An enriched finite element for crack opening and rebar slip in reinforced concrete members

摘要

Object of the paper is the simulation of reinforced concrete bars behaviour, accounting for crack opening and concrete-rebar slippage. A macro beam element with a single uniform reinforcement is studied in details in the uniaxial case. Distinct constitutive hypotheses are formulated for the materials. The CEB-FIP Model Code 90 rules the behaviour of the materials interface that is assumed to be fully dis-sipative. Steel is supposed to behave elastoplastically with hardening. Crack opening in the concrete matrix is introduced by means of a strong discontinuity approach (SDA). All the relevant equations of the problem are variationally derived from a mixed energy functional. Two enhancements of the enriched kinematics, based on polynomial or exponential shape functions, respectively, are compared with the usual SDA enhancement. As an alternative approach, high-order interpolation of the displacement field based on B-splines, both for steel and concrete, is proposed. These functions appear to be adequate in reproducing rapidly varying fields, like the stress gradients occurring in the shear lag problem near the boundaries or where slips and/or cracks occur. Their use allow to use few macro-element instead of the very dense meshing required in those areas by the traditional FE interpolations.