非線性彈材料微孔擴張問題數值解與析之對比

楊頂順(Young Ding Shun)

指導教授 ： 李顯智

國立中央大學/工學院/土木工程學系/碩士(2015年)

摘要

含微孔圓球受均佈或三軸拉力的力學問題，與材料損傷研究有關。過去三十年，相關的研究不少，有數值的分析，也有解析解。
本文旨在指出目前仍被忽略的兩個細節。其一是，有限元素法計算圓球受均佈拉力之問題時，在微孔快速擴張的臨界邊界值之計算，與精確解所描述者相當接近，會讓人以為數值解值得信賴，但是，數值解其實並不滿足材料組成律！！其二是，圓球受三軸拉力而變形，可由Hou – Abeyaratne Field 來描述，此近似的解析解推測圓形微孔會變成橢球狀。此與數值計算結果一致，故一般認為此解析解在定性上表現不錯，但本文發現此解析解在定性上與數值解之結果其實相差頗多。

關鍵字

有限元素法 ； 微孔

並列摘要

The micro-void growth problem of an elastic spherical ball subjected to triaxial loading is related to the studies of damages in materials.
A lot of analytical and numerical investigations of this problem had been carried out in the past thirty years.
The theme of this thesis is to point out two misleading facts which had been ignored by the large in the past.
The first is about the precision of the finite element solutions which had been thought to be quite reliable. We found that the numerical solutions do not even satisfy the constitutive law.
The second is about the Hou - Abeyaratne Field, which predicts that the micro-void will be deformed into an elliptical void. The ellipticity of the deformed void had been confirmed many times by numerical computations. However, we found that one important difference between the HAF and the finite element solution still exists.

並列關鍵字

finite element ； micro-void

參考文獻

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