週期載重作用下彈性孔洞的動態反應

Dynamical Growth of Void in a Neo-Hookean Sphere under a periodic load

張怡文(YI-WEN CHANG)

指導教授 ： 李顯智

國立中央大學/工學院/土木工程學系/碩士(2011年)

摘要

本文主要探討neo-Hookean 圓球孔洞運動方程，分析橡膠材料中孔洞的動態擴張。neo-Hookean圓球孔洞在自由振動下的自然頻率並非固定值，隨模型所承受之初始條件改變而改變，反映出其非線性材料之特性，且厚壁圓球之非線性特性又較薄壁圓球明顯。在不同孔洞大小下，施加不同頻率的外力，其材料孔洞會有共振及不穩定擴張，此力學行為可能造成材料模型局部分子結構破壞導致整體材料衰減。本文亦研究週期外力對圓球模型的影響，並討論共振下其動態放大係數的變化。

關鍵字

材料強度衰減 ； 孔洞擴張 ； 橡膠材料

並列摘要

This thesis studies the equation of motion of a rubber ball and the rubber ball dynamical behavior of a void in the ball. The natural frequency of rubber ball is not a fixed-value, it may be changed by assigning different initial conditions. This phenomenon reveals the character of non-linear material. The nonlinear effect on the ball with a smaller void is more obvious then that of the bigger one. The dynamical behavior of the void will change when loadings with different frequencies or speeds are applied to the surface of the rubber ball. We will focus on the unstable growth and the resonance of the void under periodic loads since such kind of growth shall cause strength degradation to the rubbers. This thesis also investigates the dynamical magnification factor for the ball.

並列關鍵字

void growth ； Rubber ； strength degradation

參考文獻

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2. A.Needleman, Void growth in an elastic-plastic medium. J.Appl. Mech., 39 (1972) 964-970.

3. A.L.Gurson, Continuum theory of ductile rupture by void nucleation and growth : Part Ⅰ- yield criteria and flow rules for porous ductile media. J.Energ.Matl.Tech.,Trans.ASME, (1977) 2-15.

4. U.Stigh, Effects of interacting cavities on damage parameter. J.Appl. Mech, 53 (1986) 485-490.

5. H.S.Hou and R.Abeyarante, Cavitation in elastic and elastic-plastic solids, J.Mech.Phys.Solids, 40 (1992) 571-592.