A large deformation theory for rate-dependent elastic–plastic materials with combined isotropic and kinematic hardening

Henann, David L.; Anand, Lallit

doi:10.1016/j.ijplas.2008.11.008

Cited by 73 publications

(65 citation statements)

References 28 publications

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“…In particular it was shown by Henann and Anand (2009) that the 3-dimensional tensorial version of this variable, A, is equivalent to an "energetic" plastic left Cauchy-Green tensor (or Finger tensor). The defect variable A evolves as the accumulated plastic strain γ p in the material varies.…”

Section: An Elasto-plastic Materials With Kinematic Hardening (Kh Mmentioning

confidence: 99%

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

Dimitriou

Ewoldt²,

McKinley

2013

Journal of Rheology

233

160

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Large Amplitude Oscillatory Shear (LAOS) is used as a tool to probe the nonlinear rheological response of a model elasto-viscoplastic material (a Carbopol microgel). In contrast to most recent studies, these large amplitude measurements are carried out in a stress-controlled manner. We outline a descriptive framework of characterization measures for nonlinear rheology under stress-controlled LAOS, and this is contrasted experimentally to the strain-controlled framework that is more commonly used. We show that this stress-controlled methodology allows for a physically intuitive interpretation of the yielding behavior of elasto-viscoplastic materials. The insight gained into the material behavior through these nonlinear measures is then used to develop two constitutive models that prescribe the rheological response of the Carbopol microgel. We show that these two successively more sophisticated constitutive models, which are based on the idea of strain decomposition, capture in a compact manner the important features of the nonlinear rheology of the microgel. The second constitutive model, which incorporates the concept of kinematic hardening, embodies all of the the essential behaviors exhibited by Carbopol. These include elasto-viscoplastic creep and time-dependent viscosity plateaus below a critical stress, a viscosity bifurcation at the critical stress, and Herschel-Bulkley flow behavior at large stresses.

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Section: An Elasto-plastic Materials With Kinematic Hardening (Kh Mmentioning

confidence: 99%

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

Dimitriou

Ewoldt²,

McKinley

2013

Journal of Rheology

233

160

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“…Obviously an isotropic hardening may be added to the theory with no difficulty through a derivative k which may be function of e p . For brevity we refer to the discussion on the nature of this hardening (which may be related to a defect energy) given in Gurtin et al (2010) and in Hennan and Anand (2009), see also Vladimirov et al (2010) for a different but more usual approach.…”

Section: The Principle Of Maximum Dissipationmentioning

confidence: 99%

“…As noted in Refs. (Hennan and Anand, 2009) and (Gurtin et al, 2010), the invariance principle does not apply to the intermediate configuration (at least in anisotropy). Aside, the intermediate configuration is uniquely obtained through "time" integration of the constitutive equations.…”

Section: Multiplicative Decomposition and Strain Rate Tensorsmentioning

confidence: 99%

“…A similar reasoning (but of more complex interpretation) may be employed in the decomposition of the plastic deformation gradient into an energetic and a dissipative part, as considered in Vladimirov et al (2010), Lion (2000), Hennan and Anand (2009) …”

Section: Multiplicative Decomposition and Strain Rate Tensorsmentioning

confidence: 99%

“…The resulting (modified) plastic velocity gradient, plastic deformation rate and plastic spin tensors are then divided into energetic and dissipative contributions. The formulation is established from a decomposition similar to (but different from) that of Lion (2000) which was used recently by Hennan and Anand (2009) and Vladimirov et al (2010) to model the Armstrong and Frederick rule in isotropic elastoplasticity and anisotropic elastoplasticity respectively, see also therein references. However, our formulation, for which we justify our preference, allows for a simpler interpretation and procedure.…”

Section: Introductionmentioning

confidence: 99%

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A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

Montáns

Benítez

Caminero

2012

Mechanics Research Communications

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In this paper we present a continuum theory for large strain anisotropic elastoplasticity based on a decomposition of the modified plastic velocity gradient into energetic and dissipative parts. The theory includes the Armstrong and Frederick hardening rule as well as multilayer models as special cases even for large strain anisotropic elastoplasticity. Texture evolution may also be modelled by the formulation, which allows for a meaningful interpretation of the terms of the dissipation equation.

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References

2012

Introduction to Finite Strain Theory for Continuum Elasto‐Plasticity

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A large deformation theory for rate-dependent elastic–plastic materials with combined isotropic and kinematic hardening

Cited by 73 publications

References 28 publications

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

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