本文將探討新虎克材料圓球的動力學反應，新虎克材料模型常用於模擬橡膠材料的力學行為，橡膠材料廣泛使用在建築物的避震器、輪胎、生醫工程材料等。本文研究橡膠材料球體含有微小孔洞分別受三種不同型式的脈衝荷重作用後使微孔的動態擴張，在脈衝荷重達一定強度後微孔迅速擴張，將形成材料結構上的弱化或破壞。本文將計算微孔在迅速且不穩定擴張時所達到脈衝荷重的臨界數值並定義之，並比較在不同形式的脈衝荷重作用時間下，材料弱化所需要的脈衝荷重強度以及其弱化嚴重程度。

This paper will explore dynamics response of the sphere of the Neo-Hookean materials. Neo-Hookean material model commonly used in the simulation of mechanical behavior of rubber materials，and they are widely used in the vibration isolations, tires, bio-materials .In this paper, we discuss the rubber spheres, which contain micro-voids and they will dynamic expand by the three types impulsive loadings, porous rapid growth after impulsive loadings up to a certain intensity , it will make the materials’structure softening or destruction.This article will calculate and define the micro-voids’impulsive loadings critical values, which in the rapid and unstable expansion situation. And comparing different impulsive loading time, the materials needed the softening impulsive loadings intensity as well as its severity.

參考文獻
1. F.A.McClintock, A criterion for ductile fracture by the growth of holes.J.Appl. Mech., 35 (1968) 363-371.
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.
6. A.N.Gent,Cavitation in rubber: a cautionary tale. Rubber Chem.Tech.,63(1990) G49-G53.
7. L. Cheng and T.F. Guo, Void interaction and coalescence in polymeric materials. Int. J. Solids Struct., 44(2007)1787-1808.
8. C. J. Quigley and D.M. Parks, The finite deformation field surrounding a mode I plane strain crack in a hyperelastic incompressible material under small-scale nonlinearity. Int. J. Fracture, 65(1994)75-96.
9. J.C. Sobotka, R.H., Jr. Dodds and P. Sofronis, Effects of hydrogen on steady, ductile crack growth: Computational studies. Int. J. Solids Struct., 46(2009)4095-4106.
10. J.M.Ball, Discontinous equilibrium solutions and cavitation in nonlinear elasticity. Phil.Trans.R.Soc.Lond,A306 (1982) 557-610.
11. C.A.Stuart, Radially symmetric cavitation for hyperelastic materials,Ann.Inst.Henri Poincare-Analyse non lineare, 2 (1985) 33-66.
12. C.O.Horgan and R.Abeyaratne, A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void. J.Elasticity, 16 (1986)189-200.
13. F.Meynard, Existence and nonexistence results on the radially symmetric cavitation problem. Quart.Appl.Math. 50 (1992) 201-226.
14. C.A.Stuart, Estimating the critical radius for radially symmetric cavitation, Quart. Appl.Math., 51 (1993) 251-263.
15. S.Biwa, Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. Int.J.Non-Linear Mech., 30 (1995)899-914
16. S.Biwa, E.Matsumoto and T.Shibata, Effect of constitutive parameters on formation of a spherical void in a compressible non-linear elastic material. J.Appl.Mech. 61 (1994) 395-401
17. H.C.Lei(李顯智) and H.W.Chang, Void formation and growth in a class of compressible solids. J.Engrg.Math., 30 (1996) 693-706.
18. R.W. Ogden, ‚Non-Linear Elastic Deformations‛.Ellis Horwood Limited,Chichester, England,1984.
19. J.N. Johnson, Dynamic facture and spallation in ductile solids. J. ppl.Phys.,52(1981)2812-2825.
20. R. Cortes, The growth of microvoids under intense dynamic loading. Int. J. Solids Struct.29(1992)1339-1350.
21. R. Cortes, Dynamic growth of microvoids under combined hydrostatic and deviatoric stresses.Int. J. Solids Struct. 29(1992)1637-1645.
22. F.L. Addessio, J.N. Johnson and P.J. Maudlin, The effect of void growth on Taylor cylinder impact experiments. J. Appl. Phys., 73(1993)7288-7297.
23. Z.P. Wang, Growth of voids in porous ductile materials at high strain rate.J. Appl. Phys.,76(1994)1535-1542.
24. J. Zheng, Y.L. Bai and Z.P. Wang, Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials. J.Phys. IV France Colloq. C8 (DYMAT 94)4(1994)765-770.
25. W. Tong and G. Ravichandran, Inertial effects on void growth in porous viscoplastic materials.Trans. ASME: J. Appl. Mech., 62(1995)633-639.
26. X.Y. Wu, K.T. Ramesh and T.W. Wright , The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading. J. Mech.Phys. Solids, 51(2003)1-26.
27. T.W. Wright and K.T. Ramesh, Dynamic void nucleation and growth in solids:
A self-consistent statistical theory. J. Mech.Phys. Solids,56(2008)336-359.
28. M.S.Chou-Wang and C.O.Horgan, Cavitation in nonlinear elastodynamics for
neo-HooKean materials. Int.J.Engrg.Sci., 27 (1989) 967-973.
29. X Yuan, Z. Zhu and C. Cheng, Qualitative analysis of dynamical behavior for an incompressible neo-Hookean spherical shell. Appl. Math. Mech.(English Edition), 26(2005)973-981.
30. X Yuan, Z. Zhu and R. Zhang, Cavity formation and singular periodic oscillations in isotropic incompressible hyperelastic materials. Int. J.Non-Linear Mech. ,41(2006)294-303.
31. P.J. Blatz and W.L. Ko , Application of finite elastic theory to the deformation of rubbery materials . Trans.Soc. Rheol. , 6 (1962) 223-251.
32. M. Navarro, et. al., Biomaterials in orthopaedics. J. R. Soc.Interface,5(2008)1137 -1158.
33. Y. Jung, et. al., Cartilaginous tissue formation using a mechano-active scaffold and dynamic compressive stimulation. J. Biomaterials Sci.—Polymer Edition, 9(2008)61-74.
34. T. Hu and J.P. Desai, Characterization of soft-tissue material properties:Large deformation analysis. ‘Medical Simulation,Proceedings’ in Lecture Notes in Computer Science, 3078(2004)28-37.
35. J.Z. Wu, et. al., Nonlinear and viscoelastic characteristics of skin under compression: experiment and analysis. Bio-Medical Mater.Eng.,13(2003)373-385.
36. Z.Q. Liu and M.G. Scanlon, Modelling indentation of bread crumb by finite element analysis,Biosystems Eng., 85(2003)477-484.
37. M. Zidi, Circular shearing and torsion of a compressible hyperelastic and prestressed tube.Int. J. Non-Linear Mech., 35 (2000) 201-209.
38. M. Zidi, Torsion and axial shearing of a compressible hyperelastic tube. Mech. Res. Comm.,26 (1999) 245-252.
39. M. Cheref, M. Zidi and C. Oddou, Analytical modelling of vascular prostheses mechanics.Intra and extracorporeal cardiovascular fluid dynamics. Comput. Mech. Pub., 1 (1998) 191-202.
40. M. Zidi, Finite torsional and anti-plane shear of a compressible hyperelastic and transversely isotropic tube. Int. J. Engrg. Sci., 38(2000)1481-1496.
41. T.J. Paulson, et. al., Shaking table study of base isolation for masonary buildings. J. Struct.Eng., 117(1991)3315-3336.
42. A.D. Luca, et. al., Base isolation for retrofitting historic buildings:Evaluation of seismic performance through experimental investigation.Earthquake Eng. Struct. Dyn.,30(2001)1125-1145.
43. B. Yoo and Y.H. Kim, Study on effects of damping in laminated rubber bearings on seismic responses for a 1/8 scale isolated test structure.Earthquake Eng. Struct. Dyn., 31(2002)1777-1792.
44. Y.M. Wu and B. Samali, Shake table testing of a base isolated model. Eng.
Struct.,24(2002)1203-1215.
45. N. Lakshmanan, et. al., Experimental investigations on the seismic response of a base-isolated reinforced concrete frame model. J.Performance Constructed Facilities, ASCE,22(2008)289-296.
46. T.H. Kim, Y.J. Kim and H.M. Shin, Seismic performance assessment of reinforced concrete bridge piers supported by laminated rubber bearings. Struct Eng. Mech., 29(2008)259-278.
47. J.F. Kang and Y.Q. Jiang, Improvement of cracking-resistance and flexural behavior
of cement-based materials by addition of rubber particles. J. Wuhan Univ. Tech.—Mater.Sci.Edition, 23(2008)579-583.
48. G. Skripkiunas, et. al., Deformation properties of concrete with rubber waste additives. Mater. Sci.—Medziagotyra, 13(2007)219-223.
49. M.K. Batayneh, et., al., Promoting the use of crumb rubber concrete in developing countries. Waste Management, 28(2008)2171-2176.
50. L. Zheng, et. al., Strength, modulus of elasticity, and brittleness index of rubberized concrete. J. Mater. Civil Eng., ASCE,20(2008)692-699.