Institute of Fundamental Technological Research

Standard higher order finite elements often perform unsatisfactory in contact problems. The major difficulties are caused by uneven distribution of nodal forces resulting in oscillating contact pressure. The paper presents a new approach that eliminates this drawback. The weight functions are chosen in such a way that even distributions of nodal forces are obtained. It is achieved by applying piece-wise linear weighting functions. Two new 3D isoparametric quadratic elements are derived: 6-node triangle and 8-node quadrilateral, and tested in many examples. The new elements have unsymmetric stiffness matrices, but the provided examples show their good performance in contact problems.

coontact problems, weighting functions, quadratic finite elements

The structure of incremental equations in plasticity is discussed with respect to the choice of control variables representing stress, strain or mixed control, while (quite independently) the yield surface may be represented in either stress, strain, or mixed space. It is concluded that the choice of state variables does not affect the analytical properties of the resulting equations, whereas the choice of control variables has a major influence on the uniqueness of the stress-strain behaviour. For an associated flow rule the most and least severe restrictions are placed by pure stress control and pure strain control, respectively.

A general constitutive model for concrete is discussed in which the total strain rate is decomposed into elastic, plastic and damage strain rates. The rate equations are formulated for all strain rate portions together with evolution rules for hardening and damage state variables. The coupling effect between damage and plastic deformation is considered by introducing yield and damage surfaces and formulating proper interaction rules. Both axisymmetric and general threedimensional stress states are considered for which monotonic and cyclic loading conditions are assumed. The model is aimed to describe material behavior for a variety of loading histories. Its applicability is illustrated by considering uniaxial, biaxial and triaxial compression with superposed shear stresses.