Vertex Effect and Confinement of Fracturing Concrete Via Microplane Model M4

A newly developed powerful version of microplane model, labeled model M4, is used to study two basic phenomena in fracturing concrete: the vertex effect, i.e., the tangential stiffness for loading increments to the side of previous radial loading path in the stress space, and the effect of confinement by a steel tube or a spiral on the suppression of softening response of columns. Comparisons with the tests show the microplane model to predict the initial torsional stiffness very closely, while the classical tensorial models with invariants overpredict this stiffness several times. In the tests performed recently, steel tubes of different thicknesses filled by concrete are squashed to about half of their initial length and very large strains with shear angles up to about 70 degree are achieved. Observations and conclusions from the investigations are provided.