Abstract
In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.
Highlights
Viscoelastic constitutive laws have been used in the engineering or mathematical literature to describe the deformed behavior of contact problems
In the recent paper [24], Yao and Huang introduced and studied a mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation, in which the contact is bilateral, the behavior of the material is described with a viscoelastic constitutive law with time-delay, and the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip
In the following we provide an elementary example of the mechanical problem, in which the constitutive law equation (3.2) holds
Summary
Viscoelastic constitutive laws have been used in the engineering or mathematical literature to describe the deformed behavior of contact problems. Using the theory of evolutionary hemivariational inequality, Migorski et al [16] proved that a nonlinear explicit time dependent elastic-viscoplastic frictional contact problem exists a unique weak solution. In the recent paper [24], Yao and Huang introduced and studied a mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation, in which the contact is bilateral, the behavior of the material is described with a viscoelastic constitutive law with time-delay, and the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip. By using the Banach’s fixed-point theorem, we establish an existence and uniqueness theorem of the solution to the quasistatic contact problems for viscoelastic materials with nonlocal Coulomb friction and time-delay. The results presented in this paper generalize and improve some known results in [12] and [22]
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.
