裂縫的存在對材料/結構的力學行為影響甚巨，尤其對於多裂縫所造成的損傷更需要確切的描述與評估。在微觀力學理論中，當一固體材料存在多裂縫時，其損傷狀況常以材料的有效勁度做為評量，此相關問題雖已有廣泛的文獻討論，一般而言，其計算方法多半相當繁複；此外，對於包含多裂縫的結構體而言，其有效勁度的分析則仍待進一步的探討。本研究因此將針對多裂縫問題提出一迴圈積分，以此積分求得裂縫形成所需的總開裂能量，再進一步計算多裂縫狀況下的有效勁度，分析中將針對材料與結構兩種特性進行研討，預期可適用於非等向彈性材料與結構之損傷分析。原則上，此迴圈積分具有與積分路徑無關之性質，極適合直接以有限元素方法進行計算；同時，由於此方法採用純量能量參數，與現有計算材料性質的其他方法相較，在應用上十分簡易。本研究預計之執行期限為三年。第一年與第二年(目前執行中)分別考慮包含多個直裂縫及彎折裂縫的材料體(亦即，均勻承載之受力體)，計算其對應之有效勁度。第三年(本年度)擬考慮含有多裂縫的結構體(亦即，非均勻承載之受力體)，首先以現有的M-積分為基礎，延伸其概念，進一步定義Mc-積分；其次，在考慮各裂縫間交互作用的情況下，建構Mc-積分結果與結構體之有效勁度的關係，用以計算結構體在不同載重狀態下的有效勁度。研究成果期能提供作為多裂縫問題損傷評估的依據。While studies related to evaluation of effective elastic moduli for multi-cracked materials have been extensively reported in the literature, problems concerned with degradation of structural integrity due to presence of multiple cracks does not draw as much attention. In this paper, an efficient method is presented to calculate the effective stiffness of two-dimensional multi-cracked anisotropic elastic materials and structures. This method is based on the concept of a path-independent contour integral. Due to the property of path-independence, accurate solution of the integration can be easily obtained by direct use of numerical schemes such as finite element method. Also, implementation of the presented approach appears to be straightforward in that the crack interaction is characterized in terms of the scalar energy parameter. The proposed research is to be conducted in three years. We are presently carrying out the research work for the second year. In the first two years, the conditions associated with the presence of multiple straight and kinked cracks are to be considered through definition of the corresponding M–integral, and then followed by derivation of the constitutive relation for the effective stiffness. In the third year, the contribution from interaction of multiple cracks in a nonhomogeneously stressed structure is to be considered. By defining the Mc–integral, the interaction is to be characterized by construction of the relation between Mc and the associated effective stiffness. The applicability of the presented approach is to be extended to determine the effective stiffness associated with degradation of structural integrity due to presence of multiple cracks. 研究期間 : 9808 ~ 9907
