This work is concerned with the influence of non-smooth yield functions on material instabilities. The loss of ellipticity condition is examined in the case of a family of non-smooth yield functions in principal stress space. A procedure for the numerical detection of loss of ellipticity in multisurface plasticity is proposed. An explicit expression of the subdifferential of the non-smooth yield function is obtained, thereby extending existing results in the literature for the Tresca and Mohr–Coulomb criteria. Structural computations show that the use of non-smooth yield functions can lead to much earlier failure prediction than in the case of a commonly used von Mises criterion.

这项工作涉及非光滑屈服函数对材料不稳定性的影响。在主应力空间中一类非光滑屈服函数的情况下，检查椭圆度条件的损失。提出了一种数值检测椭圆面多面塑性损失的方法。获得了非光滑屈服函数次微分的明确表达，从而扩展了Tresca和Mohr-Coulomb标准的文献中已有的结果。结构计算表明，与通常使用的冯·米塞斯（von Mises）准则相比，使用非光滑屈服函数可以导致更早的失效预测。