Elastic-Brittle Fraction Model for Robust Post-Peak Analysis of Masonry Structures

Abstract

The paper presents a model that splits the material cross section into a number of parallel fractions each of them having a different elastic-perfectly brittle characteristic. The idea is that the summation of all parallel fractions provides an approximation of the overall continuum softening curve. Softening is interpreted as a gradual reduction of the cross-sectional area, which it actually is from a physical point of view. Disorder and heterogeneity are introduced by assigning the fractions i different values of Young’s modulus Ei , strength fi and area Ai such that the overall fracture energy is consumed properly. The model blends well with a scaled sequentially linear solution procedure at global level tracing structural failure via successive snapping/cracking of critical fractions. Examples are included for tension, compression, combined tension-shear and combined tension-compression. The tension-shear case shows the ability of the model to capture a gradually shifting crack orientation. Preliminary structural examples are included in this paper and further results will be presented at the conference. These relate to push-over analysis of Groningen masonry building stock subjected to man-induced earthquakes from gas depletion, a currently serious problem in The Netherlands. The results show an increased robustness and stability of the post-peak response as compared to conventional incremental-iterative procedures.