A dynamic contact problem between elasto-viscoplastic piezoelectric bodies

Hadj, Tedjani; Benabderrahmane, Benyattou; Drabla, Salah

doi:10.14232/ejqtde.2014.1.49

Cited by 4 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the constant c K denotes a positive constant which may depends only on Ω α , Γ α 1 (see [9]). Over the space V α we consider the inner product given by…”

Section: The Formulation Of Variations and Necessary Initial Stepsmentioning

confidence: 99%

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Laid,

Ammar

2023

General Mathematics

View full text Add to dashboard Cite

This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments. This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.

show abstract

“…where the constant c K denotes a positive constant which may depends only on Ω α , Γ α 1 (see [9]). Over the space V α we consider the inner product given by…”

Section: The Formulation Of Variations and Necessary Initial Stepsmentioning

confidence: 99%

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Laid,

Ammar

2023

General Mathematics

View full text Add to dashboard Cite

show abstract

“…τ stands for the jump of the displacements in tangential direction. This condition shows that the shear on the contact surface depends on the bonding field and on the tangential displacement, but as long as it does not exceed the bond length L. Next, equation (8) represents the ordinary differential equation that describes the evolution of the bonding field and it was already used in [4], see also [3] for more details. Here, besides γ ν , two new adhesion coefficients are involved, γ τ and ε a .…”

Section: Problem Statement and Variational Formulationmentioning

confidence: 99%

Dynamic contact problem with adhesion and damage between thermo–electro–elasto-viscoplastic bodies

Ammar¹,

Saïdi²,

Ahmed³

2017

Comptes Rendus. Mécanique

Self Cite

View full text Add to dashboard Cite

show abstract

“…The adhesion model with contact boundary to transmit force was studied in refs. [19][20][21]. The stochastic model for vibration of a nonlinear beam was studied in ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamic contact problem with moderate displacement and time‐dependent normal

Wu¹

2022

Z Angew Math Mech

View full text Add to dashboard Cite

In the publications on existence of solutions to the dynamic contact problems, small displacement was basically assumed. To extend the qualitative study for more general applications with moderate displacement and general shape of surfaces, the normal of contact surface is treated as time‐dependent variable in the contact mechanics model. The frictional dynamic contact problem with unilateral constraint is formulated in a variational inequality. The penalized variational equation is derived with two penalty terms, verifying contact condition and applying constraint on the normal velocity, respectively. For given penalty parameter the penalized variational equation is proved to have solution, which converges to the solution of the variational inequality. The true contact boundary, varying in time, is determined in the process and the constraint condition is satisfied. The regularity of the solution is similar to the results by others under the assumption of small displacement.

show abstract

A dynamic contact problem between elasto-viscoplastic piezoelectric bodies

Cited by 4 publications

References 15 publications

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Dynamic contact problem with adhesion and damage between thermo–electro–elasto-viscoplastic bodies

Dynamic contact problem with moderate displacement and time‐dependent normal

Contact Info

Product

Resources

About