有限元软件一般将变形体当作致密体进行分析，很少考虑金属空穴损伤对成形极限的影响．基于Ｇｕｒｓｏｎ－Ｔｖｅｒｇａａｒｄ空穴型材料塑性势方程，利用正交法则在刚塑性材料的Ｌｅｖｙ－Ｍｉｓｅｓ流动规则中引入了空穴损伤对应力－应变率场的影响，给出了空穴增长率计算方法，推证了含空穴材料的刚塑性变分原理与含有空穴体积分数的有限元列式，考虑了空穴体积扩张对成形过程的影响．为研究体积成形时材料损伤、裂纹起裂及扩展奠定了基础． Finite element software generally treats deformable bodies as dense bodies and seldom considers the effects of metal hole damage on the forming limits. Based on the plastic potential equation of Gurson-Tvergaard hole-type material, the influence of hole damage on the stress-strain rate field was introduced into the Levy-Mises flow rule of rigid plastic material by orthogonal method. The calculation method of hole growth rate , The rigid plastic variational principle with hole material and the finite element formula with hole volume fraction are deduced. The effect of hole volume expansion on the forming process is considered. In order to study the volume forming material damage, crack initiation and expansion laid the foundation.