1. Physical
If you are stressed, your muscles shorten. To relax them, they need to be stretched in asana for at least a minute: the length it takes for the muscle to relax.
The sympathetic nervous system causes tension; the parasympathetic system relaxes. Any breathing technique can override the autonomic nervous system, so breath awareness should be practised in asanas.
One way of doing this, I found, was to remind students of their breath in a class, for example in a posture to inhale and exhale for a count of four.
Specific effects of certain asanas
Headstand
In headstand, you have to breathe deeply as your intestines are pushed up. Deep breathing calms the mind.
Shoulderstand
In shoulderstand, the subtle energy is pushed back to the solar plexus, where it then gets distributed throughout the body.
Cobra/Locust/Bow
In these positions, the abdomen is pressed into the floor, thus activating the digestive system and delivering more energy into the system.
2. Mental
To relax, it is important to engage the mind, as every action from the body comes from the mind. Thus by doing autosuggestion, such as at the end of a Sivananda class, the body is relaxed.
The autosuggestion at the end of the class is possibly influenced by Johannes Heinrich Schultz work on autogenic training. Here, the practitioner uses verbal cues to guide breathing and direct attention to parts of the body. A sample script from Guy’s & St Thomas’ hospital is available here: autogenic-relaxation-technique. You can also read more about autogenic techniques in Sure Ways to Self-Realization by Swami Satyananda.
Also I believe that the tense and relax technique that precedes the autosuggestion may have been influenced by Dr Edmond Jacobson’s work. A sample script from Guy’s & St Thomas’ hospital is available here: jacobsons-progressive-relaxation-technique.
3. Spiritual
Spiritual relaxation is when you come closer to your true self, unclouded by mental activity. An example is in final relaxation in a Sivananda class where you know your body is there, but you are no longer interested in it.
One of the ‘selling’ points of a Sivananda practice is the sense of relaxation which you feel after final relaxation. The combination of asana work and a subtantial relaxation (at least 10 minutes in savasana) usually makes me feel more relaxed than either a vinyasa class with a perfunctory savasana at the end or a yoga nidra.
From notes taken at a Sivananda course in active relaxation and stress reduction and my own research.