Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material

Wang Zhenqing; Shi Shouxia

Volume 17 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(8): 721-727

Wang Zhenqing, Shi Shouxia. Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material[J]. Applied Mathematics and Mechanics, 1996, 17(8): 721-727.

Citation:

Wang Zhenqing, Shi Shouxia. Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material[J]. Applied Mathematics and Mechanics, 1996, 17(8): 721-727.

Citation:

Wang Zhenqing, Shi Shouxia. Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material[J]. Applied Mathematics and Mechanics, 1996, 17(8): 721-727.

PDF( 2471 KB)

Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material

Harbin Engineering University, Harbin 150001, P. R. China

Received Date: 1995-06-02
Publish Date: 1996-08-15

Abstract

Abstract

This paper contains an asymptotic.finite-deformation analysis about theelastostatic field near the,crack-tip in an incompress rubber-like material.The eracktip.field is divided into two narrowing sectors and one expanding seclor.By the newstyain energy funcion and deformation pattern,we derive and solve the asymptoticequations.for each sector of the tip.field.The singularity of the crack-tip field isdiscussed.The curves of stress-strain of foe crack-tip.field.for an incompress rubber-like material are given and the dominant behaviors of stress and strain near the,cracktip are revealed.
- rubber-like material,
- finite-deformation,
- crack

FullText(HTML)

References(8)

References

[1]	J.K.Knowles and E.Sternberg,An asymptotic finite-deformation analysis of the elastic field near the tip of a crack,J.Elasticity,3,(2)(1973),67-108.
[2]	J.K.Knowles and E.Sternberg,Finite-deformation analysis of the elastostatic field near the tip of a crack:Reconsi deration and high-order results,.J.Elasticity,4,(3)(1974),201-233.
[3]	Y.C.Gao,Elastostatic field near the crack-tip in a rubber-like media,Theoretical and Applied Fracture Mechanics,14(1990),219-231.
[4]	Shi Zhifei and Gai Yuchen,Stress-strain field near the notch tip of a rubber sheet,Acta Mechanica Sinica.11,(2)(1995),169-177.
[5]	T.S.Gao,A rubber wedge under the tension of a line load at its tip,C.R.Acad.Sci.Paris,Sorie Ⅱ,318(1994),1-6.
[6]	T.S.Gao and Y.C.Gao,A rubber wedge under the compression of a line load,Inr.J.Solids arrd Structures,31(1994),2393-2406.
[7]	Y.C.Gao and B.Liu,A rubber cone under the tension of a concentrated force.Int.J.Solids and Structures,32,11(1995),2393-2406.
[8]	王振清,受拉情况下一类橡胶材料缺口顶端的大变形分析,工学博士学位论文,哈尔滨工程大学(1994).

Relative Articles

[1]	LI Ya, YI Zhijian, WANG Min, SU Kang. The Stress Intensity Factor of a FiniteWidth Plate With a Mode-Ⅰ Center Crack Subjected to Uniform Stress on the Crack Surface Near the Crack Tip[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1083-1091. doi: 10.21656/1000-0887.410130
[2]	LI Cong, NIU Zhongrong, HU Zongjun, HU Bin, CHENG Changzheng. Computation of Total Stress Fields for Cracked Bi-Material Structures With the Extended Boundary Element Method[J]. Applied Mathematics and Mechanics, 2019, 40(8): 926-937. doi: 10.21656/1000-0887.400013
[3]	DUAN Shujin, FUJII Koju, NAKAGAWA Kenji. Construction of General Analytic Functions With Finite Stress Concentration for Mono-Material Cracks and Bi-Material Interface Cracks[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1364-1376. doi: 10.21656/1000-0887.390030
[4]	ZHANG Li-xuan, QING Hong-jun, HU De-an. Uncertain Inversion of Crack Parameters for Plates Based on the SmXFEM[J]. Applied Mathematics and Mechanics, 2016, 37(1): 60-72. doi: 10.3879/j.issn.1000-0887.2016.01.005
[5]	LI Hao, ZHANG Yu-yu, XIAO Heng. Explicit Form of Elastic Potentials Matching General Biaxial Test Data for Elastomers[J]. Applied Mathematics and Mechanics, 2013, 34(5): 470-479. doi: 10.3879/j.issn.1000-0887.2013.05.005
[6]	ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.
[7]	LI Lin, ZHOU Zhen-gong, WANG Biao. Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack[J]. Applied Mathematics and Mechanics, 2006, 27(6): 646-654.
[8]	ZHOU Zhen-gong, WANG Biao. Dynamic Behavior of Two Parallel Symmetry Cracks in Magneto-Electro-Elastic Composites Under Harmonic Anti-Plane Waves[J]. Applied Mathematics and Mechanics, 2006, 27(5): 519-526.
[9]	GUO Jian-gang, ZHOU Li-jun, ZHANG Shan-yuan. Geometrical Nonlinear Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2005, 26(5): 614-620.
[10]	QU Gui-min, ZHOU Zhen-gong, WANG Biao. Dynamic Behavior of Two Collinear Permeable Cracks in a Piezoelectric Layer Bonded to Two Half Spaces[J]. Applied Mathematics and Mechanics, 2005, 26(10): 1152-1160.
[11]	ZHOU Zhe, QIN Ling-li, HUANG Wen-bin, WANG Hong-wei. Effective Stress and Strain in Finite Deformation[J]. Applied Mathematics and Mechanics, 2004, 25(5): 542-550.
[12]	CHEN Shu-yu, SHEN Cheng-kang, JIN Wu-gen. Study on Dynamic Constitutive Relations for Concrete With Finite Deformation[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1257-1263.
[13]	Lü Nian-chun, CHENG Yun-hong, XU Hong-min, CHENG Jin, TANG Li-qiang. Dynamic Crack Models on Problem of Bridging Fiber Pull-Out of Composite Materials[J]. Applied Mathematics and Mechanics, 2004, 25(10): 1093-1100.
[14]	ZHOU Zhen-gong, WANG Biao. Investigation of the Dynamic Behavior of Two Collinear Anti-Plane Shear Cracks in a Piezoelectric Layer Bonded to Two Half Spaces by a New Method[J]. Applied Mathematics and Mechanics, 2003, 24(1): 1-11.
[15]	ZHOU Zhen-gong, WANG Biao. The Behavior of Two Parallel Symmetric Permeable Cracks in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1211-1219.
[16]	Li Chunyu, Zhou Zhenzhu, Duan Zhuping. Dynamic Stress Field Around the Mode Ⅲ Crack Tip in an Orthotropic Functionally Graded Material[J]. Applied Mathematics and Mechanics, 2000, 21(6): 590-596.
[17]	Song Yanqi, Chen Zhida. Variational Principles of Asymmetric Elasticity Theory of Finite Deformation[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1115-1120.
[18]	Chen Zhida. Inverse Asymptotic Solution Method for Finite Deformation Elasto-Plasticity[J]. Applied Mathematics and Mechanics, 1997, 18(11): 959-966.
[19]	Liu You-wen, Jiang Chi-ping. Problems of Collinear Cracks between Bonded Dissimilar Materials under Antiplane Concentrated Forces[J]. Applied Mathematics and Mechanics, 1990, 11(10): 893-902.
[20]	Wang Hu Wang, Tsun-kuei. A Donnell Type Theory for Finite Deflection of Stiffened Thin Conical Shells Composed of Composite Materials[J]. Applied Mathematics and Mechanics, 1990, 11(9): 805-816.