<COEFFICIENT>#

Description#

Coefficient objects are used to enter the values for material coefficients. Each behavior object may have any number of coefficients to parameterize the models for different materials. The coefficients are themselves behavior objects however, and therefore have a standard format for entry. Coefficients also provide the means to add external parameter or local material variable dependencies.

Creating user-dependency on the internal variables may however significantly alter the material model, and invalidate integration methods. The only sure use for arbitrary dependencies on the integrated variables is with Runge-Kutta integration, and a time-dependent flow law. The tangent matrix may also be altered by these dependencies. Coefficients which are a function of the external parameters are however robustly implemented, and are valid for all integration methods.

Syntax#

Supposing that a material model coefficient \(C\) is required, a syntax similar to the following will be given:

C COEFFICIENT

where the term COEFFICIENT is to be replaced with a coefficient definition. The replacement syntax using the coefficient objects is given below:

C [ type ] parameters

CODE

DESCRIPTION

equivalence

coefficient which is the value of a variable

=

same as equivalence

function

coefficient which is a function of variables (see chapter Functions)

equivalence

coefficient which is the value of variables

step_wise

step-wise tabular values

default

tabular description in terms of variables

Example#

The first example is for a tabular coefficient. This example has an equivalent stress, sigeq, as a function of the cumulated flow, and the temperature. Note any number of variables may be given. If the parameter values are out of range from what is given in the table, and error will result.

sigeq epcum temperature
400.0  0.0    20.0
350.0   "    120.0
290.0   "    200.0
450.0  0.002  20.0
410.0   "    120.0.
330.0   "    200.0
500.0  0.01   20.0
460.0   "    120.0
400.0   "    200.0

The second example uses functions to describe the coefficient value. Function syntax is described more fully in the Functions chapter. Note parameter names must be on the same line as the function declaration.

young function 230. + 1.e-2*temperature + temperature^2.0;

The last example assumes a parameter is calculated in the material law called Bpa1v. This example will set the coefficient value to the value of that parameter at all times.

*kinematic nonlinear
    A1  40.0
    Bp  = Bpa1v