Abstract
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.
Highlights
Considerable progress has been achieved recently in modelling, mathematical analysis, and numerical simulations of various contact processes and, as a result, a general mathematical theory of contact mechanics is currently emerging
The piezoelectric effect is characterized by the coupling between the mechanical and electrical properties of the materials
For the first problem we study in this paper the contact is modelled with Signorini’s conditions and for the second one is modelled with normal compliance
Summary
Considerable progress has been achieved recently in modelling, mathematical analysis, and numerical simulations of various contact processes and, as a result, a general mathematical theory of contact mechanics is currently emerging. In the last two references the variational formulations of the corresponding problems were derived and existence and uniqueness results for the weak solutions were obtained. Theorems 3.4 and 3.5 state the unique weak solvability of the adhesive frictionless contact problem with Signorini and normal compliance conditions, respectively.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
