7.5. Step 5. Specify Solution-Control Parameters and Solve

Curve-fitting uses a nonlinear regression process or optionally a generic algorithm method. Your error norms can be either normalized or non-normalized. Normalized error norms (the default regression option) generally give better results than the non-normalized error norms, since normalized error gives equal weight to all of your data points.

The solution-control parameters of a nonlinear regression include:

  • Number of iterations

  • Residual tolerance

  • Coefficient change tolerance

The solution stops when both the residual tolerance and the coefficient change tolerance of your error norm are met, or if the number of iterations criteria is met. When using nonlinear regression, you must initialize your coefficients to appropriate values.

For the generic algorithm methods, also specify the lower and upper bounds of each coefficient.

The following topics are available for specifying solution-control parameters:

7.5.1. Syntax and Arguments for Specifying Solution-Control Parameters

TBFT,SOLVE,MATID,Option1,Option2,Option3,Option4, ..., Option7  ! set control parameters and solve

where:

MATID = Material reference ID number
Option1 = Category – AML
Option2 = Model name. See Table 7.4: Valid Material Models for Hyperelastic Parameter-Fitting for the models available.
Option3 = Order or number of your coefficients. See Table 7.4: Valid Material Models for Hyperelastic Parameter-Fitting for possible values.
Option4 = Curve-fitting procedure: 0 = non-normalized least squares, 1 = normalized least squares
Option5 = Maximum number of iterations
Option6 = Tolerance of residual changes
Option7 = Tolerance of coefficient changes

By default, the program uses the Levenberg-Marquardt algorithm, a nonlinear regression process, to perform the optimization process. The algorithm is a nonlinear optimization procedure that uses a combination of Gauss-Newton and gradient-descent algorithms to step through the optimization process. The generic algorithm is also available for performing the optimization.

To change solver parameters:

TBFT,SET,MATID,AML,GENR,Option3,Parname,Parval

where:

MATID = Material reference ID number
Option3 = The specified name for your curve-fitting model.
Parname = Solver parameter name (ALGO or IPOP).
Parval = Value of the solver parameter.

When Parname = ALGO, the solver algorithm changes from the default nonlinear regression process (keyword DEFA in the Parval position) to generic algorithms (keyword GA in the Parval position). When using generic algorithms, define initial population size and bounds for each parameter; bounds must have a nonzero range of values (where the maximum and minimum values cannot be equal).

To define parameter bounds:

TBFT,BNDS,MATID,AML,GENR,Option3,PARINDEX,LBNDS,UBNDS

where:

MATID = Material reference ID number
Option3 = The specified name for your curve-fitting model.
PARINDEX = Parameter index.
LBNDS = Lower value of the parameter bounds.
UBNDS = Upper value of the parameter bounds.

Define initial population via Parname = IPOP and Parval = an integer value (typically 100 to 300).

To obtain a more accurate solution, use a generic algorithm (GA) followed by the default nonlinear regression option solution.

Other solution parameters are also available (TBFT).

7.5.2. Multistep Custom Solution for Plasticity

Complex plasticity models can involve 10 to 30 or even more parameters, depending on the models selected and their order. It is not possible to capture all behaviors in a single solve operation. You can, however, use a multistep solution approach for such models.

You can input multiple sets of experimental data to solve for various plasticity behaviors. Example 3 shows how to assign attributes to various experimental data and perform the multistep solve.

Initiate up to three internal solve operations (TBFT,PSOLVE) as needed: one for simple time-independent plasticity, one for time-dependent plasticity, and one for static recovery:

TBFT,PSOLVE,MATID,AML,GENR,Option3,Option4, ..., Option7

where:

MATID = Material reference ID number
Option3 = The specified name for your curve-fitting model.
Option4 = Error norm: 0 (non-normalized) or 1 (normalized) (default).
Option5 = Maximum number of iterations.
Option6 = Tolerance of residual changes.
Option7 = Tolerance of coefficient changes.

Other solution parameters are also available (TBFT).