分佈元素模型(DEM)在結合前人改良的A-F移動硬化法則後，對材料單軸向的循環潛變行為已具備良好的模擬能力，但對雙軸向循環潛變行為仍無法適當地加以描述。而原始的A-F移動硬化法則在雙軸向之彈塑性循環加載時，會導致次降伏面發生變形，並不符合移動硬化的假設，因此本文於DEM中提出兩種硬化法則之修正，首先修正原來的A-F移動硬化法則，以避開降伏面變形的問題，接著修改Ziegler所提出的移動硬化法則，使之能產生循環潛變之行為。為了驗證修正後的DEM模型，我們針對CS 1070進行循環潛變行為的模擬分析，並與文獻上的實驗結果做一比較。

The Distributed Element Model (DEM) in combination with the modified A-F kinematic hardening rule (A-F rule) is capable of adequately describing the uni-axial behavior of cyclic creep (ratcheting) of materials. However, it still has the disadvantage of not being able to describe appropriately multi-axial behavior of cyclic creep. The original A-F rule would lead to a subsequent yield surface which changes its shape during the bi-axial elastic-plastic cyclic loading and would not fit in with the assumption of kinematic hardening rule. Thus we propose two modifications of hardening rule in DEM. Firstly, we modify the original A-F rule to avoid the shape change of the yielding surface. Secondly, we modify the Ziegler kinematic hardening rule to make it proper for modeling of cyclic creep. To verify the modified DEM, we consider the simulation of ratcheting of CS 1070, and the results are compared with experimental results, which are obtained from the literature.

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