一类非关联材料：n-单调材料
A class of non--associated materials: n--monotone materials
摘要：
广义标准物质由极大循环单调算子控制，并由凸势建模。Géry de Saxcé的隐式标准物质是用双凸双势函数来模拟的。我们分析了由极大n-单调算子和Fitzpatrick函数建模的n-单调材料的中间类。回顾了Robert Hooke提出的弹性材料模型，并坚持了本构律的线性、同轴性和单调性，说明了Fitzpatrick基于凸分析的n-单调算子表示为寻找n-单调材料的最佳双势函数模型提供了一种建设性的方法。放弃线性本构关系的对称性，我们发现n-单调性是材料表征和分类的一个相关标准。
英文摘要：
Generalized Standard Materials are governed by maximal cyclically monotone operators and modeled by convex potentials. Géry de Saxcé's Implicit Standard Materials are modeled by biconvex bipotentials. We analyze the intermediate class of n-monotone materials governed by maximal n-monotone operators and modeled by Fitzpatrick's functions. Revisiting the model of elastic materials initiated by Robert Hooke, and insisting on the linearity, coaxiality and monotonicity properties of the constitutive law, we illustrate that Fitzpatrick's representation of n-monotone operators coming from convex analysis provides a constructive method to discover the best bipotential modeling a n-monotone material. Giving up the symmetry of the linear constitutive laws, we find out that n-monotonicity is a relevant criterion for the materials characterization and classification.
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