Modeling and analysis of history‐dependent contact problem for fractional Thermo‐viscoelastic Materials

In this paper, we consider frictionless contact problems involving a thermo‐viscoelastic body and a thermally conductive foundation. The constitutive law incorporates Caputo‐type time‐fractional derivatives to characterize the displacement behavior. The contact is free of friction and is represented by a condition that encompasses normal compliance and a memory term. We formulate the model variationally and establish the existence of a weak solution. The proofs are grounded in the Galerkin method and theories pertaining to results associated with fractional calculus. To illustrate the effectiveness of our approach, we include several numerical simulations demonstrating its performance.