當材料受力變形到一定程度時，其內部的微孔和微裂縫，就會由一直閉合的狀態迅速擴張成有限大的孔洞和裂縫，或者是原本穩定擴張的有限大孔洞變為不穩定的急速擴張，產生整體材料的強度(例如拉力強度)衰減 (degradation)，所以研究材料中孔洞擴張的行為，可提供研究材料強度衰減的學理根據。本計劃分析橡膠材料中孔洞的動態擴張。橡膠材料在土木工程，機械和生物工程有不少應用，例如i)建築物隔震器，ii)橋樑支承橡皮墊，iii) 取代混凝土中傳統骨材的摻料，iv)隔震樁樁頭的橡皮墊 v)輪胎，vi)生物醫學材料和vii)噴射引擎的固體燃料等。橡膠屬非線性彈性材料，目前研究非線性彈性孔洞動態問題的文獻中，採用的材料模型皆為新虎克材料模型，此材料模型與實際橡膠材料的行為相差甚遠。本計劃採用由真實實驗數據推導出的Ogden材料模型和Blatz-Ko材料模型，故此可補前人研究之不足。當施加不同的外加拉力時，橡膠材料中微孔或有限大孔洞的動態行為將有所不同。本研究專注於，微孔的突然張開及有限大孔洞的共振及不穩定擴張，因為這些力學行為會造成橡膠材料的局部分子結構破壞，而引致橡膠材料整體強度衰減。本計劃分兩年執行，第一年研究Ogden 橡膠材料中的微孔及有限大孔洞動態行為，第二年則研究Blatz-Ko 橡膠材料中的微孔及有限大孔洞動態行為。 Micro-voids and micro-cracks in solid materials will grow suddenly into finite voids and cracks when sufficient large loadings are applied to the materials. Under similar conditions, the growth of finite voids will also become unstable. And the strength of the materials will be degraded due to such kinds of unusual growth of micro-voids and finite voids. This project analyzes the dynamical behavior of micro-voids or finite voids in rubbers. Rubbers are useful in civil and mechanical engineering. Its applications can be found in i) vibration isolators, ii) bearings of bridges, iii) rubberized concrete, iv) vibration isolated piles, v) tires, vi) bio-materials, and vii) fuel of jet engines. Rubbers are nonlinear elastic. The material model used in the existing literatures about the dynamic void growth in nonlinear elastic materials is the neo-Hookean material model, which, however, fails to describe the behavior of real rubbers. And the merit of this research project is that the material models used by us, i.e., the Ogden material model and the Blatz-Ko material model, were derived from the experimental data of real rubbers. The dynamical behavior of the micro-voids or finite voids will change when different tensile tractions are applied to the rubbers. We will focus on the sudden growth and the resonant growth of the micro-voids (or the resonant growth and unstable growth of finite voids) since such kinds of growth shall cause strength degradation to the rubbers. This project will be carried out in two years. In the first year the dynamic void growth problems will be studied for the rubber described by the Ogden material model. In the second year, the Blatz-Ko material model will be adopted. 研究期間 : 9808 ~ 9907
