Modelling crack propagation in concrete structures with a two scale approach

Abstract

SUMMARYA simplified computational technique based on a refined global-local method is applied to the failure analysis of concrete structures. The technique distinguishes the scale of the structure, modelled with large size finite elements, from the scale at which material non-linearity occurs due to progressive cracking and macro-crack propagation. The finite element solution is split into two parts: a linear elastic analysis on a coarse mesh over the entire structure and a non-linear analysis over a small part of the structure where a dense finite element grid is employed. In the non-linear calculation, a non-local damage model is implemented. These two computations are coupled with the help of an iterative scheme. The size and location of the region where a non-linear analysis is performed, is adapted to follow the development of the damage zone. Numerical examples of mode I fracture of concrete specimens with straight and curved cracks are presented.

Bridging multi-scale approach to consider the effects of local deformations in the analysis of thin-walled members

“…From Eq. (18), by decomposing the shell displacement vector into boundary and internal displacement vectors, one obtains (19) The stiffness matrixK of the shell model in Eq. (8), is partitioned such that specified boundary displacements are multiplied with sub-matrixK T b .…”

“…In Eq. (19), δf s is the vector of variations in specified external loads that falls into the multiscale analysis domain and δf @i& j is the vector of variations in traction forces at the boundaries of the multi-scale analysis domain. Specified displacements and loads in Eq.…”

“…Common to these next generation numerical methods is that, the partition of unity concept is exploited to allow overlapping decomposition of the analysis domain so that a local enrichment can be incorporated seamlessly [15][16][17][18]. In various types of problem which naturally give rise to multiple scales in the deformation fields, such as crack propagation e.g., [19], or localized damage problems e.g., [20] multi-scale numerical analysis techniques have been effectively used. In particular the Bridging multi-scale method, which was originally developed to enrich the nodal values of the FEM solution with meshfree solution [21], provides a basis to couple problems based on two different physical assumptions.…”

Multi-scale overlapping domain decomposition to consider local effects in the analysis of pipes

“…In which naturally give rise to multiple scales in the deformation fields, such as crack propagation e.g. (Haidar et al, 2003;Mosler, 2005), or localized damage problems e.g. (Mosler, 2005) multi-scale numerical analysis techniques have been effectively used.…”

Multi-Scale Overlapping Domain Decomposition to Consider Elasto-Plastic Local Buckling Effects in the Analysis of Pipes

“…Common to these numerical methods is that the partition of unity concept is exploited to allow overlapping decompositions of the analysis domain so that a local enrichment can be seamlessly incorporated [18][19][20][21]. In various types of problems which naturally give rise to multiple scales in the deformation fields, such as crack propagation e.g., [22], or localized damage problems e.g., [23] multiscale numerical analysis techniques have been effectively used. In particular, the Bridging multi-scale method, which was originally developed to enrich the nodal values of the FEM solution with mesh-free solution [24], provides a basis to couple problems based on two different physical assumptions.…”