材料中的孔洞在材料受到一定程度的外力後，會突然不穩定地擴張，此現象是裂縫住外延伸的重要機制，因為裂縫在往外延伸前，其尖端附近會先出現孔洞擴張之現象，故了解孔洞擴張有助於裂縫延伸的研究。另外，也有助於了解含有缺陷的材料的弱化現象。本計劃第一個重點是研究橡膠材料中微孔的非對稱擴張，其特色是採用由真實實驗數據推導出的材料模型進行分析，有別於過往文獻祇採用過度簡化的材料模型進行的研究（過往的研究為了得到解析解而採用簡化的材料模型）。本計劃將計算出各種真實與簡化材料模型的微孔開孔準則曲面，並比較它們的差異，藉以說明材料組成律之分析，除了要用理論模型比對單軸、雙軸和三軸實驗數據外，也要對比微孔開孔實驗，同時也說明過往文獻中採用簡化的材料模型所得結果之誤差。本計劃的另一重點是橡膠材料中有限大孔洞的非對稱變形，利用數值解與Hou 和Abeyaratne 的近似解析解（簡稱HAF）作對比，以找出HAF 的誤差。此研究的意義在於，近年HAF常被運用於描述有限大孔洞的非對稱變形，並藉以導出含孔洞橡膠的材料組成律，但其實HAF僅在描述微孔的非對稱變形時有滿意的結果，並不適用於描述有限大孔洞的非對稱變形，所以我們詳細的探討HAF在各種材料模型中會有多少的誤差。Voids in materials will grow unstably when the external tensile loads applied to the materials are large enough. This phenomenon is an important mechanism of the crack propagation because voids will occur around the crack tip before the crack propagates. So the understanding about the growth of voids is helpful for the study of crack propagations as well as the strength degradation of materials with defects. The first subject of this project is the asymmetric expansion of a micro-void in rubber. We consider the material models which are derived from experimental data of rubbers. This makes our study different from those reported in the past literatures since only simplified material models were considered in them. (The simplified models were considered because analytical results can be obtained more easily in this way.) We shall construct the cavitation surfaces, the criteria for the sudden growth of the micro-voids, for these real material models and simplified models. Comparison between these cavitation surfaces will also be made in order to illustrate two points. The first point is, when deriving material models one needs not only the uni-axial, bi-axial and tri-axial tests but also the cavitation test of the material. The second point is the cavitation surfaces derived in the existing literatures may have large errors. The second subject treated in this project is the asymmetric deformations of a finite void in rubber. We shall compute the asymmetric deformations numerically and compare them with those described by the analytically approximate expressions obtained by the “Hou and Abeyaratne Field”(Abbreviated as HAF), an analytical formula for the deformations of a circular void derived by Hou and Abeyaratne in their paper in 1982. This aims to evaluate the error of HAF. The meaning of this study is that HAF had been adopted in the recent years by some scholars to describe deformations of finite voids when deriving constitutive laws for porous rubber-like materials. However, HAF only works well for micro-voids and large error may occur when it is applied to describe deformations of finite voids. So, we want to conduction a detail analysis about the validity of HAF for deformations of finite voids. 研究期間：10008 ~ 10107
