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, 34000 Kragujevac, Serbia

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

Von Mises Model Yield condition Stress integration

Gurson Model Yield condition

Rate of change of porosity

SHELL CONDITIONS Geometry and basic kinematics of shell finite element

STRESS INTEGRATION PROCEDURE Increments of plastic strains and porosity

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

Deviatoric stresses and porosity at end of time step

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

CONSISTENT TANGENT ELASTIC-PLASTIC MATRIX

EXTENSION TO LARGE STRAINS

EXAMPLES 1. Necking of a thin sheet

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

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

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.