弹塑性应力-应变曲线的斜率恒等式及其验证和应用

Slope identity of elastoplastic stress-strain curve and its verification and application

斜率是描述本构关系曲线特征的重要参数。弹塑性应力-应变关系曲线中涉及到应力-应变曲线的切线、卸载曲线以及塑性-弹性应变曲线的3个重要斜率,这些斜率在塑性和损伤本构理论以及弹塑性变形相互关系的研究中均有重要应用。从理论上找到了这3个斜率之间关系的微分型和差分型两类恒等式,并用煤岩较高应力下的加卸载应力-应变数据对其进行了验证。结果表明,这两类恒等式均是完全成立的。最后给出了斜率恒等式在弹塑性变形相互关系研究中的一个应用,即证明了李铀提出的弹性-塑性应变曲线在εp-εe空间的平移关系等价于塑性应变相等点的斜率比值应相等。

The slopes of loading, unloading curves of stress-strain relation and the slope of the corresponding elastic strain-plastic strain curve（e-p curve） are critical constitutive parameters. They play important role in elasto-plasticity, damage theories and the analysis of elastic and plastic deformations. The three slopes are mutually related. Here, a difference-type and a differential-type identities of the three parameters are respectively derived theoretically and verified later with the test data of a coal sample. The results show that these two identities are both correct. Then an application of the slope identity to studying the relation between the elastic and plastic strains presented by Li You is given. It is equivalent to an equality of two slopes ratios. found that the ＂translation relation＂ of e-p curve in εP - εe space is