Constant Rate Damage Model Reference

The Constant Rate Damage model emulates the breaking of bonds in brittle fracture growth. It can also be used to predict bond strengths.

This model has applications such as:

Oil and gas drilling, where the rock surface is represented by particle clumps and repeated passes of the drill cause cumulative damage.
Pharmaceutical tablet manufacture, where tablets are formed from compressed powder and the strength of internal bonds, predicting breakage resistance, can be predicted from force and time of compression.
Mowing and harvesting, and bulk properties of polymers, where breakable fibers are represented by Flexible Fiber particles in conjunction with the Constant Rate Damage model.

If neither Constant Rate Damage nor Simple Failure is selected, the bonds between particles are treated as unbreakable.


Theory	See Constant Rate Damage.
Provided By	[physics continuum] > Models > Multiphase Interaction > Phase Interactions > Phase Interaction [n] > Models > Optional Models
Example Node Path	Continua > Physics 1 > Models > Multiphase Interaction > Phase Interactions > Phase Interaction 1 > Models > Constant Damage Rate
Requires	Under Lagrangian Multiphase, select Particle Type: DEM Particles Under Multiphase Interaction: Select Phase Interaction Topology: DEM Phase Interaction if it has not been automatically selected. Set the First Phase and Second Phase properties of DEM Phase Interaction to DEM Lagrangian phases. Select Optional Models: Hertz Mindlin, Walton Braun, or Linear Spring Optional Models Parallel Bonds or Bonded Particles are not required if the Flexible Fiber model is selected under Lagrangian Phase Models.
Properties	Key properties are: Softening Rate. See Constant Rate Damage Model Properties.
Activates	Model Controls (child nodes)	Bond Strength, Initial Damage
	Field Functions	Bond Damage, Bond Tensile Strength. See Discrete Element Method Field Function Reference.

This model represents damage to bonds on a scale from 0 (undamaged) to 1 (broken). The amount of energy needed to break a bond is proportional to a dimensionless scalar, the softening rate, $k_{r}$ in Eqn. (3296).

Constant Rate Damage Model Properties

Softening Rate: The higher the value, the more work (energy) needed to completely break the bonds, or equivalently, the more strain for a given bond strength. The rate is a dimensionless scalar, $k_{r}$ in Eqn. (3296). Set the value higher than 1 to achieve stability. The default value is 2.

Bond Strength

Specifies the method for assigning and updating maximum tensile strength for the bond. An undamaged bond begins to fail if tensile stress $δ_{m}$ exceeds $δ_{max}$ in Eqn. (3292).

Method: No Failure (unbreakable bonds, the default) and the standard methods for a scalar profile are available for this value.
Dimensions: The dimensions of $δ_{max}$ , Stress. (Read only.)
Update option: When set to Initialize only, the maximum tensile stress $δ_{max}$ is defined when two particles form a bond and remains the same as long as the bond lasts. When Initialize and update is activated, $δ_{max}$ is updated every sub-step according to the profile selected under Method.

Initial Damage

Specifies the method by which the initial bond damage is calculated. The standard methods for a scalar profile and Weibull distributed are available for this value. Weibull distributed assigns a strength to each bond, selected from a normal distribution with mean (Lambda, default value 0.5), standard deviation (k, default value 1), and upper and lower limits selected by the user. The default range is [0, 1], and values outside that range are changed to the nearer of 0 or 1.