论文标题
弹性完美塑料固体的数学模型的统一：凸分析方法
Unification of the mathematical model of elastic perfectly plastic solids: a convex analysis approach
论文作者
论文摘要
这里提出了针对控制弹性完美塑料材料的本构法的新数学公式。特别是，这表明弹性应变速率和塑性应变速率相对于切线锥和屈服域的正常锥形成正交分解。还表明，应力速率可以看作是弹性应力张量切线锥上的投影。这种方法导致了弹性塑料定律的连贯数学公式，并简化了相关流动进化方程的所得系统。一个或两个产量功能的情况进行了详细处理。详细制定了Von Mises和Tresca收益标准的实例，以证明新形式主义在应用中的有用性。
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition with respect to the tangent cone and the normal cone of the yield domain. It is also shown that the stress rate can be seen as the projection on the tangent cone of the elastic stress tensor. This approach leads to a coherent mathematical formulation of the elasto-plastic laws and simplifies the resulting system for the associated flow evolution equations. The cases of one or two yields functions are treated in detail. The practical examples of the von Mises and Tresca yield criteria are worked out in detail to demonstrate the usefulness of the new formalism in applications.
