Sequentiallylinearcontinuum modelforconcretefracture

A sequentially linear continuum model for concrete fracture is proposed. The model approxi- mates the tensile softening stress-strain curve as a saw-tooth diagram. After a linear analysis, the critical ele- ment, i.e. the element for which the stress is most close to the current peak in the saw-tooth diagram, is traced. Next, the stiffness of that element is reduced and the process is repeated. The sequence of critical states gov- erns the global force-displacement diagram. The elements with reduced stiffness reveal the cracked areas. In fact, the elements are removed in a stepwise manner. The definition of the envelope of the saw-tooth curve uses the notions of fracture energy, tensile strength and crack band width. A notched beam is analysed. Mesh- objectivity can be achieved by adapting both the strength peaks of the saw-tooth diagram as well as the ulti- mate strain of the diagram to the element dimensions. The potential of the model for large-scale fracture analysis is demonstrated. The very sharp snap-backs associated with brittle fracture of an unreinforced ma- sonry facade automatically come out with sequentially linear analysis, whereas nonlinear analysis of the fa- cade using smeared or discrete crack models show substantial difficulties despite the use of arc-length schemes. l INSPIRATION FOR THIS STUDY lead to cracking. The aim is to predict (post-peak) crack widths as this is the main damage process that 1.1 Settlement damage in large-scale masonry governs the risk. Fig. 1 shows the results for a dis- facade placement controlled smeared crack analysis and for an arc-length controlled discrete crack analysis, in The fracture model proposed in this paper was in- terms of the angular distortion, which is related to spired by practice-oriented research on settlement the magnitude of the settlement trough, versus the damage for masonry structures. Underneath the his- maximum crack width in the facade. Fig.