Aikido teachers often make reference to this phenomenon of the unbendable arm. The Japanese term is orenaite, which means something close to, "The arm that is not to be bent." Notice that this is not really the same thing as "the unbendable arm." It is an advisory to not bend your arm - not to be so strong that your arm can't be bent.
Unbendable arm is really a posture and a mobility thing - not a strength thing. The goal is to be light enough on your feet that it takes less pressure to move you than to bend the arm. So the arm becomes this relaxed feeler that moves your body when it starts bearing weight. The only strength that is needed here is sufficient core strength to maintain a natural, upright posture.