The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations

Chen Liangsen; Zhao Xinghua; Fu Minfu

Volume 20 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(6): 559-568

Chen Liangsen, Zhao Xinghua, Fu Minfu. The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 559-568.

Citation:

Chen Liangsen, Zhao Xinghua, Fu Minfu. The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 559-568.

Citation:

Chen Liangsen, Zhao Xinghua, Fu Minfu. The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 559-568.

PDF( 409 KB)

The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations

1.
Institute of Engineering Mechanics, University of Nanchang, Nanchang 330029, P R China;
2.
Shanghai Institute of Appl Math Mech, Shanghai University, Shanghai 200072, P R China

Received Date: 1998-04-14
Publish Date: 1999-06-15

Abstract

Abstract

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.
- objective rates,
- elastic-plastic constitutive relation,
- simple shear oscillation

FullText(HTML)

References(9)

References

[1]	Agah-Tehrani A, Lee E H, Mallett R L. The theory of elastic-plastic deformation of finite strain with induced anisotropy modeled as combined isotropic-kinematical hardening[J].J Mech Phys Solids,1987,35(5):519～539.
[2]	Dienes J K. On the analysis of rotation and stress rate in deforming bodies[J].Acta Mech,1979,32(3-4):217～232.
[3]	Szabo L, Balla M. Comparison of some stress rates[J].Int J Solids Struct,1989,25(3):279～297.
[4]	陈良森,赵兴华.带弹性范围物质理论和背应力的定义[J].应用数学和力学,1999,21(5):452～460.
[5]	扶名福,杨德品,黄模佳.有限变形模糊损伤弹塑性[M].北京:航空工业出版社,1995,20～21.
[6]	Casey J, Naghdi P M. Further constitutive results in finite plasticity[J]. Q J Mech Appl Math,1984,37(2):231～259.
[7]	Casey J, Naghdi P M. On the relationship between the Eulerian and Lagrangian description of finite rigid plasticity[J].Arch Rational Mech Anal,1988,102(4):351～375.
[8]	Nagtegaal J C, De Jong J E. Some aspects of nonisotropic work hardening in finite strain plasticity[A].In: Proc Workshop on Plasticity of Metals at Finite Strain[C].Div Appl Mech Stanford University,Rensselaer Polytechnic Institute,65,1982,56～106.
[9]	Nemat-Nasser S. On finite plastic flow of crystalline solids and geomaterials[J].J Appl Mech,1983,50(4b):1114～1126。

Relative Articles

[1]	ZHANG Guangjiang, YANG Deze, CHU Xihua. Study on Constitutive Relations and Boundary Value Problems of Granular Materials Based on Artificial Neural Networks[J]. Applied Mathematics and Mechanics, 2024, 45(2): 155-166. doi: 10.21656/1000-0887.440248
[2]	WANG Xiaoming, XIAO Heng. Comprehensive Simulation of Shape Memory Alloys Based on a Finite Elastoplastic Model[J]. Applied Mathematics and Mechanics, 2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067
[3]	ZHENG Ying-ren, KONG Liang, LIU Yuan-xue. Plastic Constitutive Relation and Plastic Constitutive Theory for Engineering Materials[J]. Applied Mathematics and Mechanics, 2014, 35(7): 713-722. doi: 10.3879/j.issn.1000-0887.2014.07.001
[4]	JIANG Wu-gui, HUANG Ming-hui. Analysis of Simple Shear Endochronic Equations for Finite Plastic Deformation[J]. Applied Mathematics and Mechanics, 2005, 26(1): 77-82.
[5]	SHEN Xin-pu, SHEN Guo-xiao, CHEN Li-xin. Investigation on Elasto-Plastic Constitutive Model Coupled With Damage for Localization Phenomena[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1249-1256.
[6]	LI Fan-chun, ZHAO Wen-sheng, TANG Long-sheng. Elastic-Viscoplastic Fieds Near The Tip of a Propagating Crack Under Anti-Plane Shear[J]. Applied Mathematics and Mechanics, 2004, 25(9): 983-990.
[7]	ZHOU Wang-min, FAN Tian-you, YIN Shu-yuan. Crack Problem Under Shear Loading in Cubic Quasicrystal[J]. Applied Mathematics and Mechanics, 2003, 24(6): 637-643.
[8]	LIU Teng-xi, HUANG Shi-qing, FU Yi-ming. The Constitutive Equations for Mixed Hardening Orthotropic Material[J]. Applied Mathematics and Mechanics, 2003, 24(2): 192-196.
[9]	CAI Xian-hui, WU Rui-feng, XU Shi-bin. Research on the Inelastic Seismic Responses of Shear-Type Multistorey Buildings With Regular Asymmetry[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1129-1134.
[10]	SHEN Xin-pu, Zenon Mroz, XU Bing-ye. Constitutive Theory of Plasticity Coupled With Orthotropic Damage for Geomaterials[J]. Applied Mathematics and Mechanics, 2001, 22(9): 927-933.
[11]	Chen Liangsen, Zhao Xinghua. A Mathematical Theory of Materials with Elastic Range and the Definition of Back Stress Tensor[J]. Applied Mathematics and Mechanics, 1999, 20(5): 452-460.
[12]	Shen Lijun, Pan Lizhou, He Fubao. Study on the Generalized Prandtl-Reuss Constitutive Equation and the Corotational Rates of Stress Tensor[J]. Applied Mathematics and Mechanics, 1998, 19(8): 689-696.
[13]	Li Fanchun, Qi Hui. The Asymptotic Solution to the Antiplane Shear Dynamic Crack-Tip Field in an Elastic Strain-Softening Viscoplastic Material[J]. Applied Mathematics and Mechanics, 1997, 18(2): 161-167.
[14]	Yin Fuxin, Sun Huanchun. A Condensed Method for Linear Complementary Equations of Elasto-Plastic Problems[J]. Applied Mathematics and Mechanics, 1995, 16(10): 861-871.
[15]	Jiang Chi-ping. Longituanal Shear Problems of Collinear Rigid Line Inclusions in Anisotropic Materials[J]. Applied Mathematics and Mechanics, 1994, 15(2): 147-154.
[16]	Xu Li-gong, Ran Zheng. A Calculating Method of Shock Wave Oscillating Frequency Due to Turbulent Shear Layer Fluctuations in Supersonic Flow[J]. Applied Mathematics and Mechanics, 1991, 12(8): 729-735.
[17]	Zhao Zu-wu. Strain Path Theory of Plastic Constitutive Relation[J]. Applied Mathematics and Mechanics, 1990, 11(7): 581-590.
[18]	Gao Yang, E. T. Onat. Rate Variational Extremum Principles for Finite Elastoplasticity[J]. Applied Mathematics and Mechanics, 1990, 11(7): 617-624.
[19]	Zhang Pei-yuan, Tang Yu. The Constitutive Equation Resemblance of Elastic-Plastic Multiphase Solid[J]. Applied Mathematics and Mechanics, 1990, 11(10): 921-930.
[20]	Tsien Shou-i, Chang Ken-ta. The Elastoplastic Constitutive Relation of Generalized Cap Model for Rock Medium[J]. Applied Mathematics and Mechanics, 1983, 4(3): 369-377.