A Nonlinear Boundary Element Coupling formulation for three-dimensional bond-slip analysis

Resumo

This study presents a numerical coupling formulation for the bond-slip modelling of 3D reinforced do-
mains. This formulation is based on the Lagrangian 3D Boundary Element Method (BEM) and the 1DBEM/BEM

coupling. In this technique, the material matrix (solid 3D domain) is represented by the 3D BEM displacements

integral equation. Numerical integration and singularity subtraction are implemented for plane elements. A one-
dimensional approach of the BEM (1DBEM) represents the embedded reinforcing bars. The 1DBEM is based

on the axial fundamental solution for elastic 1D domains, which can be easily found in the literature. The inter-
action between the matrix and reinforcements is described by an adherence force over the reinforcements’ line,

which is interpolated by high-order polynomial functions. The adherence force is accounted as a body force into
the 3D BEM formulation. The bond-slip effects are accounted by considering relative displacements between
reinforcement and matrix. An adherence law represents the relation between slip and adherence force. Thus,
Newton-Raphson solution technique can be utilised to solve the nonlinear problem. The boundary formulation is
applied herein to represent the pullout test, which is essentially 3D. In this regard, a connection element is used
to properly enforce the prescribed displacement directly at the reinforcing bar in a region outside the 3D solid.
The numerical results of the pullout test model show excellent agreement with experimental data. Therefore, the
proposed formulation can be considered stable, accurate and robust.