Difference between Continuum Damage Mechanics approach and Fracture Mechanics approch

Hello Praveen,

In below I share with you some understanding on CDM and FM.

I think that the most basic difference between the both is that CDM falls within the standard continuum mechanics framework with continuous displacement field (hence, FEM implementation is rather easy) while in FM, the displacement is discontinuous through the crack face, so you need to use special techniques such as remeshing, meshless or xfem to model this discontinuity in the displacement field.

You can think like this, according to CDM, you smear out the crack over a failure zone where the displacement is still continuous but very high strain. 

I am interesting to discuss more on this.

Phu

In Continuum Damage Mechanics (CDM), cracks occur at a level and number such that they are modeled as smeared out continuously. In Fracture Mechanics (FM) some small number of cracks are considered which are of size of the scale of interest. To generalise, CDM is useful to model the degradation of a mechanical body leading up to macrocracks and FM is useful for modeling the mechanical body after cracks on the scale of the structure have formed.

In CDM, the engineer imagines that some of the material has become ineffective at resisting loads. For example, if 20% of the material in the cross-section of a bar has become ineffective at resisting loads and the remaining 80% of the material still behaves as the material normally would, CDM would analyse as though the bar is a normal bar with a full area of material with 80% of the strength and stiffness of the real material. This is extended to multiple dimensions.

In FM, some crack is analysed. Its geometry is important and affects the behaviour of the structure. Traditionally small numbers (think on the order of one) of cracks could be analysed, though modern computational methods allow the engineer to model many cracks. Often the cracks in FM are too large to model as though they were smeared out.

I hope this has helped you with your understanding somewhat.