Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Liu, Chein‐Shan; Chang, Chun-Ming

doi:10.1016/j.ijsolstr.2004.09.035

Cited by 10 publications

(7 citation statements)

References 43 publications

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“…The following section describes the most relevant plasticity yield criteria, with emphasis on their particularities (see [1][2][3][4][5][6][7][8]). …”

Section: Plasticity Yield Criteriamentioning

confidence: 99%

“…An accurate description of the structure, formation and behaviour of a solid elastic-plastic material requires knowledge of the limiting stress, among other facts, it can withstand before it becomes plastic [1][2][3][4][5][6][7][8]. In fact, plasticity concepts are widely used in a number of scientific and engineering field applications (in materials science, physics of solids, mechanical engineering, aeronautical engineering, geophysics, biomechanics and chemistry, among others) [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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A unified approach for plasticity yield criteria on the tangent space to the Cauchy tensor

Luque-Raigon

Campoamor-Stursberg

2011

Mathematics and Mechanics of Solids

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A new model for elucidating the geometrical foundations of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts, in addition to elementary hypotheses based on well-established experimental evidence. Its theoretical development involves the analysis of tensor functions and provides a series expansion that allows the functional stress dependence of plasticity yield criteria to be predicted. The theoretical framework for the model includes a series of spatial coefficients that provide a more flexible theory for in-depth examination of symmetry and anisotropy in compact solid materials. It describes the classical yield criteria (such as those of Tresca, Von Mises, Hosford, Hill, etc.) and accurately describes the anomalous behaviour of metals, such as aluminium, which was elucidated by Hill (Theoretical plasticity of textured aggregates. Math Proc Camb Phil Soc 1979; 85: 179-191). Further, absolutely new instances of stress dependence are predicted; this makes it highly useful for fitting experimental data with a view to studying the phenomena behind plasticity.

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“…The following section describes the most relevant plasticity yield criteria, with emphasis on their particularities (see [1][2][3][4][5][6][7][8]). …”

Section: Plasticity Yield Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A unified approach for plasticity yield criteria on the tangent space to the Cauchy tensor

Luque-Raigon

Campoamor-Stursberg

2011

Mathematics and Mechanics of Solids

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“…On the other hand, a larger q is, a more profound ratcheting effect reveals. In order to suppress the ratcheting and relaxation effects, and get a trade-off between these two tendencies we may decrease the value of q from a larger value q 2 to a smaller value q 1 by letting (Liu and Chang, 2005) qðkÞ ¼ q 1 þ ðq 2 À q 1 Þ expðÀkkÞ; 1 6 q 1 6 q 2 6 2.…”

Section: Strain Ratchetingmentioning

confidence: 99%

Reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting

Liu

2006

International Journal of Solids and Structures

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Perfectly elastoplastic constitutive model is modified through a smoothing factor introduced by Liu [ Liu, C.-S., 2003. Smoothing elastoplastic stress-strain curves obtained by a critical modification of conventional models. Int. J. Solids Struct. 40, 2121Struct. 40, -2145]. The new model allows plasticity to happen in a non-zero-measure yield volume in stress space, rather than that of conventional zero-measure yield surface, and within the yield volume the plastic modulus is varying continuously. It endows a specific strain-hardening rule of flow stress and is able to describe the phenomena of strain hardening, cyclic hardening, the Bauschinger effect, mean-stress relaxation, strain ratcheting, out-of-phase hardening, as well as erasure-of-memory. In order to suppress the over prediction of ratcheting we consider a scalar function of smoothing factor, which can simulate the saturation behavior of uniaxial/multiaxial strain ratcheting. These effects are demonstrated through numerical examples. The existence of stress equilibrium point and limiting surface is a natural result without requiring an extra design. Moreover, the non-linear constitutive equations can be converted into a linear system for augmented stress in the Minkowski space, of which the symmetry group is a proper orthochronous Lorentz group SO o (5, 1). The augmented stress is a time-like vector, moving on hyperboloids inside the cone. When taking the Prager kinematic hardening rule into account we can simulate some cyclic behaviors of SAE 4340 and grade 60 steels within a certain accuracy through the use of only three material constants and a fixed smoothing factor. To simulate the ratcheting behaviors of SS304 stainless steel we allow the smoothing factor to be an exponential decaying function of k.

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“…Such yield models often make their applications more unwieldy manipulations, particularly in relation to wishfully analytical solutions. In order to avoid such problems, many researchers today still prefer to use Hill's quadratic yield model on developing new theories (Alexandrov and Kontchakova, 2005;Atienza et al, 2005;Bocciarelli et al, 2005;Boumaiza et al, 2006;Cao and Wang, 2000;Capsoni et al, 2001;Choi et al, 2006a,b;Colak, 2004;Dafalias, 2000;Deshpande et al, 2001;Haddadi et al, 2006;Han, 2002;Han et al, 2002;Hill, 2000Hill, , 2001Hu and Wang, 2002;Karabin et al, 2003;Khalfallah et al, 2002;Kim et al, 2000;Kleiber et al, 2002;Kuroda, 1997Kuroda, , 1999Tvergaard, 2001, 2004;Legarth, 2003Legarth, , 2004Legarth, , 2005Legarth and Richelsen, 2006;Li and Yu, 2006;Liu and Chang, 2005;Oñate and Flores, 2005;Olso and Kyriakides, 2003;Pickett et al, 2004;Potirniche et al, 2006;Pourboghrat et al, 2000;Singh and Ray, 2002;Song et al, 2005;Sriram and Wagoner, 2000;Stoughton, 2000;Sun et al, 2004;Tamuzs et al,...…”

Section: Introductionmentioning

confidence: 99%

A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals

Hu¹

2007

International Journal of Plasticity

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Non-canonical Minkowski and pseudo-Riemann frames of plasticity models with anisotropic quadratic yield criteria

Cited by 10 publications

References 43 publications

A unified approach for plasticity yield criteria on the tangent space to the Cauchy tensor

A unified approach for plasticity yield criteria on the tangent space to the Cauchy tensor

Reconcile the perfectly elastoplastic model to simulate the cyclic behavior and ratcheting

A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals

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