We consider a dynamic contact problem with wear between two elastic-viscoplastic piezoelectric bodies. The contact is frictional and bilateral which results in the wear of contacting surface. The evolution of the wear function is described with Archard's law. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

We consider a mathematical frictionless contact problem between two electro-elastic bodies. The contact is modelled with normal compliance and adhesion. We provide a variational formulation for the problem and prove the existence of a unique weak solution. The proofs are based on arguments of time-dependent variational inequalities, the Cauchy-Lipschitz Theorem and the Banach Fixed-Point Theorem. Then, a discrete scheme is introduced based on the nite element method to approximate the spatial variable. Furthermore, we provide optimal a priori error estimates for the displacements, the electric potential and the bonding at the contact interface.

We study of a quasistatic frictional contact problem between two thermo-electroelastic bodies with adhesion. The temperature of the materials caused by elastic deformations. The contact is modelled with a version of normal compliance condition and the associated Coulomb’s law of friction in which the adhesion of contact surfaces is taken into account. 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 anduniqueness result on parabolic equalities, differential equations and fixed point arguments.

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.

In this paper we derive useful results regarding the asymptotic properties of new set of monic polynomials primitives of orthogonal polynomials on the unit circle, called second order polar polynomials.