Based on two kinds of visco-elastic plastic damage constitutive equations according to “hypothesis of strain equivalence” and “hypothesis of complementary energy”

the principle of minimum dissipative energy is applied to visco-elastic plastic damage theory of solid materials. The nonlinear evolution equations of visco-plastic strain

damage variable and strengthening or softening parameter of damaged materials are presented. Visco-elastic plastic damage constitutive equations and three nonlinear evolution equations of damaged material

are considered and two different visco-elastic plastic damage models A and B of solid materials are established

and these two model are examined. Finally

the visco-elastic plastic dynamic damage problem of a concrete gravity dam due to earthquake load are analyzed by adopting visco-elastic plastic damage models A. Results show that this model can be used to analyze the dynamic damage of concrete gravity dam.