zbMATH — the first resource for mathematics

On constitutive relations at finite strain: Hypo-elasticity and elasto- plasticity with isotropic or kinematic hardening. (English) Zbl 0571.73001
Author reconsiders ”generalizing” of the constitutive relations of infinitesimal strain theories of classical plasticity with isotropic or kinematic hardening, and elasto-plasticity, to the finite strain case in order to develop theories that are physically plausible and overcome such anomalies as stresses that are oscillatory in time. Such stresses arise in some treatments of the topic. Paper has mostly to do with choice of stress rates in such generalizations. Hypo-elastic materials are also considered. Detailed numerical examples are presented.
A thorough, detailed treatment of interest to research engineers familiar with other fundamental works in the field.
Reviewer: R.H.Lance

74A20 Theory of constitutive functions in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
74B20 Nonlinear elasticity
Full Text: DOI
[1] Nagtegaal, J.C.; de Jong, J.E., Some aspects of non-isotropic workhardening in finite strain plasticity, (), 65-102
[2] Lee, E.H.; Mallett, R.L.; Wertheimer, T.B., Stress analysis for anisotropic hardening in finite-deformation plasticity, rept., (1982) · Zbl 0524.73046
[3] Lee, E.H., Finite deformation effects in plasticity theory, (), 75-90
[4] Rubinstein, R.; Atluri, S.N., Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analysis, Comput. meths. appl. mech. engrg., 36, 277-290, (1983) · Zbl 0486.73081
[5] Atluri, S.N., ()
[6] Truesdell, C., The simplest rate theory of pure elasticity, Comm. pure appl. math., 8, 123-132, (1955) · Zbl 0064.42003
[7] Oldroyd, J.G., On the formulation of rheological equations of state, (), 523-541 · Zbl 1157.76305
[8] Cotter, B.A.; Rivlin, R.S., Tensors associated with time-dependent stress, Quart. appl. math, 13, 177-182, (1955) · Zbl 0065.39603
[9] Truesdell, C.; Noll, W., The nonlinear field theories of mechanics, () · Zbl 0779.73004
[10] Dienes, J.K., On the analysis of rotation and stress rate in deforming bodies, Acta mech., 32, 217-232, (1979) · Zbl 0414.73005
[11] Atluri, S.N., On some new general and complementary energy theorems for the rate problem of classical, finite strain elastoplasticity, J. structural mech., 8, 1, 36-66, (1980)
[12] Truesdell, C., Hypo-elasticity, J. rational mech. anal., 4, 83-133, (1955), (see some corrections, 1019-1020). · Zbl 0064.42002
[13] Truesdell, C., Hypo-elastic shear, J. appl. phys., 27, 441-447, (1956)
[14] Rivlin, R.S., Further remarks on the stress-deformation relations for isotropic materials, J. rational mech. anal., 4, 681-702, (1955) · Zbl 0064.42101
[15] Hill, R., On the classical constitutive relations for elastic/plastic solids, (), 241, (The Folke Odquist Volume)
[16] McMeeking, R.M.; Rice, J.R., Finite element formulations for problems of large elastic-plastic deformation, Internat. J. solids and structures, 11, 601-616, (1975) · Zbl 0303.73062
[17] Thomas, T.Y.; Thomas, T.Y., On the structure of stress-strain relations, and combined elastic and Prandtl-reuss stressstrain relations, (), 720-726, resp. · Zbl 0065.18007
[18] Prager, W., A new method of analyzing stresses and strains in work-hardening plastic solids, J. appl. mech., 23, 493-496, (1956) · Zbl 0074.41003
[19] Arygris, J.H.; Doltsinis, J.St., On the large strain inelastic analysis in natural formulation—part I. quasistatic problems, Comput. meths. appl. mech. engrg., 20, 213-251, (1980) · Zbl 0437.73065
[20] Argyris, J.H.; Doltsinis, J.St.; Pimenta, P.M.; Wüstenberg, H., Thermomechanical response of solids at high strains—natural approach, Comput. meths. appl. mech. engrg., 32, 3-57, (1982) · Zbl 0505.73062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.