The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Abstract

This study applies the Boundary Element Method (BEM) for the fracture failure modelling of three-dimensional concrete structures subjected to concentrated boundary conditions. The non-requirement of domain mesh by the BEM enables high accuracy in the domain fields assessment in addition to less complex remeshing procedures during crack propagation. However, concentrated boundary conditions often occur in fracture mechanics. The Lagrangian version of the BEM enforces such boundary conditions approximately by small length elements, which lead to numerical instabilities or even inaccurate problem representation. This study proposes a formulation for representing properly concentrated boundary conditions within the Lagrangian BEM framework. Nonlinear fracture mechanics describes the material failure processes herein. The classical cohesive crack approach governs the nonlinear energy dissipation processes, in which constant and tangent operators solve the resulting nonlinear system. Three applications demonstrate the accuracy of the proposed formulation, in which the BEM responses are compared against numerical and experimental results available in the literature.

Dipole‐based BEM formulation for three‐dimensional cohesive crack propagation modelling

“…It is important to mention that NLFM and cohesive crack growth modelling have not been explored totally in the three dimensional case within BEM, [52][53][54] which inspired the developments proposed herein. Rocha and Leonel 52 analysed the three-dimensional cohesive crack propagation using the subregion BEM technique whereas Chaves et al 53,54 used the continuum strong discontinuity approach (CSDA) for the same purpose. It is worth citing that [52][53][54] assumed predefined crack paths based on experimental responses.…”

“…Rocha and Leonel 52 analysed the three-dimensional cohesive crack propagation using the subregion BEM technique whereas Chaves et al 53,54 used the continuum strong discontinuity approach (CSDA) for the same purpose. It is worth citing that [52][53][54] assumed predefined crack paths based on experimental responses. Differently, the DBEM and the herein proposed dipole-based formulation enables the cohesive crack propagation modelling, in which the crack surfaces geometry evolves as a function of loading and stresses values, i.e.…”