A compressible approach in finite element analysis of rubber-elastic materials

The need for a methodology to determine the stiffness characteristics of elastomeric seals with complex geometry has prompted an investigation using a commercially available finite element code. Axial and radial compression of O-rings, as well as the influence of restraining grooves and friction, are investigated. Axisymmetric analyses are performed, and their results are compared with those obtained by other researchers who assumed plane strain conditions. The differences in the results of the axisymmetric and plane strain loading conditions increase with the level of compression, except for one loading case. The method of reduced integration is shown to effectively handle the problem of high localized hydrostatic stresses, which are especially enhanced in confined geometries, and to provide accurate results. Stiffness characteristics of O-ring seals having a range of geometric and material properties are given in a nondimensional form. This form allows for general modeling of the O-ring stiffness as a f...

Analysis of Elastomeric O-Ring Seals in Compression Using the Finite Element Method

Topology optimization and internal resonances in transverse vibrations of hyperelastic plates

This paper gives a bibliographical review of the finite-element methods (FEMs) applied to the analysis and simulation of rubber and rubber-like materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1976-1997. The following topics are included: incompressible elasticity problems in general, mechanical and material properties, a finite-element library for incompressible materials, contact problems, fracture mechanics, machine elements/structures, material processing and other topics.

http://iopscience.iop.org/article/10.1088/0965-0393/6/2/007/pdf

Rubber and rubber-like materials, finite-element analyses and simulations: a bibliography (1976-1997)

With advances in technology, hyperelastic materials are seeing increased use in varied applications ranging from microfluidic pumps, artificial muscles to deformable robots. They have also been proposed as materials of choice in the construction of components undergoing dynamic excitation such as the wings of a micro-unmanned aerial vehicle or the body of a serpentine robot. Since the strain energy potentials of various hyperelastic materials are more complex than quadratic, exploration of their nonlinear dynamic response lends itself to some interesting consequences. In this work, a structure made of a Mooney-Rivlin hyperelastic material and undergoing planar vibrations is considered. Since the stresses developed in a Mooney-Rivlin material are at least a quadratic function of strain, a possibility of 1:2 internal resonance is explored. A Finite Element Method (FEM) formulation implemented in Matlab is used to iteratively modify a base structure to get its first two natural frequencies close to the ratio 1:2. Once a topology of the structure is achieved, the linear modes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the hyperelastic structure can be used to develop a nonlinear two-mode model of the structure. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. It is shown that the strain energy potential for the Mooney-Rivlin material makes it possible for internal resonance to occur in such structures.Copyright © 2013 by ASME

Stephen Jordan

Papers

The integration of analysis and testing for the simulation of the response of hyperrelastic materials