What is continuum damage mechanics?

Answer 1

The topic is related to engineering/design/analysis of machine parts and structures or 'elements'. "continuum" means visualizing the element as if comprising of a single (fictitious) material, even though it might be heterogeneous (like concrete = cement+metal+sand+water+air). Thus with the term continuum, we could easily state the properties of the material of element with a few parameters like Young's modulus, Poisson ratio and modulus of rupture.

Damage, here refers to the cracking or crushing of material due to forces beyond the capacity of material. Or simply, material failure. Due to the continuum concept, these material failures will not be treated as a localized failure of a particular point/molecule/atom. Instead it is treated as a smeared (or spread) damage contributed by the combined response of a defined area. Thus we over come the trouble due to singularity in our mathematical model or formula.

To clarify, consider a point has failed. The stress carried by it is force/area. The area corresponding to the damaged point = zero, because the said point is no more the part of the material and hence area contributed by it in opposing the force = zero. Then stress = force/0 = infinity! Such a concept is difficult to formulate.

Hence instead of a point being disconnected, we say that a small area of known dimension has yielded, ie, damaged. Thus eliminating the 'infinity'.

So finally CDM refers to the response of structural elements that are manifested with 'cracks' or failed points when subjected to some known external forces.