In the past century, in many industries, such as, metal forming industry, it has been important to predict ductile damage and fracture of metals under complex loadings. Regarding damage mechanics, one of the most classical models is the GTN, which was originated from Gurson and later enhanced by Tvergaard and Needleman. The inprovement was achieved by introducing an equivalent void volume fraction f and two more parameters called q 1 and q 2 into the yield function of Gurson’s model.

In the past century, in many industries, such as, metal forming industry, it has been important to predict ductile damage and fracture of metals under complex loadings. Regarding damage mechanics, one of the most classical models is the GTN, which was originated from Gurson and later enhanced by Tvergaard and Needleman. The inprovement was achieved by introducing an equivalent void volume fraction f and two more parameters called q 1 and q 2 into the yield function of Gurson’s model.