Displaying similar documents to “Dynamic frictional contact of a viscoelastic beam”

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete...

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Mikaël Barboteu, Krzysztof Bartosz, Piotr Kalita (2013)

International Journal of Applied Mathematics and Computer Science

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We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The...

Numerical analysis and simulations of quasistatic frictionless contact problems

José Fernández García, Weimin Han, Meir Shillor, Mircea Sofonea (2001)

International Journal of Applied Mathematics and Computer Science

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A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

Carsten Carstensen, Petr Plecháč (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm...

Thick obstacle problems with dynamic adhesive contact

Jeongho Ahn (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...

Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem

Ioan Rosca, Mircea Sofonea (1994)

Applications of Mathematics

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This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented.