VM253

VM253
Gurson Hydrostatic Tension Benchmark - 3D Analysis

Overview

Reference:

N. Aravas, "On the Numerical Integration of a Class of Pressure Dependent Plasticity Models", International Journal for Numerical Methods in Engineering, Vol. 24, pp. 1395-1416, Section 5.2, Figure 7 (1987).

Analysis Type(s):

Static analysis (ANTYPE = 0)

Element Type(s):

3D 8-Node Structural Solid Elements (SOLID185)

3D 20-Node Structural Solid Elements (SOLID186)

Input Listing:

vm253.dat

Test Case

The model is a three dimensional bin with all sides equal to unity. An applied displacement of 0.15" is applied at the nodes corresponding to x = 1, y =1, and z =1. To prevent rigid body motion, the model is constrained in the x direction at x = 0, y-direction at y = 0, and z-direction at z = 0.

Figure 430: Representative Finite Element Model

Material Properties

Gurson Material Model

Elastic Material Model

E = 1000000 lb/in²

ν = 0.30

Geometric Properties

L = H = W = 1"

q₁ = 1.5

q₂ = 1.0

q₃ = q₁²

ε_n = 0.3

f_o = 0.04

f_n = 0.04

s_n = 0.1

ε_n = 0.3

σ_y = E/300.0

n = 0.1

Loading

U_app = 0.15" @ x = 1"

U_app = 0.15" @ y = 1"

U_app = 0.15" @ z = 1"

U_x = 0 @ x = 0"

U_y = 0 @ y = 0"

U_z = 0 @ z = 0"

Analysis Assumptions and Modeling Notes

A 3D analysis is performed with both SOLID185 and SOLID186 elements. Two material models are introduced into the model, an elastic and Gurson model. The elastic model is based upon a power law and is presented for hardening purposes. The coefficients for input were taken from the reference provided.

Due to the nonlinear behavior and complexity of the problem, it is suggested to first increase the number of substeps within the solution module until convergence is reached or perform mesh refinement. Within the provided input listing, the hydrostatic pressure data is gathered for a specified node and plotted against the volumetric strain.

Graphical Results Comparison

Figure 431: Material Behavior of Specimen

Numerical Results Comparison

Volumetric Strain	Target	Mechanical APDL	Ratio
Results using SOLID185
0.10	1.62	1.6204	1.0002
0.24	1.00	1.0096	1.0096
0.40	0.62	0.6207	1.0012
Results using SOLID186
0.10	1.62	1.6204	1.0002
0.24	1.00	1.0096	1.0096
0.40	0.62	0.6207	1.0012