Corpus delicti is the body of evidence; the essence of the crime. This is different from the statutory elements of the crime, which include things such as: the statute that the criminal was found guilty for, the Jurisdictional information, the mens rea, conduct of the accused, materiality, and any other elements that can be used to prove the guilt of the accused.
Without the statutory elements of the crime, it is difficult to find the accused guilty without the corpus delicti. In the past it was usually a rule not to convict until the corpus delicti could be established. For example, a murder takes place and a dead body is found. The dead body is the corpus delicti; the body of evidence, so to speak. There have been times in the past where a person would have been accused of murder, and then after the convicted was put to death, the supposed victim was later found to be alive and well. There may have been statutory elements that showed that the crime was committed, but in a scenario like the one above, it was apparent that the corpus delicti was never proven or found before committing the convicted to his sentencing.
The changes made over time for the insanity plea defense have not made things easier for the convicted to get a not-guilty verdict for their crimes. From what I could find, the earliest attempt to define legal insanity came from a 1843 which found a paranoid schizophrenic not guilty after killing a politician. This case has become known as the "M'Naghten Rule."
"Every man is to be presumed to be sane, and ... that to establish a defense on the ground of insanity, it must be clearly proved that, at the time of the committing of the act, the party accused was laboring under such a defect of reason, from disease of mind, and not to know the nature and quality of the act he was doing; or if he did know it, that he did not know he was doing what was wrong."...