Abstract：Free energy potential functions, as the most important contents of the standard generalized material model, could be usually expressed as scalar productions of irreversibly thermodynamically variables and their conjugate ones. In this essay, the author analyzed the mathematical and physical meanings of dissipative potential function based upon the definitions and theorems of damage state, process, action and pseudo potential. Then one general method to depict the pseudo potential and its theoretical base of damage process was discussed. Subsequently, we studied the connection among damage action, pseudo potential and free energy. As the result of foregoing research, the writer gave the free energy function compatible with the previous constraint. The elementary discrete equations of continuum damage mechanics were derived from the damage action functional equation based on the variation of the incremental minimization principles.
2010, Vol. 31 
