Description: |
The use of the discrete crack approach and Nonlinear Fracture Mechanics opened the possibility of accurately modelling fracture behaviour of quasi-brittle materials, such as concrete, mortar and masonry. In this approach, it is assumed that microcracking localises into a surface of discontinuity, designated fictitious crack. Traditionally, the discontinuities are modelled by interface elements within the scope of the finite element method. In this case, some numerical problems exist related to the fact that the discontinuities must evolve along the finite element boundaries, although the crack path is not usually known in advance. More recently, the possibility of embedding strong discontinuities in finite elements overcame these difficulties. In general, in these formulations constant strain triangles are used and constant jumps ar and, as a consequence, both the discontinuity jumps and the tractions are discontinuous across element boundaries. In this work, two variationally consistent innovative strong embedded< discontinuity formulations are introduced: i) the Discrete Strong Discontinuity Approach (DSDA); and ii) the Generalised Strong Discontinuity Approach (GSDA). Their main characteristics are: i) non-homogeneous jumps are introduced in each parent element using the shape functions of an interface element in the parent element; ii) additional edge nodes are global nodes and, since they are shared by two elements at a common boundary, iii) continuous jumps and tractions across interelement boundaries are automatically obtained; and iv) no stress locking is found. In the DSDA the discontinuity jumps are transmitted by means of a rigid body motion, whereas in the GSDA stretching is also included. Several benchmark tests concerning mode-I, mixed mode and mode-II fracture are computed and the numerical results are compared to the corresponding experimental results. It is emphasised that all numerical results are similar to the available experimental data, even with coarse meshes. As a final result of this work, an efficient and robust numerical tool has been introduced for modelling fracture behaviour of quasi-brittle materials, which is already being applied so several ongoing projects.
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