Related papers: Existence Results for the Time-incremental Elastic…
Contact problems with Coulomb friction in linear elasticity are notoriously difficult and their mathematical analysis is still largely incomplete. In this paper, a model problem with heterogeneous friction coefficient is considered in…
We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting ideas originating in our recent paper [4], we exhibit an…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
We consider the elasticity problem in a %heterogeneous domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb-friction conditions. Problem is non-linear, the dissipative functional…
Based on the plenty method, this paper describes a numerical method for 2D non-smooth contact problems with Coulomb friction and bilateral constraints and its application to the simulation of statics and dynamics for a frictional…
In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of…
This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for…
This paper presents an application of Canonical duality theory to the solution of contact problems with Coulomb friction. The contact problem is formulated as a quasi-variational inequality which solution is found by solving its…
The quasistatic normal-compliance contact problem of isotropic homogeneous linear visco-elastic bodies with Coulomb friction at small strains in Kelvin-Voigt rheology is considered. The discretization is made by a semi-implicit formula in…
This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincar\'{e}-Steklov…
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…
We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality…
We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation…
A fourth-order elliptic problem of Leray-Lions type is considered for combined nonlinearities and Sobolev-critical growth with Navier and Dirichlet boundary conditions. By combining variational methods and critical point theory, the…
We consider obstacle problems for nonlinear stochastic evolution equations. More precisely, the leading operator in our equation is a nonlinear, second order pseudomonotone operator of Leray-Lions type. The multiplicative noise term is…
We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\epsilon}]$, for initial data of the form $\epsilon U_0$, where $T$ depends only on…
The thin obstacle problem or $n$-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic…
We consider the dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles (the stops). We model the contact with Signorini's complementary…
A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure…
We consider a history-dependent variational inequality (P) which models the frictionless contact between a viscoelastic body and a rigid obstacle covered by a layer of soft material. The inequality is expressed in terms of the displacement…