I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form of work energy theorem that is valid for rigid as well as non rigid bodies and for conservative as well as non-conservative force? I would like a work-energy equation that would be valid for point particles, rigid bodies and non-rigid bodies.
Good question! In my opinion as a physics teacher, the work-kinetic energy theorem is one of the worst things perpetrated on beginning physics students, and its ill-effects stay with us and cloud things up for a long time
Work is nothing but energy transfer. A change in kinetic energy for an object is a change in one of its properties. So the Work-Kinetic Energy Theorem:
$$ W = \mathbf F\cdot\mathbf d = \Delta KE $$
says that a transfer of energy, resulting from a force exerted through a distance, results in a change in this particular property of an object. Elevating this fact to a special theorem tends to obscure in our minds the useful fact that it is true for all changes in properties that (and here's your generalization, which I call the Law of Change):
Any change in any system's properties is always associated with a transfer of energy into or out of it, which is always associated with force exerted through distance, which, in turn, is always associated with a change in motion or position.
The "generalized work energy theorem" is extremely simple:
The work done on or performed by the system equals the difference in energy of the system. The energy of the system is the sum of all different kinds of energies of your system: kinetic, potential, chemical, etc.
How does the work split across different types of energies? I can't tell you, that really depends on the body in question.
Ultimately, you only have two "energies": potential energy of conservative forces and kinetic energy. All other energies, such as heat or chemical energy or the like constitute an effective description of something that ultimately can be described by kinetic and potential energy only. Stored heat energy is undirected kinetic energy of internal degrees of freedom (how to model that is one of the questions of statistical mechanics and condensed matter theory). Chemical energy is mostly potential energy of atomic bonds and atoms. Reversible deformation results in potential energy from potential energy in distorted atomic bonds. There is no simple equation to accurately model all of it for every system - otherwise we wouldn't use effective descriptions and physicists would be out of work soon.