VM56

VM56
Hyperelastic Thick Cylinder Under Internal Pressure

Overview

Reference:

J. T. Oden, Finite Elements of Nonlinear Continua, McGraw-Hill Book Co., Inc., New York, NY, 1972, pp. 325-331.

Analysis Type(s):

Static, Large Deflection Analysis (ANTYPE = 0)

Element Type(s):

2D 8-Node Stuctural Solid Elements (PLANE183)

3D 8-Node Structural Solid Elements (SOLID185)

3D 10-Node Tetrahedral Structural Solid Elements (SOLID186)

Input Listing:

vm56.dat

Test Case

An infinitely long cylinder is made of Mooney-Rivlin type material. An internal pressure of P_i is applied. Find the radial displacement at the inner radius and the radial stress at radius R = 8.16 in (center of 1st element).

Figure 79: Hyperelastic Thick Cylinder Problem Sketch

Figure 80: Hyperelastic Thick Cylinder Models

Material Properties

Geometric Properties

Mooney-Rivlin material coefficients

A = 80 psi

B = 20 psi

r_i = 7.0 in

r_o = 18.625 in

P_i = 150 psi

Analysis Assumptions and Modeling Notes

The problem is solved first using PLANE183 and then using SOLID185 / SOLID186. Due to circumferential symmetry, only a small sector need be modeled. The height (and width for SOLID185) of the elements in the finite element model is chosen such that the elements have a reasonable aspect ratio. Only radial degrees of freedom are active. The total pressure is applied in two load increments. To approximate incompressible behavior, Poisson's ratio is set close to 1/2 (0.49) and reduced integration is requested. Temperature-dependent properties are used in the PLANE183 portion solely for verification purposes.

Results Comparison

		Target[1]	Mechanical APDL	Ratio
PLANE183	u_r (inner radius), in	7.180	7.491	1.043
PLANE183	Stress_r (element 1), psi	-122.0	-122.772	1.006
SOLID185	u_r (inner radius), in	7.180	7.491	1.043
SOLID185	Stress_r (element 1), psi	-122.0	-126.471	1.037
SOLID186	u_r (inner radius), in	7.180	7.433	1.035

Based on fully incompressible assumption, ν = 1/2