History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems. (June 2022)

• Record Type: Journal Article
• Authors: Hao, Jianwei; Wang, JinRong; Han, Jiangfeng
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 6(2022)
• Page Start: 1032
• Page End: 1052
• Publication Date: 2022-06
• Subjects: Frictionless quasistatic contact problem -- history-dependent fractional differential hemivariational inequalities -- time-delay system -- Rothe method -- fixed-point theorem; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211054185
• Languages: English
• ISSNs: 1081-2865

Abstract

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.