Existence results for unilateral contact problem with friction of thermo-electro-elasticity

• Published in: Applied mathematics and mechanics Vol. 36; no. 7; pp. 911 - 926
• Main Authors: Benaissa, H., Essoufi, El-H., Fakhar, R.
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.07.2015; Laboratoire de Recherche en Mathématique, Informatique et Sciences de l'Ingénieur(MISI), Settat 26000, Morocco%Laboratoire de Science des Matériaux, des Milieux et de la Modélisation(LS3M),Université Hassan 1, Khouribga 25000, Morocco
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; 变分不等式; 弹性本构关系; 接触问题; 摩擦法; 数学模型; 耦合系统; 解的存在性; 静态过程; 35J85; static frictional contact; 74S05; thermo-piezoelectric material; frictional heat generation; variational inequality; Signorini’s condition; 74M15; fixed point process; 74M10; 74F15; 47J20; 49J40; O29; 74G30; Tresca’s friction; O343.6; Tresca's friction; Signorini's condition
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-015-1957-9

This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini＇s conditions and Tresca＇s friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is de- rived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.