带弹性范围物质理论和背应力定义

A Mathematical Theory of Materials with Elastic Range and the Definition of Back Stress Tensor

1.
Institute of Engineering Mechanics, Nanchang University, Nanchang 330029, P R China;
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要: 在推广Lucchesi和Podio-Guidugli(1988)的带弹性范围物质理论的基础上,表明了背应力作为Cauchy应力空间中屈服面“中心”的定义存在问题.背应力是Lagrange型变量,只能定义在Lagrange型应力空间上.
- 带弹性范围物质理论 /
- 弹塑性本构 /
- 背应力
Abstract: In this paper,the theory of materials with elastic range by Lucchesi and Podio-Guidugli (1988) has been generalized.It has also shown that there are some difficulties on the definition of back stress as the"center" of the yield surface in the Cauchy space.The back stress tensor is Lagrangian,and must be defined in the Lagrangian stress space.
- theory of materials with elastic range /
- elastic-plastic constitutive relation /
- back stress

[1]	Agah-Tehrani A,Lee E H,Mallett R L,et al.The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematical hardening[J].J Mech Phys Solids,1987,35(5):519～539.
[2]	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.
[3]	Casey J,Naghdi P M.A prescription for the identification of finite plastic strain[J].Int J Engng Sci,1992,30(10),1257～1278.
[4]	Lucchesi M.Podio-Guidugli P.Materials with elastic range:a theory with view to applications,Part Ⅰ[J].Arch Rational Mech Anal,1988,102(1):23～43.
[5]	Nemat-Nasser S.On finite plastic flow of crystalline solids and geomaterials[J].J Appl Mech,1983,50(4):1114～1126.
[6]	Noll W.A mathematical theory of the mechanical behavior of continuous media[J].Arch Rational Mech Anal,1958,2(3):197～226.
[7]	Zheng Q S.On the generalization of constitutive laws from their arotational forms[J].Acta Mech,1992,91(1-2):97～105.
[8]	Dafalias Y F.Issues on the constitutive formulation at large elsatic-plastic deformations,Part Ⅰ:Kinematics[J].Acta Mech,1987,69(1-4):119～138.
[9]	Dafalias Y F.Issues on the constitutive formulation at large elastic-plastic deformations,Part Ⅱ:Kinematics[J].Acta Mech,1988,73(1-4):121～146.
[10]	Naghdi P M.A critical review of the state of the finite plasticity[J].J Appl Math Phys (ZAMP),1990,4(3):315～394.