准脆性材料和摩擦材料的屈服准则：对有角曲面的推广
Yield criteria for quasibrittle and frictional materials: a generalization to surfaces with corners
摘要：
屈服函数（或相变函数）的凸性及其与相应屈服表面（或相变表面）的凸性的关系对于新屈服（或相变）标准的发明、定义和与实验的比较是必不可少的。这个问题以前只在表面光滑的假设下得到解决，但是具有拐角的屈服面（例如Hill，Tresca或Coulomb-Mohr屈服准则）在塑性理论中具有根本的重要性。本文将函数及相应曲面的凸性与非光滑屈服面和相变面的凸性相联系的一个命题加以推广，并推广了非光滑弹性势函数的一个定理。虽然前者的这些概括是至关重要的屈服和相变条件，后者可能会发现应用的势能函数描述相变材料，或材料与不连续锁定在张力，或接触的一个身体与离散的弹性/摩擦支持。
英文摘要：
Convexity of a yield function (or phase-transformation function) and its relations to convexity of the corresponding yield surface (or phase-transformation surface) is essential to the invention, definition and comparison with experiments of new yield (or phase-transformation) criteria. This issue was previously addressed only under the hypothesis of smoothness of the surface, but yield surfaces with corners (for instance, the Hill, Tresca or Coulomb-Mohr yield criteria) are known to be of fundamental importance in plasticity theory. The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions. While the former of these generalizations is crucial for yield and phase-transformation condition, the latter may find applications for potential energy functions describing phase-transforming materials, or materials with discontinuous locking in tension, or contact of a body with a discrete elastic/frictional support.
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