VM-WB-MECH-070

VM-WB-MECH-070
Hyperelastic Thick Cylinder Under Internal Pressure

Overview

Reference:	Oden, J. T. (1972). Finite Elements of Nonlinear Continua (pp. 325-331). New York, NY: McGraw-Hill Book Co., Inc.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Static, Large Deflection Analysis
Element Type(s):	2-D Structural Solid Elements

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. Use a global mesh size of 1 in along with a mapped face meshing.

Figure 93: Schematic

Material Properties

Geometric Properties

Mooney-Rivlin material coefficients:

C10 = 80 psi

C01 = 20 psi

D1 = 0 /psi

r_i = 7.0 in

r_o = 18.625 in

P_i = 150 psi

Analysis

Because of the loading conditions and the infinite length, this problem is solved as a plane strain problem. A one-fourth symmetry model is used. The total pressure is applied in two load increments 90 and 150 psi. Stress and Deformation are expressed in cylindrical coordinate system.

Results Comparison

Results	Target	Mechanical	Error (%)
Deformation at inner radius in radial direction, in	7.18	7.1819	0.026
Radial Stress at r = 8.16 in, psi	-122	-122	0