Some comments on the paper “Microplane constitutive model and metal plasticity” (Brocca M and Bažant ZP, 2000, Appl Mech Rev53(10) 265–281)

Abstract

First of all, here are some comments on the microplane model MP1. On the microplane level, the yield condition is given by the function (5.11) 1Display Formulaf(σ)=σD2+σL2+σM2−k2=0It should be stressed that, for obtaining a global yield condition from the local one, some global criterion independent of the chosen coordinate system must be used eg, Display Formulamaxn f(σ,n)=0or Display FormulaS+f(σ,n)ds(n)=c>0,where n is a normal to the unit sphere S, and S+ is the domain on S where Display Formulaf(σ)≥k2.Criterion (2) defines a surface (in the σ-space) of the first onset of global plasticity, criterion (3)—a surface of more extended plasticity. It is clear that, for k>0, the S+⊂S and S+ may never coincide with the full unit sphere.