LAW92 describes the Arruda-Boyce material model, which can be used to model
hyperelastic behavior. This model is based on the statistical mechanics of a material with a
cubic representative volume element containing eight chains along the diagonal directions.
It assumes that the chain molecules are located on the average along the diagonals of
the cubic in principal stretch space.
Material Parameters
The strain energy density function is:
The material constant, are:
First strain invariant
principal engineering stretch
A material with LAW92 can be defined in two different ways:
Parameter Input
Shear modulus, bulk modulus and strain stretch ()
Where, only the above 3
parameters with clear physical meaning are necessary to define the
material.
is shear modulus at zero
strain.
Where,
Bulk coefficient at zero strain
Defines the limit of stretch
Also called locking stretch. It specifies the
beginning of the hardening phase in tension (locking strain
in tension). Default = 7.0.
Figure 1. Locking Stretch
In parametric input, Poisson’s ratio is computed as:
Function Input
Poisson ratio and Itype must be
defined. Itype defines which type of engineering
stress strain test data that is being used as input.Figure 2. Itype = 1: Uniaxial data test Figure 3. Itype = 2: Equibiaxial data test Figure 4. Itype = 3: Planar data test
Poisson's Ratio and Material Incompressibility
If function input is defined, parameters are ignored and Radioss
will calculate the material constant by fitting the input function. A nonlinear
least squares algorithm is used to fit the Arruda-Boyce parameters by Radioss. The curve fitting is performed using the assumption
that Poisson’s value is close to 0.5, which means the material is incompressible.
Similar to the other hyperelastic material models, Poisson ratio values closer to
0.5 result in high bulk modulus and a lower timestep. For a good balance between
incompressibility and a reasonable timestep, a Poisson’s ratio value of 0.495 is
recommended.
The material fitting information can be found in the Starter output file
(*0000.out). Figure 5. LAW92 function example
The fitting error and fitted material parameters are printed in the Starter output
file.Figure 6.
Viscous (Rate) Effects
/VISC/PRONY must be used with LAW92 to include viscous
effects.
References
1 Arruda, E. M.
and Boyce, M. C., 1993, “A three-dimensional model for the large stretch behavior of
rubber elastic materials”, J. Mech. Phys. Solids, 41(2), pp. 389–412