A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures

Eterovic, Adrian Luis; Bathe, Klaus‐Jürgen

doi:10.1002/nme.1620300602

Cited by 312 publications

(192 citation statements)

References 23 publications

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“…This coupled constitutive model is implemented in the hyperelastic large strain framework in a corotational formulation with the total Lagrange formalism, which was shown to be easily implemented in finite element codes (Eterovic and Bathe, 1990;Cuitino and Ortiz, 1992). The modeling strategy involves the following elements:…”

Section: Introductionmentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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A large strain hyperelastic phenomenological constitutive model is proposed to model the highly nonlinear, rate-dependent mechanical behavior of amorphous glassy polymers under isothermal conditions. A corotational formulation is used through the total Lagrange formalism. At small strains, the viscoelastic behavior is captured using the generalized Maxwell model. At large strains beyond a viscoelastic limit characterized by a pressure-sensitive yield function, which is extended from the Drucker-Prager one, a viscoplastic region follows. The viscoplastic flow is governed by a non-associated Perzyna-type flow rule incorporating this pressure-sensitive yield function and a quadratic flow potential in order to capture the volumetric deformation during the plastic process. The stress reduction phenomena arising from the post-peak plateau and during the failure stage are considered in the context of a continuum damage mechanics approach.The post-peak softening is modeled by an internal scalar, so-called softening variable, whose evolution is governed by a saturation law. When the softening variable is saturated, the rehardening stage is naturally obtained since the isotropic and kinematic hardening phenomena are still developing. Beyond the onset of failure characterized by a pressure-sensitive failure criterion, the damage process leading to the total failure is controlled by a second internal scalar, so-called failure variable. The final failure occurs when the failure variable reaches its critical value. To avoid the loss of solution uniqueness when dealing with the continuum damage mechanics formalism, a non-local implicit gradient formulation is used for both the softening and failure variables, leading to a multi-mechanism non-local damage continuum. The pressure sensitivity considered in both the yield and failure conditions allows for the distinction under compression and tension loading conditions. It is shown through experimental comparisons that the proposed constitutive model has the ability to capture the complex behavior of amorphous glassy polymers, including their failure.

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Section: Introductionmentioning

confidence: 99%

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

Nguyễn

Lani

Pardoen

et al. 2016

International Journal of Solids and Structures

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“…For the isotropic elastic stress-strain law it can be shown that [1,4]: with the following stress expressions which follow from the dissipation inequality…”

Section: Constitutive Frameworkmentioning

confidence: 99%

“…where f , f are the yield functions defined respectively in the spatial and the rotated descriptions, b E is the elastic Finger tensor, L v means the Lie derivative,γ ,λ are consistency parameters (the flow tensors are taken as unitary) and β, B are the back stresses in the spatial and rotated configurations respectively [4], i.e.,…”

Section: Constitutive Frameworkmentioning

confidence: 99%

“…Note that using the principal rotated configuration (using Eq. 10) requires the solution of an eigenproblem [7] whereas in the other approaches this computation may be avoided through the use of proper approximations for the exponential and logarithmic functions of a tensor [3,4] and the explicit solution for the square root of a tensor [9] (all of them independent of whether the eigenvalues are equal or not). On the other hand, no advantage is obtained in kinematic hardening using the configuration of Eq.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

“…Different strain functions have been used, but those based on the logarithmic strains are of special interest. Their additive nature [2] and the use of the exponential mapping for the flow rule made possible the use of small strain algorithms for the plastic part; see Weber and Anand [3], Eterović and Bathe [4]. Similar frameworks have been used by different authors, among them we cite the works of Perić, Owen and Honnor [5], Cuitiño and Ortiz [6], and Simó [7].…”

Section: Introductionmentioning

confidence: 99%

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On the stress integration in large strain elasto-plasticity

Montáns¹,

Bathe²

2003

Computational Fluid and Solid Mechanics 2003

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We briefly compare three algorithms for large strain elastoplastic analysis in which the logarithmic strain tensor is used to measure the deformations. The first and second algorithms are based on using, respectively, the elastic stretch matrices in the right basis and left basis of the polar decomposition of the trial elastic deformation gradient, and the third algorithm uses the left basis and the Finger deformation tensor.

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Exponential Map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals

Miehé

1996

Int. J. Numer. Meth. Engng.

140

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SUMMARYThis paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity.The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp : sI(3) -+ SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of singlecrystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the retum algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.

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A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures

Cited by 312 publications

References 23 publications

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

On the stress integration in large strain elasto-plasticity

Exponential Map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals

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