Abaqus - ductile damage - multiaxial damage evolution

Dear all,

Maybe this is a total noob question, as my thoughts took a wrong turn somewhere, or I misinterpreted the documentation, and I hope someone can clarify to me the meaning of the two columns describing the 3D dependency for the ductile damage - damage evolution tabular. 

I am trying to model a microstructure consisting of a matrix and some inclusions. For the matrix I'd llike to include some damage model incl. element deletion. Von Mises plasticity is sufficient in my case, and I was hoping to use "ductile damage". For ductile damage, the damage initialization can be easily entered in dependence on the triaxiality factor, as shown in the screenshot below. However, for damage evolution i don't get how phi1 and phi2 are defined for an element or an integration point respectively. 

 

In the documentation, I couldn't find a clear statement what these "Mode Mix Ratios" mean for a volume element. 

 

https://help.3ds.com/2025/english/dssimulia_established/SIMACAEMATRefMap/simamat-c-damageoverview.htm

About Progressive Damage and Failure: gives an overview and describes the general procedure 

leads to: 

  • https://help.3ds.com/2025/english/dssimulia_established/SIMACAEELMRefMap/simaelm-c-connplastbehav.htm?contextscope=all#simaelm-c-connplastbehav-modemixratio

    Connector Plastic Behavior: at least some information....

    If the coupled plasticity definition includes at least two terms in the associated potential definition (see Defining Derived Components for Connector Elements), a mode mix ratio can be defined to reflect the relative weight of the first two terms in their contribution to the potential. The mode mix ratio can be used in connector hardening definitions to specify dependencies in equivalent yield force or moment and, in plastic motion-based connector damage definitions (see Connector Damage Behavior), to specify dependencies in both damage initiation and damage evolution. It is defined as

    Ψm=(2π)tan−1(FI/FII),

    where FI is the force/moment in the first component specified for the plasticity potential and FII is the force/moment in the second component specified for the same potential. Ψm=0.0 if FI=0.0, Ψm=1.0 if FII=0.0, and Ψm is somewhere in between −1.0 and 1.0 if neither is 0.0.

  • https://help.3ds.com/2025/english/dssimulia_established/SIMACAEELMRefMap/simaelm-c-cohesivebehavior.htm?contextscope=all

    which had the most useful information. However, this is written for a cohesive element, where the normal direction is clearly defined. In my case, ductile damage => damage evolution, a "normal direction" is not really defined. So what do the directions n,s,t translate to when I am not using a cohesive but a general tet element? I am having issues understanding what the normal and two shear directions mean at the integration point of a general tet or brick element.

    What I have available as data is stress strain curves with different triaxialities (parameter or lode angle) including stress tensor and strains/displacements from lower level simulations. But I have simply no idea what to put in this table for phi1/phi2.

     

    Any ideas appreciated.