homogeneous and isotropic contact problem having small deformations (Mahmoud et al 2013).…”

Section: As 2mentioning

confidence: 99%

Analysis of Nip Mechanics Model for Rolling Calender Used in Textile Industry

Gupta¹,

Kanth²

2018

JSSCM

View full text Add to dashboard Cite

Calendering is programmed finishing technique in the textile industry where the texture is squeezed between two or more rolls with a goal to obtain desired fragile quality, radiance and translucency. The essential guideline of calendering is to open the material to the joined impact of dampness, warmth and weight until the point texture gains an extraordinarily smooth and light reflecting surface. The essential mechanical action of the rolling calender is to cause the fibers of the web to reshape and deform around one another to get the desired smoothness. In this examination, an attempt has been made to develop a non-Hertzian nip mechanics model for finding the contact width of rolling calender and simulate this model to explore the impacts of design and process parameters such as load applied, bulk modulus, bonding time, diameter of the roll and cover thickness on contact width.

show abstract

“…The surfaces of the two contacting bodies possess a constant residual surface tension (τ s ) i in the unstrained state and the surface Lame's constants (μ s ) i and (λ s ) i , where i denotes to surfaces of body 1 and body 2, respectively. The mathematical formulation of the problem can be expressed as follows [34]: Neglecting the effects of body and inertia forces, the governing equilibrium equations of the bulk for quasistatic analysis can be written as…”

Section: Problem Statementmentioning

confidence: 99%

“…For the formulation of the contact solution algorithm, an incremental iterative procedure is used. Incorporating the surface energy effects and applying the virtual work principle yield the following weak form of the equilibrium equations [34]:…”

Section: Finite Element Modelmentioning

confidence: 99%

Analysis of nanocontact problems of layered viscoelastic solids with surface energy effects under different loading patterns

Rahman

Mahmoud

2015

Acta Mech

View full text Add to dashboard Cite

Surface stresses have a remarkable effect on nanocontact response of layered viscoelastic solids, especially under specific loading patterns. In the framework of nonlinear viscoelastic contact mechanics, a numerical model is developed to investigate the quasistatic nanocontact response of elastically layered viscoelastic solids under different loading patterns. The developed model accounts for surface energy effects by adopting the complete Gurtin-Murdoch surface elasticity model. The Schapery's constitutive viscoelastic creep model is used for the stress, strain, and time relationships. The transient term in the creep compliance is expressed by Prony's series. Frictionless contact condition is assumed throughout the contact interface. The equilibrium contact configuration, in which the contact constraints are exactly satisfied without any need for an appropriate value for the penalty parameter, is obtained by using the Lagrange multiplier method in the framework of the Newton-Raphson procedure. The developed model is applied to study and analyze the quasistatic nanocontact response of two different problems under different loading patterns. Results show the significant effect of the type of loading pattern and its rate on the nanocontact response of elastically layered viscoelastic solids.

show abstract

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

Cited by 16 publications

References 31 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

Analysis of Nip Mechanics Model for Rolling Calender Used in Textile Industry

Analysis of nanocontact problems of layered viscoelastic solids with surface energy effects under different loading patterns

Contact Info

Product

Resources

About