What is the property of not shattering, in for example a brisant explosion, called? And what kind of steel would I want that has this property?
A material's resilience describes its ability to absorb energy by deforming elastically. Its ductility (or malleability, there is a slight difference between the terms, but its not relevant here) represents how much energy it can absorb via plastic deformations. Its toughness encompasses both elastic and plastic deformations.
These terms are actually quantifiable and are equal to the area beneath the stress-strain diagram. Resilience equals the area under the elastic regime, ductility under the plastic regime, and toughness under the entire curve (and is therefore equal to the sum of the material's resilience and ductility).
If the second part of your question was asking for specific steels, that's out-of-scope for this site, given how different steels are available in different countries.
I believe @squigbobble is on the right track. The issue is related to crack propagation, namely the energy to propagate the crack in the material. The reason ductility plays a big roll here is that ductility "dulls" the tip of this crack requiring greater energy to continue opening it. This slows the rate of crack propagation significantly.