Using Softening Laws

Some materials allow the use of softening laws. This section briefly lists the properties. Softening law properties are assigned within a material definition that uses the law:

Material (matid),(name),(type)
      . . .
   SofteningI (Law_Name or number)
   (Law properties)
      . . .
Done

where the SofteningI command selects a law (using the law name or number from the list below) and note that a softening material may have more than one softening law. The law selection is followed by commands to set any properties specific to that law. Available softening materials can use softening laws.

The following list has the available softening laws:

  1. Linear - Linear softening law
  2. Exponential - Exponential softening law
  3. CubicStep - Cubic function softening law
  4. DoubleExponential - a two-exponential softening law

All laws correspond to a monotonically decreasing function f(δ) with f(0) = 1 and f(δmax) = 0 where δmax is the maximum cracking strain. Click any one law above to see the softening function and the properties needed for that law.

More documentation on these softening laws is available on the OSUPDocs Wiki.

Linear Softening (number=1)

The linear softening law is f(δ) = 1 - δ/δmax. The input property is:

Note that you do not enter δmax. It is determined at run time because it is affected by particle volume, initiation stress, and crack orientation.

Exponential Softening (number=2)

The exponential softening law is f(δ) = exp(-kδ). The input properties are:

Note that you do not enter k. It is determined at run time because it is affected by particle volume, initiation stress, and crack orientation.

Cubic Function Softening (number=3)

This softening law is a cubic function that changes slope after initiation and then decays to failure. If the initial slope after failure is zero, it is a cubic step function given by f(δ) = 1 + (δ/δmax)2(2(δ/δmax)-3.). Other forms are explained on OSUPDocs Wiki. The input properties are:

Note that you do not enter δmax. It is determined at run time because it is affected by particle volume, initiation stress, and crack orientation. This law is similar to linear softening except has zero slope at both initiation and failure.

Two Exponential Softening Law (number=4)

This two-exponential softening law can model a peak and decay after initiation or just double exponential decay. Details of the function are explained on OSUPDocs Wiki. The input properties are: