Isotropic Hardening

Multi-linear Isotropic Hardening: (Default)

The multi-linear hardening is defined by a series of plastic strain/yield stress points.

Figure 1  The multi-linear point definitions

The points must have ascending values. In other words, for plastic strains  and yield stress , where i indicates the point number:

 and

There must be at least 2 points. The first plastic strain value  must be zero and the first yield stress  must be greater than zero.

RecurDyn treats the isotropic yield stress (nearly) constant after the multi-linear point. Specifically, RecurDyn treats the isotropic hardening modulus as 1 after the last point defined by the user in the multi-linear table above.

In other words, if the last point defined by the user is  and the yield stresses , it is equivalent to RecurDyn automatically defining a final point:

if , the yield stress for multi-linear hardening is defined as

where,  is the isotropic hardening modulus of the i^th isotropic hardening segment, which is defined as

•     Multi-linear table buttons:

•    Add: Add a new plastic strain / yield stress point to the end of the table.

•    Insert: Insert a new plastic strain / yield stress point into the table below the currently selected row.

•    Delete: Delete the currently selected row of the table.

•    Import: Import the data for the table from a text file. Note that the data current data loaded into the table will be discarded before importing a file.

•    Export: Export the table to a text file.

Bilinear Isotropic Hardening:

The bilinear isotropic hardening is defined by only 2 parameters:

•    Initial Yield Stress ()

•    Isotropic Hardening (): the isotropic hardening modulus

Figure 2  Bilinear input fields

The initial yield stress  and the isotropic hardening modulus must be greater than zero. The yield stress at any time is given by

For the bilinear isotropic hardening, set Nonlinear Hardening fields  and  equal to zero.

Nonlinear Isotropic Hardening:

Nonlinear isotropic hardening is defined by 4 parameters:

•    Initial Yield Stress ()

•    Isotropic Hardening () : the isotropic hardening modulus

•   

•   

Figure 3  Nonlinear input fields

The initial yield stress  and the nonlinear constants  and  must be greater than zero. The isotropic hardening modulus(Hi) must be greater than zero. The yield stress at any time is given by