Let say you've made your barbed wire with an Array modifier + Curve modifier. If you just want them to bend, you just need to subdivide your curve and move its handles, it will bend the barbed wire. If you want to bend + animate, here is a solution:
- Select your curve, enter in Edit mode and W > Subdivide it enough.
- Select each handle and ctrlH > Hook to New Object.
- This has created empties that you can use to move the handle, thus bend your barbed wire as you want.
- To make it more convenient and be able to reset the empties to their 0 position you can create an armature, and inside this armature create as many bones as you have empties.
- Now switch your armature in Pose mode and select the first bone.
- Select the corresponding empty, re-click on the bone, and ctrlP > Bone. Do the same for each empty.
- Now the bones control the empties that control the handles, and you can come back to the basic curve position going in the armature Pose mode and altG to reset.
This solution will allow you to have a very flexible barbed wire, but if you don't need complicated movements you can use the Mesh Deform modifier or Bendy Bones, as Mathmaniage said.