ABSTRACT
Here, C is calculated C = FTF and F is the deformation gradient tensor.
In this study, the strain energy function W was represented as an isotropic component for the matrix rubber, and the anisotropic component for the reinforcing fibers was as follows:
isoW ani( ) ( , ) ( )aW+ M (2)
The following Mooney-Rivlin model was introduced for the isotropic component of FRR,
W c piso 1 1 2 2c( )I 3 ( )3I ( )J − 1 (3)
where c1 and c2 are material constants, and p is hydrostatic pressure. J is calculated as J = det(F). I1 and I2 are the first and second invariants of the volume-preserved right Cauchy-Green deformation tensor C :
C C32 / (4)
and,
I I of f J
( ) : ( ) ( ) : ) :
/ C I CJ I C CCo I (5)
For the anisotropic component, the following functions were introduced:
W W
( , , ) ( , ) ( , )
( ) M W M
M+ (6)
1 INTRODUCTION
Fiber-Reinforced Rubber (FRR) is a material in which the stiffness of rubber is enhanced by fibers. This material is used in components such as V-packing and O-rings. Its mechanical properties are complicated because of the uncompressible properties of matrix rubber and the anisotropic properties of the reinforcing fibers. Also, it is necessary to consider permanent set and stress softening properties because FRR undergoes cyclic deformation.
