Analytical stress solutions of a closed deformation path with stretching and shearing using the hypoelastic formulations

被引:22
作者
Lin, RC [1 ]
Schomburg, U
Kletschkowski, T
机构
[1] GKSS Forschungszentrum Geesthacht GmbH, Inst Werkstoffforsch, D-21502 Geesthacht, Germany
[2] Univ Bundeswehr, D-22039 Hamburg, Germany
关键词
hypoelasticity; spin tensor; corotational coordinate frame; objective stress rate;
D O I
10.1016/S0997-7538(03)00031-7
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
In the present work a set of hypoelastic analytical stress solutions of a closed deformation path, consisting of four deformation phases with stretching and shearing, is developed. The rate constitutive equations, based on the Oldroyd, Truesdell, Cotter-Rivlin, Jaumann, Green-Naghdi and logarithmic stress rates, are exploited. According to a representation principle of the material spin tensors, issued in Mao et al. (1998a, 1998b), a set of new and concise representation equations of the spin tensors for the four deformation phases is derived. The derived spin equations play a crucial role for formulating the hypoelastic closed-form corotational-rate-based stress solutions of the specific deformation path. The analytical stress solutions as functions of the deformation phases are illustrated and complete comparisons between the residual stresses at the end of the deformation path are performed. These analytical stress solutions, as a set of living examples of applying the hypoelastic equations, support the conclusion that in all spatial hypoelastic rate equations only the one based on the logarithmic stress rate is consistent with elasticity. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.
引用
收藏
页码:443 / 461
页数:19
相关论文
共 20 条
[1]  
BELYTSCHKO T, 2000, NONLINEAR FINITE ELE, P134
[2]  
Bemstein B., 1960, ARCH RATION MECH AN, V6, P90
[3]   RELATIONS BETWEEN HYPO-ELASTICITY AND ELASTICITY [J].
BERNSTEIN, B .
TRANSACTIONS OF THE SOCIETY OF RHEOLOGY, 1960, 4 :23-28
[4]   ANALYSIS OF ROTATION AND STRESS RATE IN DEFORMING BODIES [J].
DIENES, JK .
ACTA MECHANICA, 1979, 32 (04) :217-232
[5]   STUDIES OF FINITE-ELEMENT PROCEDURES - STRESS SOLUTION OF A CLOSED ELASTIC STRAIN PATH WITH STRETCHING AND SHEARING USING THE UPDATED LAGRANGIAN JAUMANN FORMULATION [J].
KOJIC, M ;
BATHE, KJ .
COMPUTERS & STRUCTURES, 1987, 26 (1-2) :175-179
[6]  
LEHMANN T, 1991, EUR J MECH A-SOLID, V10, P395
[7]   REMARKS ON GENERAL CLASS OF MASS LAWS FOR LARGE ELASTOPLASTIC FORM CHANGES [J].
LEHMANN, T .
INGENIEUR ARCHIV, 1972, 41 (04) :297-&
[8]  
Lehmann T., 1972, ROMANIAN J TECHN SCI, V17, P1077
[9]  
Lin RC, 2002, INT J NUMER METH ENG, V55, P1053, DOI [10.1002/nme.536, 10.1002/mne.536]
[10]  
LIN RC, 2002, THESIS U FEDERAL ARM