A frictionless contact problem for elastic-viscoplastic materials with normal compliance: Numerical analysis and computational experiments

2002 ◽  
Vol 90 (4) ◽  
pp. 689-719 ◽  
Author(s):  
J.R. Fernández-García ◽  
M. Sofonea ◽  
J.M. Via no
Keyword(s):  
Numerical Analysis ◽  
Contact Problem ◽  
Computational Experiments ◽  
Normal Compliance ◽  
Frictionless Contact

Numerical analysis and simulations of a dynamic frictionless contact problem with damage

2006 ◽  
Vol 196 (1-3) ◽  
pp. 476-488 ◽  
Author(s):  
M. Campo ◽  
J.R. Fernández ◽  
K.L. Kuttler ◽  
M. Shillor ◽  
J.M. Viaño
Keyword(s):  
Numerical Analysis ◽  
Contact Problem ◽  
Frictionless Contact

scholarly journals Numerical Analysis of a Sliding frictional contact problem with Normal Compliance and Unilateral Contact

2020 ◽  
Author(s):  
Yahyeh Souleiman ◽  
Mikael Barboteu
Keyword(s):  
Numerical Analysis ◽  
Contact Problem ◽  
Frictional Contact ◽  
Nonlinear Partial Differential Equations ◽  
Viscoelastic Body ◽  
Sliding Contact ◽  
Memory Term ◽  
Optimal Order ◽  
Normal Compliance ◽  
Order Error

Abstract This paper represents a continuation of [15] and [18]. Here, we consider the numerical analysis of a non trivial frictional contact problen in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint, and is associated to a sliding version of Coulomb's law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

scholarly journals Analysis of electroelastic frictionless contact problems with adhesion

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
Mircea Sofonea ◽  
Rachid Arhab ◽  
Raafat Tarraf
Keyword(s):  
Contact Problem ◽  
Contact Problems ◽  
Time Dependent ◽  
Stiffness Coefficient ◽  
Normal Compliance ◽  
Unique Weak Solution ◽  
Frictionless Contact ◽  
Contact Surfaces ◽  
Signorini Contact ◽  
Variational Formulations

We consider two quasistatic frictionless contact problems for piezoelectric bodies. For the first problem the contact is modelled with Signorini's conditions and for the second one is modelled with normal compliance. In both problems the material's behavior is electroelastic and the adhesion of the contact surfaces is taken into account and is modelled with a surface variable, the bonding field. We provide variational formulations for the problems and prove the existence of a unique weak solution to each model. The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.

Sign in / Sign up

Export Citation Format

Share Document