Removing Soft Elements for Increasing Performance (SOFT_DELETE)

The SOFT_DELETE option offers the possibility of removing soft elements based on different criteria.

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OPT_PARAM

During a topology optimization process, the given mass is distributed within the design area. At the end of the optimization, the resulting structure consists of hard (filled) and soft (void) elements. The soft elements have a negligible influence on the stiffness of the resulting structure but they are still relevant for the number of degrees of freedom of the structure.

In Tosca Structure, the SOFT_DELETE option offers the possibility of removing soft elements based on different criteria. The free nodes are also removed from the calculation model. The deleted elements are reactivated if required, in case that the force flow changes during the optimization. Mesh of a bending beam with hard (red) and soft (blue) elements (The elements in the holes have been deleted by SOFT_DELETE algorithm) is presented in the following figure.

Important:
  • SOFT_DELETE is turned on after the 5th iteration, and only if the relative change of the objective is less than a certain limit. This is done to prevent unstable configurations that might occur in the first iterations from remaining unchanged.
  • SOFT_DELETE can be used to stabilize geometrically nonlinear models where solver instabilities can occur due to degenerated or fully collapsed void elements.

SOFT_DELETE Based on Neighboring Elements

This option offers the possibility of removing soft elements which only have soft neighboring elements. To use this feature, an element group must be specified. If any of the elements enclosed in the sphere spanned by the <radius> has a relative density higher than the <threshold>, the element in origin will not be deleted. This method is activated as follows: 


OPT_PARAM
  ID_NAME              = optimization_control
  OPTIMIZE             = id_of_optimize
  ...
  SOFT_DELETE          = <element_group>, <radius>
  SOFT_DELETE_METHOD   = STANDARD ( AGGRESSIVE ), <threshold>
  ...
END_

For SOFT_DELETE_METHOD = STANDARD, removal of elements is done ensuring that there are no detached and floating elements caused by the soft delete. For SOFT_DELETE_METHOD = AGGRESSIVE, removal of elements is done based on the relative density without detachment checks. In this case, detached and floating elements can be caused by the soft delete.

Important:
  • Some solvers have problems dealing with such elements, but not the Abaqus solver.
  • Check of elements in <radius> will still be performed but this procedure is independent of detachment checks.
  • An optional threshold can be defined. Default threshold for SOFT_DELETE using STANDARD or AGGRESSIVE is 0.05.
  • For SOFT_DELETE_METHOD = STANDARD or AGGRESSIVE, the default value of the <radius> is the average element edge length of the model. If the <radius> is defined by the user, it is considered to be an absolute value. This means that the corresponding units should be taken into account. Changing the default value is only necessary if the sizes of mesh elements vary strongly.
  • Post-processing must be performed on the original (complete) model.
  • If it occurs that there is a group of hard elements separated from the rest of the material by layers of soft elements, these soft elements will not be removed by SOFT_DELETE for SOFT_DELETE_METHOD = STANDARD. This is done to prevent solvers from being started with inconsistent input files. In addition, some soft elements might remain if they connect hard elements that otherwise would be able to move with respect to each other (that is, those that have a common edge but not a common face).

SOFT_DELETE Based on Maximum Elemental Shear Strain

If the elements in the soft delete area are deleted based on the maximum elemental shear strain, the following must be defined:


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = MAX_SHEAR_STRAIN, <t_shear>
  SOFT_DELETE          = <element_group>
  .....
END_

Meaning if an individual element shear strain is larger than the threshold <t_shear> then the element is removed. Traditionally, the shear threshold <t_shear> for MAX_SHEAR_STRAIN is positive. The threshold value must be set by the user. Default settings are not available as the value strongly depends on different model parameters (material properties).

In the following example, the elements having an elemental shear strain larger than 0.80 should be removed considering all elements in the structure:


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = MAX_SHEAR_STRAIN, 0.80
  SOFT_DELETE          = ALL_ELEMENTS
  .....
END_

SOFT_DELETE Based on Minimum Elemental Principal Strain

If the elements in the soft delete area are deleted based on the minimum elemental principal strain, the following must be defined:


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = MIN_PRINCIPAL_STRAIN, <t_min_prin>
  SOFT_DELETE          = <element_group>
  .....
END_

Meaning if an individual element minimal principal strain is lower than the threshold <t_min_prin> then the element is removed.

Traditionally, the minimum principal threshold <t_min_prin> for MIN_PRINICIPAL_STRAIN is negative. The threshold value must be set by the user. Default settings are not available as the value strongly depends on different model parameters (material properties).

In the following example, the elements having an elemental minimal principal strain lower than -0.80 should be removed considering all elements in the structure:


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = MIN_PRINCIPAL_STRAIN, -0.80
  SOFT_DELETE          = ALL_ELEMENTS
  .....
END_

SOFT_DELETE Based on Maximum Plastic Strain

If the elements in soft delete are deleted based on the maximum equivalent plastic strain (Abaqus equivalent: PEEQ), the following must be defined in soft delete: 


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = PLASTICITY, <t_plastic>
  SOFT_DELETE          = <element_group>
  .....
END_

Meaning if the equivalent plastic strain in an individual element is higher than the threshold <t_plastic> then the element is removed.

Traditionally, the equivalent plastic strain threshold <t_plastic> is positive. The threshold value must be set by the user. Default settings are not available as the value strongly depends on different model parameters (material properties).

Important: This option can only be used for the elastic-plastic constitutive material law.

SOFT_DELETE Based on Relative Volume Compression

If the elements in soft delete are deleted based on the minimum relative deformed elemental volume, the following must be defined in soft delete: 


OPT_PARAM
  .....
  SOFT_DELETE_METHOD   = VOLUME_CHANGE, <t_rel_vol>
  SOFT_DELETE          = <element_group>
  .....
END_

If an individual relative deformed elemental volume

Vrel=Vdeform−VorgVorg

with Vorg =original elemental volume and Vdeform= elemental volume in deformed configuration is lower than the threshold <t_rel_vol> then the element is removed.

Traditionally, the relative deformed elemental volume threshold <t_rel_vol> for VOLUME_CHANGE is negative. The threshold value must be set by the user. Default settings are not available.

Important:
  • Often the elemental strains cannot be written as results for shell and membrane elements. Thus, the only option is to use VOLUME_CHANGE for SOFT_DELETE.
  • For examples with very large deformation, soft delete seems to be more stable using VOLUME_CHANGE instead of MAX_SHEAR_STRAIN and MIN_PRINCIPAL_STRAIN.
  • Normally, the strain measure used for the element removal depends on the element type.
  • Strain measure used for the element removal can depend upon the constitutive material modeling.
  • Finding a useful strain measure used for the element removal requires several optimization executions.
  • The strains used in the strain measures for the elemental removal are from the previous optimization iteration. Thus, it is recommended to have a slow optimization iteration update of the design variables for having consistency in the removal of the elements that can be obtained using the following settings: 
    
OPT_PARAM
  .....
  DENSITY_UPDATE   = CONSERVATIVE
  DENSITY_MOVE     = 0.10
  .....
END_

For each optimization iteration, the file TOSCA.OUT will contain information for the progress regarding the SOFT_DELETE. This information can be rather useful for choosing a correct value for the SOFT_DELETE with respect to strain measure. For example, for SOFT_DELETE_METHOD = MAX_SHEAR_STRAIN the following useful information can be found in TOSCA.OUT:



For example, for SOFT_DELETE_METHOD = MIN_PRINCIPAL_STRAIN the following useful information can be found in TOSCA.OUT:

Important:
  • Finding the correct threshold for SOFT_DELETE may require some trial and error. The threshold value for MAX_SHEAR_STRAIN, MIN_PRINCIPAL_STRAIN, PLASTICITY or VOLUME_CHANGE must be set explicitly by the user. Default settings are not available as the value strongly depends on different model parameters (material properties).
  • Using reduced speed in the design variable update (DENSITY_MOVE, DENSITY_UPDATE) improves the accuracy of the results.