Does convexity of yield surfaces in plasticity have a physical significance?
Does convexity of yield surfaces in plasticity have a physical significance?
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DOI：
10.1177/1081286517721599
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发表时间：
2018-09
影响因子：
2.6
通讯作者：
R. Glüge;S. Bucci
中科院分区：
文献类型：
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作者：
R. Glüge;S. Bucci
函数或集合的凸性是经常需要的重要数学性质。在屈服函数φ (T)（或弹性范围）的情况下，几乎所有的经验和基于机制的屈服函数都具有这种性质。然而，要求正塑性耗散并不一定排除非凸屈服函数，这一点得到了实验观察到的非凸屈服函数这一事实的证实，尽管这种情况很少发生。因此，我们要问这个好的数学性质是否反映了物质的物理性质。这是研究在弹塑性，小应变，二维设置。看来，至少在这种情况下，没有特定的材料性能可以归因于屈服函数的凹凸性。
Convexity of a function or set is an often needed and important mathematical property. In the case of yield functions ϕ ( T ) (or elastic ranges) in terms of stresses, almost all empirical and mechanism-based yield functions have this property. However, requiring positive plastic dissipation does not necessarily exclude non-convex yield functions, which is confirmed by the fact that non-convex yield functions are observed experimentally, although this rarely happens. We therefore ask whether this nice mathematical property reflects a physical material property. This is investigated in an elastic–plastic, small strain, 2D setting. It appears that, at least in this setting, no specific material property can be attributed to the convexity of the yield function.