1. APPLICATION OF THE GENERAL ALGORITHM FOR 3-D DEFORMATION OF THE GURSON ELASTIC-PLASTIC MATERIAL TO SMALL AND LARGE STRAIN SHELL CONDITIONS MILOS KOJIC, Ph. D., Professor, Faculty of Mechanical Engineering, University of Kragujevac Senior Research Scientist, Harvard University IVO VLASTELICA, Ph. D., Professor, High Technical School, Cacak MIROSLAV ZIVKOVIC, Ph. D., Associate Professor, Faculty of Mechanical Engineering, University of Kragujevac Ulica Sestre Janjic, Kragujevac, Serbia

2. IMLICIT STRESS INTEGRATION FOR METAL PLASTICITY MODELS. 1
IMLICIT STRESS INTEGRATION FOR METAL PLASTICITY MODELS Von Mises Model Gurson Model

3. Von Mises Model
Yield condition
Stress integration

4. Gurson Model
Yield condition

5. Rate of change of porosity

6. SHELL CONDITIONS
Geometry and basic kinematics of shell finite element

7. STRESS INTEGRATION PROCEDURE Increments of plastic strains and porosity

8. Basic equations to be satisfied at end of time step Equivalence of plastic work Yield condition

9. Deviatoric stresses and porosity at end of time step

10. Plasticity calculations,
Initial values
Trial elastic state If
Plasticity calculations
a) Iteration on
b) Iteration on
Equation (25)
Next time step
Update the variables and go to step 1
Table 1 Computational steps for stress integration

11. CONSISTENT TANGENT ELASTIC-PLASTIC MATRIX

12. EXTENSION TO LARGE STRAINS

13. EXAMPLES 1. Necking of a thin sheet

15. 2. Plactic bulding of a circular plate under pressure
R=24 mm, =1.00 mm
E=68 Gpa ,
, =0.3, q1=q3=1.5; q2=1; fo=0.002

17. 3. Tension of plate with hole
E=201 GPa; n=0.3
q1=q3=1.5; q2=1; f0=0.002
L=120 mm B= 20 mm d=10 mm

19. CONCLUSIONS
AN IMPLICIT STRESS INTEGRATION PROCEDURE, BASED ON THE GOVERNING PARAMETER METHOD (GPM), IS DEVELOPED FOR GURSON MATERIAL MODEL
EXTENSION TO LARGE STRAIN CONDITIONS IS PRESENTED
THE PROCEDURE IS IMPLEMENTED INTO FE PROGRAM PAK, IN SHELL FINITE ELEMENTS.
THE PROCEDURE AND THE DEVELOPED SOFTWARE ARE SUITABLE FOR GENERAL ENGINEERING APPLICATIONS.