Issue 29

A. Caporale et alii, Frattura ed Integrità Strutturale, 29 (2014) 19-27; DOI: 10.3221/IGF-ESIS.29.03 26 In Fig. 5, six failure curves are plotted: the black curves refer to , 0 v m f  whereas the turquoise curves refer to , 10 v m f  . Moreover, the solid curves are the failure curves in bi-axial compression; the dotted curves are the intersection of the failure surfaces with the plane  3 σ 0.01 e GPa, where 3 σ e is the third of the three coordinate axes of the stress space where the failure surface is plotted; the dashed curves are the intersection of the failure surfaces with the plane   3 σ 0.01 e GPa (for the dotted and dashed curves, the load direction is different from       T 1 2 ˆ ˆ 0 n ). As it is expected, the admissible domain bounded by the failure curve increases in presence of a negative 3 σ e (compression) and decreases in presence of a positive 3 σ e (traction). -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00  e 2  (GPa)  e  (GPa)    = 0.7, f v,m = 0, f v,eq = 40,  e 3 = 0  e 3    = 0.7, f v,m = 0, f v,eq = 40,  e 3 = 0.01 GPa    = 0.7, f v,m = 0, f v,eq = 40,  e 3 = - 0.01 GPa    = 0.8, f v,m = 10, f v,eq = 30,  e 3 = 0    = 0.8, f v,m = 10, f v,eq = 30,  e 3 = 0.01 GPa    = 0.8, f v,m = 10, f v,eq = 30,  e 3 = -0.01 GPa Figure 5 : Failure curves in bi-axial and tri-axial compression. C ONCLUSIONS n this work, a micromechanical model is used for estimating the failure curves of cement concrete in bi-axial and tri- axial compression. The concrete failure is due to the creation and evolution of voids in the cement paste. The void evolution decreases the tangent stiffness to the concrete stress-strain curve and the concrete compressive strength is attained when this tangent line becomes horizontal. This condition is used to determine the failure curves of concrete in bi-axial and tri-axial compression. Mori-Tanaka and Eshelby homogenization methods are used to determine the overall behavior of concrete. The micromechanical analyses show which values of the void evolution parameters represent better the concrete behavior. As a future development, micromechanical methods different from the Mori-Tanaka one will be used and different evolution laws of the voids will be considered in the attempt to capture better the multi-axial concrete behavior. A CKNOWLEDGMENTS his research was carried out in the framework of the DPC/ReLUIS 2014 – AQ DPC/ReLUIS 2014-2016 project (theme: reinforced concrete structures) funded by the Italian Department of Civil Protection. R EFERENCES [1] Bruno, D., Greco, F., Lonetti, P., Blasi, P.N., Sgambitterra, G., An investigation on microscopic and macroscopic stability phenomena of composite solids with periodic microstructure, International Journal of Solids and Structures, 47 (2010) 2806-24. I T