Dynamic contact problem with thermal effect

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Justyna Ogorzaly

AbstractWe consider a model of a dynamic frictional contact between the body and the foundation. In this model the contact is bilateral. The behaviour of the material is described by the elastic-viscoplastic constitutive law with thermal effect. The variational formulation of this model leads to a system of two evolution hemivariational inequalities. The aim of this paper is to prove that this system of inequalities has a unique solution. The proof is based on the Banach fixed point theorem and some results for hemivariational inequalities.

2008 ◽  
Vol 18 (02) ◽  
pp. 271-290 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA

We consider a class of abstract second-order evolutionary inclusions involving a Volterra-type integral term, for which we prove an existence and uniqueness result. The proof is based on arguments of evolutionary inclusions with monotone operators and the Banach fixed point theorem. Next, we apply this result to prove the solvability of a class of second-order integrodifferential hemivariational inequalities and, under an additional assumption, its unique solvability. Then we consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is dynamic, the material behavior is described with a viscoelastic constitutive law involving a long memory term and the contact is modelled with subdifferential boundary conditions. We derive the variational formulation of the problem which is of the form of an integrodifferential hemivariational inequality for the displacement field. Then we use our abstract results to prove the existence of a unique weak solution to the frictional contact model.


2017 ◽  
Vol 23 (3) ◽  
pp. 359-391 ◽  
Author(s):  
Mikaël Barboteu ◽  
Leszek Gasiński ◽  
Piotr Kalita

Using the time approximation method we obtain the existence of a weak solution for the dynamic contact problem with damping and a non-convex stored elastic energy function. On the contact boundary we assume the normal compliance law and the generalization of the Coulomb friction law which allows for non-monotone dependence of the friction force on the tangential velocity. The existence result is accompanied by two numerical examples, one of them showing lack of uniqueness for the numerical solution.


2009 ◽  
Vol 19 (08) ◽  
pp. 1295-1324 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA

We study a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is static, the material behavior is described with a linearly electro-elastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is in the form of a system of two coupled hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on an abstract result on operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our results are valid.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.


2018 ◽  
pp. 1-31
Author(s):  
Mikhail Pavlovich Galanin ◽  
Nikolay Nikolaevich Proshunin ◽  
Aleksandr Sergeevich Rodin

Author(s):  
Chisato Mukai ◽  
Tetsuji Nakamoto ◽  
Yusuke Kondo ◽  
Chihiro Masaki ◽  
Atsumi Ohta ◽  
...  

ABSTRACT Objective Shortwave diathermy causes increase in temperature from deep inside the body, results in upregulation of metabolism, and has analgesic effects. In this study, we explored the potential application of shortwave diathermy in the maxillofacial region by monitoring internal and external temperature changes, changes in blood flow, and resting saliva secretion under shortwave diathermy for subjects with and without dental metal restorations (MR) to confirm the safety and the limitation of shortwave diathermy for dental medicine. Materials and methods Twenty young healthy subjects were recruited (10 subjects with MR and 10 subjects without MR). Shortwave exposure was achieved with condenser-type probes placed on the bilateral mandibular angles, and the intraoral temperature was monitored. For functional analysis, unstimulated whole saliva before and after exposure was collected. The temperature and blood flow distributions of the exposed areas were then monitored by thermography and twodimensional (2D) laser Doppler flowmetry. Results Shortwave exposure for 20 minutes induced significant temperature increases in all groups (p ≤ 0.05). The subjects reported no discomfort. When subjects without MR held gold or titanium crowns in their mouths, the thermal effect by shortwave diathermy was reduced. Resting saliva upon exposure only increased significantly in metal-free subjects, and amylase concentration was also increased, but the level of the salivary stress biomarker chromogranin A was unchanged. Furthermore, thermography showed that shortwave diathermy significantly increased the surface temperature for cheek skin and the buccal mucosa; however, this increase failed to elevate surface blood flow. Conclusion Shortwave diathermy induces temperature increases in the maxillofacial region. MR did not cause excessive heating, on the contrary, reduce the thermal effect of shortwave radiation. The temperature rise maintains upregulation in salivary function, which could be utilized safely in dental medicine. How to cite this article Mukai C, Nakamoto T, Kondo Y, Masaki C, Ohta A, Hosokawa R. Clinical Evaluation of Dental Metal Hazards and Therapeutic Effects of Shortwave Diathermy in Dental Medicine. Int J Prosthodont Restor Dent 2012;2(3): 88-95.


1994 ◽  
Vol 05 (02) ◽  
pp. 215-217
Author(s):  
T.Y. Fan ◽  
H.G. Hahn ◽  
A. Voigt

In this study a three-dimensional transient dynamic contact problem is solved, and a theorem relating the contact stress and displacement over an elliptic region is proved. Numerical results for the contact displacement-time variation clearly demonstrate the effect of inertia induced by the dynamic stress.


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