On the asymptotic behavior of solutions of anisotropic viscoelastic body

Abstract

The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends to zero, is proved, and the limit solution is identified in a new data system. We show that when the thin layer disappears, its traces form a new contact law between the rigid plane and the viscoelastic body. In which case, a generalized weak form equation is formulated, the uniqueness result for the limit problem is also proved.

Analysis of a Frictionless Electro Viscoelastic Contact Problem with Signorini Conditions

“…Considerable progress has been achieved recently in modeling, mathematical analysis, and numerical simulations of various contact processes and, as a result, a general mathematical theory of contact mechanics is currently emerging. Mathematical structures underlie general contact problems with different constitutive laws for materials, varied geometries, and different contact conditions, [1,2]. The piezoelectric effect is characterized by the coupling between the mechanical and electrical properties of materials.…”