Vertex effect and confinement of fracturing concrete via microplane model M4

A newly developed powerful version of microplane model, labeled model M4, is exploited to study two basic phenomena in fracturing concrete: (a) The vertex effect, i.e., the tangential stiffness for loading increments to the side of a previous radial loading path in the stress space, and (b) the effect of confinement by a steel tube or a spiral on the suppression of softening response of columns. In the former problem, the microplane model is used to simulate the torsional response of concrete cylinders after uniaxial compression preloading to the peak compression load or to a post-peak softening state. Comparisons with new tests carried out at Northwestern University 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 plasticity of metals, this phenomenon is called the 'vertex effect' because its tensorial modeling requires the yield surface to have a vertex, or corner, at the current state point of the stress space). In the latter problem, microplane model simulations of the so-called 'tube squash' tests are presented and analyzed. In these tests, recently performed at Northwestern University, 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 degrees are achieved. The tests and their simulations show that, in order to prevent softening (and thus brittle failure and size effect), the cross section of the tube must be at least 16% of the total cross section area, and the volume of the spiral must be at least 14% of the volume of the column. When these conditions are not met, which comprises the typical contemporary designs, one must expect localization of damage and size effect to take place.