I understand the same behavior is available in Abaqus Explicit, and that cohesive elements can also be used in Explicit, but I don't see the reason why this wouldn't be available in Abaqus Standard...
It is available. Use the *DEBOND keyword with TYPE=VCCT or TYPE=ENHANCED VCCT in conjunction with *FRACTURE CRITERION to specify the criterion for onset and propagation of damage. Abaqus uses the Virtual Crack Closure Technique (VCCT) to compute the energy release rates and applies a cohesive law to simulate damage.