(Sadr) is a term indicating the chest or breast which has been expanded and opened to accept and embrace Islam. In contrast however, the surrender to Real Islam takes place within every atom of the Muslim.
Islam means peace and the person who follows this peace is called the Muslim. From another root meaning of the word, Islam means complete submission and surrender, and the person who submits and surrenders himself to the will of his Lord is the person who has accepted Allah as his Creator, Sustainer, Lord and the Master of the Day of Judgement.
So from both the definitions Islam means a way of life for people who have opted to follow peace as opposed to chaos, order as opposed to disorder, discipline as opposed to indiscipline, submission as opposed to refusal, surrender as opposed to insolence, obedience as opposed to disobedience etc. All these things combined together to define Islam as away of life by which a person becomes a follower of peace and not a follower of chaos. And the followers of peace are the Muslims whose duty it is: "to establish peace and what is good, and to prevent chaos and what is evil, and they are the best people." (Al-Qur'an 3:110)