中文摘要：

自由能势函数是不可逆热力学量及其共轭量的标量泛函,是广义标准材料模型的重要组成.论文根据损伤状态、过程、作用和伪势的定义和定理,分析了损伤耗散势的数学和物理含义,探讨了损伤耗散势的理论基础和描述耗散势的一般理论方法.研究了耗散势、损伤作用和自由能势函数的相互关系,给出了满足上述基本原理的自由能表达式,基于增量最小原理的变分形式得到了损伤理论基本方程的数值离散方程,实验模拟验证了该文理论和数值方法的正确性和有效性.

英文摘要：

Free energy potential function is expressed as the scalar productions of irreversibly thermodynamical variables and their conjugate ones.In this paper,the authors analyzed the mathematical and physical meanings of dissipative potential functions based upon the definitions and theorems of damage state,process,action and pseudo potential.Then the general method to depict the pseudo potential and the theoretical base of damage process were discussed.The interrelation between damage action,pseudo potential and free energy is studied in detail to give a free energy function satisfying with the above basic theorem.The elementary discrete equations of continuum damage mechanics were derived from the damage action functional equation based on the variational of the incremental minimization principles.The simulation results of experimental verify the reasonability and affectivity of the proposed method.