VM201

VM201
Rubber Cylinder Pressed Between Two Plates

Overview

Reference:

T. Tussman, K-J Bathe, "A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis", Computers and Structures, Vol. 26 Nos 1/2, 1987, pp. 357-409.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D 4-Node Structural Solid Elements (PLANE182)

3D 8-Node Structural Solid Elements (SOLID185)

2D Target Segment Element (TARGE169)

3D Target Segment Element (TARGE170)

2D/3D Node-to-Surface Contact Elements (CONTA175)

Meshing Facet (MESH200)

Input Listing:

vm201.dat

Test Case

A long rubber cylinder is pressed between two rigid plates using a maximum imposed displacement of δ_max. Determine the force-deflection response.

Figure 312: Rubber Cylinder Problem Sketch

Material Properties

Geometric Properties

Mooney-Rivlin Constants

C1 = 0.293 MPa

C2 = 0.177 MPa

r = 200 mm

δ_max = 200 mm

Analysis Assumptions and Modeling Notes

A plane strain solution is assumed based on the geometry of the problem. Due to geometric and loading symmetry, the analysis can be performed using one quarter of the cross section. All nodes on the left edge (X = 0) are constrained, UX = 0. All nodes on the top edge (y = 0) are coupled in UY. An imposed displacement of -0.1 m acts upon the coupled nodes.

This problem was solved in several ways:

A 2D model using PLANE182 with CONTA175 elements
A 3D model using SOLID185 with CONTA175 elements
A 2D model using PLANE182 with CONTA175 element and solved using the Lagrange Multiplier method.
A 3D model using SOLID185 with CONTA175 element and solved using the Pure Lagrange Multiplier method.

In the 3D case, a MESH200 element is used as the target face for the automatic generation of contact elements. The target surface is given a high contact stiffness (KN = 2000 MPa) to model a rigid surface and no contact stiffness is required to be specified while performing the solution using Lagrange Multipliers method.

Results Comparison

	Target[1]	Mechanical APDL	Ratio
PLANE182 with 2D CONTA175
Force at Displacement = 0.1 (N)	250.00	266.05	1.064
Force at Displacement = 0.2 (N)	1400.00	1397.06	0.998
SOLID185 with 3D CONTA175
Force at Displacement = 0.1 (N)	250.00	266.33	1.065
Force at Displacement = 0.2 (N)	1400.00	1398.79	0.999
PLANE182 with 2D CONTA175 with KEYOPT (2) = 3
Force at Displacement = 0.1 (N)	250.00	266.20	1.065
Force at Displacement = 0.2 (N)	1400.00	1400.42	1.000
SOLID185 with 3D CONTA175 with KEYOPT (2) = 4
Force at Displacement = 0.1 (N)	250.00	266.40	1.066
Force at Displacement = 0.2 (N)	1400.00	1400.48	1.000

Determined from graphical results. See T. Tussman, K-J Bathe, "A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis", pg. 385, fig. 6.14.

Figure 313: Displaced Shape

Figure 314: Force vs. Displacement