Constitutive modelling of elastomers using the finite element method
Author(s)
Hogan., John
Type
Thesis
Abstract
This thesis presents a new approach to incorporate an important class of constitutive models into finite element software. A method to implement non-Gaussian network models is proposed which involves the exact determination of the inverse Langevin function and its derivative. Non-Gaussian models describe the general deformation behaviour of elastomers correctly using only two material parameters and so offer a distinct advantage over other constitutive theories for these materials. Despite this they have not been widely used in the finite element analysis of elastomeric components because traditional methods of implementation rely on a series approximation for the inverse Langevin function. In the new approach a simple iterative procedure is employed to determine the exact value of the inverse Langevin function. This in turn allows exact expressions for the principal stresses and principal components of the tangent modulus to be derived. These quantities are then transformed to the base directions of the active coordinate system. Using this approach two of the most well known non-Gaussian network models, the three chain model of James and Guth and the eight chain model of Arruda and Boyce have been implemented in the FE code ABAQUS using the user defined material subroutine facility known as UMAT. UMAT routines have been developed to analyse plane stress, plane strain, axisymmetric and three-dimensional problems. To enhance the ability of the non-Gaussian network models to describe the mechanical behaviour of filled elastomers, time dependent effects are introduced into the constitutive formulations by employing a theoretical framework for finite strain viscoelasticity. Strain softening effects are also introduced, using continuum damage mechanics. The ability of these modified network models to reproduce the mechanical behaviour of filled elastomers is determined by comparison with a series of experiments conducted on neoprene and polyurethane.
Version
Open Access
Date Awarded
2000
Advisor
O’Dowd, Dr Noel
Dear
Sponsor
Engineering and Physical Sciences Research Council; The Minnesota Mining and Manufacturing Company.
Publisher Department
Department of Mechanical Engineering
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)