Numerical comparison of isotropic hypo- and hyperelastic-based plasticity models with application to industrial forming processes

Brepols, Tim; Vladimirov, Ivaylo N.; Reese, Stefanie

doi:10.1016/j.ijplas.2014.06.003

Cited by 59 publications

(37 citation statements)

References 98 publications

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“…This is rather cheap as the solution of the 2 2, or 3 3, inverse is given trivially in closed form. It is most certainly cheaper than adding one tensor equation in the non linear system (33). Keeping in mind that the proposed integration is carried out at every integration point for each load step, and at each global Newton-Raphson iteration, the large advantage of the present algorithm in terms of computational effort becomes clear.…”

Section: Remarkmentioning

confidence: 99%

“…In Brepols et al . , the authors found that the results obtained from the simulation of sheet metal forming applications are very close, either by using hyperelastic‐based models or by using the two classical hypoelastic‐based models; Jaumann and Green‐Naghdi rates.…”

Section: Integration Algorithmmentioning

confidence: 99%

“…In the case of large deformation elastoplasticity, with a hypoelastic‐based approach, Equation will be replaced by a linear relationship of an arbitrary objective rate of the Kirchhoff stress τ and the elastic rate of deformation tensor d e . When considering the Jaumann rate as in ABAQUS/Standard, with no essential elastic volume change ( τ ≈ σ ), this leads to .

bold-italicσ^{o} = bold-italic \dot{σ} - bold-italicw bold-italicσ + bold-italicσ bold-italicw = bold-italicD {bold-italicd}^{e},

where w is the skew‐symmetric part of the spatial velocity gradient

bold-italicw = \frac{1}{2} ((), bold-italicl - {bold-italicl}^{T})

…”

Section: Integration Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

Wali

Autay

Mars

et al. 2015

Numerical Meth Engineering

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Summary In this paper, an anisotropic material model based on a non‐associated flow rule and nonlinear mixed isotropic‐kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the non‐associated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on fully implicit backward Euler's method. The resulting problem is reduced to only two simple scalar equations. The consistent local tangent modulus is obtained by exact linearization of the algorithm. All numerical development was implemented into user‐defined material subroutine for the commercial finite element code ABAQUS/Standard. The performance of the present algorithm is demonstrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Remarkmentioning

confidence: 99%

Section: Integration Algorithmmentioning

confidence: 99%

bold-italicσ^{o} = bold-italic \dot{σ} - bold-italicw bold-italicσ + bold-italicσ bold-italicw = bold-italicD {bold-italicd}^{e},

where w is the skew‐symmetric part of the spatial velocity gradient

bold-italicw = \frac{1}{2} ((), bold-italicl - {bold-italicl}^{T})

…”

Section: Integration Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

Wali

Autay

Mars

et al. 2015

Numerical Meth Engineering

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“…The last one is the exact elastoplastic constitutive equation possessing the potential ability of describing the finite elastoplastic deformation and rotation accurately. Therefore, it has been studied widely by Menzel and Steinmann (2003), Wallin et al (2003), Dettmer and Reese (2004), Menzel et al (2005), Wallin and Ristinmaa (2005), Vladimirov et al (2008Vladimirov et al ( , 2010, Hashiguchi and Yamakawa (2012), Brepols et al (2014), etc. after the proposition of the multiplicative decomposition of the deformation gradient tensor into the elastic and the plastic parts by Kroner (1960), Lee and Liu (1967), Lee (1969), Mandel (1971Mandel ( , 1973 and Kratochvil (1973).…”

Section: Introductionmentioning

confidence: 99%

Basic constitutive equation in multiplicative hyperelastic-based plasticity

Hashiguchi

2017

Mechanical Engineering Letters

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The exact formulation of the multiplicative hyperelastic-based plastic constitutive equation is given for the conventional elastoplastic constitutive equation with the yield surface enclosing the purely-elastic domain undergoing the isotropic and the kinematic hardenings in this article. The generalized flow rules for the plastic strain rate and the rate of kinematic hardening variable and their related plastic spins are incorporated in this formulation.

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“…Using these derivations as a starting point further research has been conducted dealing with the elastic-plastic torsion problem , the application of the Sturm's comparison theorem in the finite shear problem Liu and Hong [2001] and the Lie symmetries of the governing equations [Liu, 2004]. Very recent developments are those by Zhu et al [2014]; Xiao et al [2014] dealing with the constitutive modeling of metals under cyclic loadings and Brepols et al [2014] dealing with a material model which can be used in industrial metal forming processes. Related is also the recent work by Shutov and Ihlemann [2014], where the idea of the logarithmic rate is discussed within a recently introduced symmetry concept, namely that of weak invariance.…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

Soldatos

Triantafyllou

2016

Int. J. Appl. Mechanics

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In this work we present a new rate type formulation of large deformation generalized plasticity which is based on the consistent use of the logarithmic rate concept. For this purpose, the basic constitutive equations are initially established in a local rotationally neutralized configuration which is defined by the logarithmic spin. These are then rephrased in their spatial form, by employing some standard concepts from the tensor analysis on manifolds. Such an approach, besides being compatible with the notion of (hyper)elasticity, offers three basic advantages, namely:(i) The principle of material frame-indifference is trivially satisfied.(ii) The structure of the infinitesimal theory remains essentially unaltered.(iii) The formulation does not preclude anisotropic response.A general integration scheme for the computational implementation of generalized plasticity models which are based on the logarithmic rate is also discussed. The performance of the scheme is tested by two representative numerical examples.

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Numerical comparison of isotropic hypo- and hyperelastic-based plasticity models with application to industrial forming processes

Cited by 59 publications

References 98 publications

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

Basic constitutive equation in multiplicative hyperelastic-based plasticity

Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

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