A symmetric over-nonlocal microplane model M4 for fracture in concrete

This paper analyzes the effectiveness of a nonlocal integral-type formulation of a constitutive law such as microplane model M4 in which the yield limits soften as a function of the total strain for prediction of fracture propagation. For a correct regularization of the mathematical problems caused by the softening behavior, an ‘‘over-nonlocal’’ generalization of the type proposed by Vermeer and Brinkgreve [Vermeer, P.A., Brinkgreve, R.B.J., 1994. A new effective non-local strain measure for softening plasticity. In: Chambon, R., Desrues, J., Vardoulakis, I. (Eds.), Localization and Bifurcation Theory for Soil and Rocks, Balkema, Rotterdam, pp. 89–100.] is adopted. Moreover, the symmetric weight function, proposed by Borino et al. [Borino, G. Failla, B., Parrinello, F., 2003. A symmetric nonlocal damage theory. International Journal of Solids and Structure 40, 3621–3645.] for damage mechanics, is introduced for the calculation of the nonlocal averaging of the total strain upon which the yield limits depend. The capability of the proposed model for reproducing the stress and strain fields in the vicinity of a notch is also investigated. Finally, the symmetric over-nonlocal generalization of microplane model M4 has been applied for the simulation of a mixed-mode fracture test such as the four-point-shear test and the test of axial tension at constant shear force [Nooru-Mohamend, M.B., 1992. Mixed-mode fracture of concrete: an experimental approach. Doctoral Thesis Delft University of Thechnology, Delft, The Netherlands.]