Comparison of Isotropic Elasto-Plastic Models for the Plastic Metric Tensor  $$C_p=F_p^T\, F_p$$ C p = F p T F p

Neff, Patrizio; Ghiba, Ionel–Dumitrel

doi:10.1007/978-3-319-39022-2_8

Cited by 7 publications

(12 citation statements)

References 37 publications

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“…Based on the results of the present paper, it is clear that the quadratic Hencky energy coupled to multiplicative plasticity will never lose LH-ellipticity in elastic unloading. This claim has been detailed in [36,35,34]. We do not know of any other elastic energy in which the ellipticity domain and the elastic domain coincide in this way.…”

Section: Discussionmentioning

confidence: 92%

An ellipticity domain for the distortional Hencky logarithmic strain energy

2015

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Section: Discussionmentioning

confidence: 92%

An ellipticity domain for the distortional Hencky logarithmic strain energy

2015

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“…The push-forward term in (6b) has been used in Remark 9.4.12 of [8] and Remark 5 of [36], whereas the inelastic metric tensor in (6c) has been analyzed in [10], cf. [37] for a thorough discussion and comparison. All models in (6), however, exhibit a drawback: the influence of the inelastic gradient terms amplifies when inelastic slips evolve and accommodate large inelastic strains.…”

Section: Spurious Hardening From Gradients In the Stored Energymentioning

confidence: 99%

“…The restriction p G < 2 * will be instrumental for (31) and (37). The definition of weak solutions follows directly from (13).…”

Section: Analysis Of the Modelmentioning

confidence: 99%

A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

Davoli

Roubček

Stefanelli

2021

Mathematics and Mechanics of Solids

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Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic strain gradient theories. In particular, we observe that a dependence of the stored energy density on inelastic strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative inelastic model of creep type, where a higher-order energy contribution is provided by the gradients of the elastic strain and of the plastic strain rate, thus preventing the onset of spurious hardening under large slips. The combination of Kelvin–Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model. The existence of weak solutions is proved by way of a Faedo–Galerkin approximation.

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“…In a purely phenomenological context, we have another way to measure the incompatibility of the plastic distortion F p itself via the so-called dislocation density tensor Curl x F p (x) (see for instance [15,16]). Following the works of Davini and Parry [61], Cermelli and Gurtin [14] and Epstein [62], [125][126][127][128] it has been shown that the differential operator (the "true dislocation density tensor") 6 1 det…”

Section: Corresponding Authorsmentioning

confidence: 99%

A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor

Ebobisse

Neff

2019

Mathematics and Mechanics of Solids

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In this paper we derive a novel fourth order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with isotropic hardening and Kröner's incompatibility tensor inc(ε p ) := Curl [(Curl ε p ) T ], where ε p is the symmetric plastic strain tensor. Here, gauge-invariance denotes invariance under diffeomorphic reparametrizations of the reference configuration, suitably adapted to the geometrically linear setting. The model features a defect energy contribution which is quadratic in the tensor inc(ε p ) and it contains isotropic hardening based on the rate of the plastic strain tensorε p . We motivate the new model by introducing a novel rotational invariance requirement in gradient plasticity, which we call micro-randomness, suitable for the description of polycrystalline aggregates on a mesoscopic scale and not coinciding with classical isotropy requirements. This new condition effectively reduces the increments of the non-symmetric plastic distortionṗ to their symmetric counterpartε p = symṗ. In the polycrystalline case, this condition is a statement about insensitivity to arbitrary superposed grain rotations. We formulate a mathematical existence result for a suitably regularized non-gauge-invariant model. The regularized model is rather invariant under reparametrizations of the reference configuration including infinitesimal conformal mappings. Appendix 322 Aifantis writes in [4, p. 218]: "... In conformity with established results -that the plastic strain rateεp is a state variable, rather than the strain εp itself."3 The plastic spin in the finite deformation flow theory of plasticity is defined as the skew-symmetric part of the so-called plastic distortion rate i.e., Wp := skew(ḞpF −1 p ) , while its counter-part in the small strain theory is simply skew(ṗ) , where p is the non-symmetric infinitesimal plastic distortion.

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Comparison of Isotropic Elasto-Plastic Models for the Plastic Metric Tensor $$C_p=F_p^T\, F_p$$ C p = F p T F p

Cited by 7 publications

References 37 publications

An ellipticity domain for the distortional Hencky logarithmic strain energy

An ellipticity domain for the distortional Hencky logarithmic strain energy

A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor

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