We consider multigrid methods for problems in linear elasticity which are robust with respect to the Poisson ratio. Therefore, we consider mixed approximations involving the displacement vector and the pressure, where the pressure is approximated by discontinuous functions. Then, the pressure can be eliminated by static condensation. The method is based on a saddle point smoother which was intr...

We consider a quasistatic frictionless contact problem for an electro-viscoelastic body with damage. The contact is modelled with normal compliance. The adhesion of the contact surfaces is taken into account and modelled by a surface variable, the bonding field. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potent...

In this paper goal-oriented error control based on dual weighted residual error estimations (DWR) is applied to frictional contact problems. A mixed formulation of the contact problem is used to derive a discretization. It relies on the introduction of Lagrange multipliers to capture the frictional contact conditions. The discretization error is estimated in terms of functionals (the quantities...

The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit o...

We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ε and the stiffness of order 1/ε where ε is a positive real...

We extend the applicability of the augmented dual-mixed method introduced recently in [4, 5] to the problem of linear elasticity with mixed boundary conditions. The method is based on the Hellinger–Reissner principle and the symmetry of the stress tensor is imposed in a weak sense. The Neuman boundary condition is prescribed in the finite element space. Then, suitable Galerkin least-squares typ...

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constituti...

In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint. More recently, the authors have derived stable mixed stress/displ-acement formulations using linear/linear interpolations to enhance stress accuracy in both linear and non-linear problems. In both cases, the Variational Multi Scale (VMS) stabilizati...

This paper presents a finite element formulation suitable for large-strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue. First, an experimentally derived strain energy function is obtained from literature. This function is implemented in finite elements using the mixed pressure-displacement formulation. A ...

The problem of crack path selection in piezoelectric bimaterials is considered in this paper. Based on the Stroh formulation for anisotropic material and GreenÕs functions for piezoelectric bimaterials, the crack problem is expressed in terms of coupled singular integral equations at ®rst, and then the equations are used to solve for stress and electric displacement ®elds numerically. A crack i...