Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen f�r gro�e elasto-plastische Form�nderungen

Lehmann, Th.

doi:10.1007/bf00533769

Cited by 78 publications

(18 citation statements)

References 24 publications

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“…Earlier, a common choice was the well-known Zaremba-Jaumann rate o r d =/" + rW-Wr with the vorticity tensor ~,u the antisymmetfic part of the velocity gradient. However, Lehmann [8], [9]~ Dienes [4J, and NagtegaaI and de Jong [13] disclosed that elastoplastidty and hypoelasticity models with Zaremba-Jaumann rate predict oscillatory shear stress responses with increasing shear strain. These spurious oscillation phenomena prompted reexamination of basic aspects underlying large strain elastoplasticity models, including the validity of the o decomposition (2.1), the definition of an appropriate stress rate ~*, etc.…”

Section: = (23)mentioning

confidence: 99%

“…Earlier, the Zaremba-Jaumann rate was given prominence. Since unexpected shear oscillation phenomena with monotonically increasing shearing strain were discovered by Lehmann [8], [9], Dienes [4], Nagtegaal and de Jong [13], and others, a number of Eulerian rate type elastoplasticity models at large strains have been proposed using various definitions of stress rates different from the Zaremba-Jaumann rate, such as Oldroyd rate, Cotter-Rivlin rate, Truesdell rate, and Green-Naghdi rate, etc. Usually, the large simple shear problem, which characterizes the large torsion problem of thin-walled cylindrical tubes in a sense of suitable approximation as shown later, is used to test and justify reasonableness and applicability of various models suggested, refer to, e.g., Truesdell [22], Lee, Mallett and Wertheimer [71, Dafalias [3], Loret [11], Atluri [1], Johnson and Bammann [5], Moss [12], Paulun and Pecherski [18], Reed and Atluri [19], Metzger and Dubey [10], Szabd and Balla [21], Tsakmakis and Haupt [23], Yang, Cheng and Hwang [30], Xia and Ellyin [24], and others.…”

Section: Introductionmentioning

confidence: 99%

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Analytical perturbation solution for large simple shear problems in elastic-perfect plasticity with the logarithmic stress rate

2001

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Summary.The large simple shear deformations in elastic-perfectly plastic bodies are studied using the self-consistent elastic-perfectly plastic J2-flow model based on the logarithmic stress rate, recently established by these authors [2]. The application of the logarithmic stress rate in the elastic rate equation of hypoetastic type leads to an exact finite hyperelastic solution. The plastic solution is shown to be governed by a first-order nonlinear ordinary differential equation with a small dimensionless material parameter multiplying the highest derivative, for which the initial condition is related to the elastic-plastic transition and prescribed in terms of the just-mentioned small parameter. A singular perturbation solution is derived for large plastic strain by utilizing the method of matched expansions. The solution obtained is shown to be in a satisfactory manner close to the numerical solution by a Runge-Kutta integration procedure with high accuracy. Remarks are given to explain a phenomenon of instability concerning the shear stress.

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Section: = (23)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical perturbation solution for large simple shear problems in elastic-perfect plasticity with the logarithmic stress rate

2001

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“…When d = 1, = 2 and = 1, the linear elastic anisotropy inspired by Valanis [28], Zysset and Curnier [29] and Bigoni and Loret [30] is recovered. Moreover, when B = I, the linear isotropic elasticity is obtained from Equation (20).…”

Section: The Plastic Dependent Nonlinear Free-energy Densitymentioning

confidence: 99%

“…Moreover, the elastic stiffness degradation observed experimentally by Connoly and Kuwano [32], Kuwano and Jardine [11] and Hoque and Tatsuoka [33] could easily be taken into account in the function d(e p ), as proposed recently by Gajo and Bigoni [13], but this effect was disregarded here because it was felt that further experimental data would be required for a proper calibration of elastic stiffness degradation, especially under cyclic loading. From the elastic potential (20), the stress r can immediately be derived:…”

Section: The Plastic Dependent Nonlinear Free-energy Densitymentioning

confidence: 99%

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Hyperelastic modelling of small‐strain stiffness anisotropy of cyclically loaded sand

Gajo

2009

Num Anal Meth Geomechanics

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SUMMARYExperimental evidence shows that soil stiffness at very small strains is strongly anisotropic and depends on the stress level and void ratio. In particular, stiffness anisotropy varies considerably in sand when subjected to cyclic loading, following the stress cycles applied. To model this behaviour, an innovative hyperelastic formulation based on the elastoplastic coupling is incorporated in a new kinematic hardening elastoplastic model. The proposed hyperelastic-plastic model is the first to be capable of correctly simulating all aspects of the small-strain behaviour of granular materials subjected to monotonic and cyclic loads. This hyperelastic formulation is generally applicable to any elastoplastic model.

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A particle-in-cell solution to the silo discharging problem

Więckowski

Youn

Yeon

1999

Int. J. Numer. Meth. Engng.

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The problem of ow of a granular material during the process of discharging a silo is considered in the present paper. The mechanical behaviour of the material is described by the use of the model of the elasticplastic solid with the Drucker-Prager yield condition and the non-associative ow rule. The phenomenon of friction between the stored material and the silo walls is taken into account-the Coulomb model of friction is used in the analysis. The problem is analysed by means of the particle-in-cell method-a variant of the ÿnite element method which enables to solve the pertinent equations of motion on an arbitrary computational mesh and trace state variables at points of the body chosen independently of the mesh. The method can be regarded as an arbitrary Lagrangian-Eulerian formulation of the ÿnite element method, and overcomes the main drawback of the updated Lagrangian formulation of FEM related to mesh distortion. The entire process of discharging a silo can be analysed by this approach. The dynamic problem is solved by the use of the explicit time-integration scheme. Several numerical examples are included. The plane strain and axisymmetric problems are solved for silos with at bottoms and conical hoppers. Some results are compared with experimental ones.In the past, the problem was analysed under some assumptions leading to signiÿcant simpliÿcation, or even disregard of the principles of continuum mechanics. Simple expressions for stress and velocity distributions are given, for example by Jenike and Shield [1] and Walters [2].Recently, the problem has been analysed on the basis of continuum mechanics by several authors. The related initial-boundary value problems are solved using numerical techniques, in particular the ÿnite element method. As pioneering works on this ÿeld, those written by Eibl and co-workers [3; 4] should be cited here. In the ÿnite element method, two di erent descriptions of motion have been used in the analysis of the considered problem: the Eulerian description, and the Lagrangian one. In the Eulerian description, the granular material is treated as a non-classical uid [3-6]the analysis is most useful in the case of continuous reÿlling a silo with the material. When the Lagrangian description is used [6][7][8], the solid model of the granular material is applied; in this case the whole discharging process can be analysed.Another approach, based on the discrete element formulation, has been suggested recently by Langston et al. [9;10], where material grains are modelled as spherical and cylindrical particles. This technique seems to be useful when the ratio between the diameters of the silo outlet and the material grain is not high.In the present paper, the entire process of discharging a silo is analysed. The ow of a granular material in a silo is highly distorted. This causes severe problems in computational modelling of such a process. When the updated Lagrangian formulation of the ÿnite element method is used to describe this large displacement, large strain problem, the original...

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Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen f�r gro�e elasto-plastische Form�nderungen

Cited by 78 publications

References 24 publications

Analytical perturbation solution for large simple shear problems in elastic-perfect plasticity with the logarithmic stress rate

Analytical perturbation solution for large simple shear problems in elastic-perfect plasticity with the logarithmic stress rate

Hyperelastic modelling of small‐strain stiffness anisotropy of cyclically loaded sand

A particle-in-cell solution to the silo discharging problem

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