A frictionless contact problem for elastic-viscoplastic materials with adhesion and thermal effects

Abstract

We consider a mathematical problem for frictionless contact between a thermo-elastic-viscoplastic body with adhesion and an obstacle. We employ the thermo-elastic-viscoplastic with damage constitutive law for the material. The evolution of the damage is described by an inclusion of parabolic type. The evolution of the adhesion field is governed by the differential equationβ = H ad β , ξ β , R ν (u ν), R τ (u τ). We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

“…This area is extensively explored in engineering structures, due to its temperature-dependent characteristics. Several articles have tackled the thermopiezoelectric contact problem with friction [5,[9][10][11][12][13], thermo-elasto-visco-plasticity [14][15][16], and thermo-visco-elasticity [17,18]. These studies are rooted in variations in constitutive laws and contact conditions [19][20][21][22][23][24][25].…”