Andaluzia Matei

Efficient Algorithms for Problems with Friction

In this paper, a nonconforming discretization method for the frictional contact between two bodies subjected to antiplane shear deformation is considered. The method is based on a mixed variational formulation where dual basis functions are used for the discretization of the Lagrange multiplier. Under some regularity assumptions on the solution, an optimal a priori error estimate is obtained. To solve the discrete nonlinear problem an inexact primal-dual active set strategy is introduced. Finally, numerical examples confirming the theoretical result for the a priori error estimate and illustrating the performance of the algorithm are presented. The results can easily be generalized to the case of Coulomb friction. For this case a numerical example is given.

On the behavior of the solution of a viscoplastic contact problem

We consider a mathematical model which describes the frictionless contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic and the contact is modeled with normal compliance and unilateral constraint. We provide a mixed variational formulation of the model which involves a dual Lagrange multiplier, and then we prove its unique weak solvability. We also prove an estimate which allows us to deduce the continuous dependence of the weak solution with respect to both the normal compliance function and the penetration bound. Finally, we provide a numerical validation of this convergence result.

An evolutionary mixed variational problem arising from frictional contact mechanics

We consider an abstract mixed variational problem which consists of a system of an evolutionary variational equation in a Hilbert space X and an evolutionary inequality in a subset of a second Hilbert space Y, associated with an initial condition. The existence and the uniqueness of the solution is proved based on a fixed point technique. The continuous dependence on the data was also investigated. The abstract results we obtain can be applied to the mathematical treatment of a class of frictional contact problems for viscoelastic materials with short memory. In this paper we consider an antiplane model for which we deliver a mixed variational formulation with friction bound dependent set of Lagrange multipliers. After proving the existence and the uniqueness of the weak solution, we study the continuous dependence on the initial data, on the densities of the volume forces and surface tractions. Moreover, we prove the continuous dependence of the solution on the friction bound.

Weak solutions for contact problems involving viscoelastic materials with long memory

We consider an antiplane model which describes the contact between a deformable cylinder and a rigid foundation, under the small deformation hypothesis, for quasistatic processes. The behaviour of the material is modelled using a viscoelastic constitutive law with long memory and the frictional contact is modelled using Tresca’s law. We focus on the weak solvability of the model, based on a weak formulation with dual Lagrange multipliers.

A Variational Approach for an Electro‐Elastic Unilateral Contact Problem

Abstract We consider a mechanical model which describes the frictionless unilateral contact between an electro‐elastic body and a rigid electrically non‐conductive foundation. For this model, a mixed variational formulation is provided. Then, using elements of the saddle point theory and a fixed point technique, an abstract result is proved. Based on this result, the existence of a unique weak solution of the mechanical problem is established.

Elastic antiplane contact problem with adhesion

Abstract. We study a mechanical problem modeling the antiplane shear deformation of a linearly elastic body in adhesive contact with a foundation. The material is assumed to be homogeneous and isotropic and the process is quasistatic. The adhesion process on the contact surface is modeled by a surface internal variable, the bonding field, and the tangential shear due to the bonding is included. We establish the existence of a unique weak solution for the problem, by construction of an appropriate mapping which is shown to be a contraction on a Banach space.

History-dependent mixed variational problems in contact mechanics

We consider a new class of mixed variational problems arising in Contact Mechanics. The problems are formulated on the unbounded interval of time

Nonlinear feedback control and artificial intelligence computational methods applied to a dissipative dynamic contact problem

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