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Patrizio Neff - One of the best experts on this subject based on the ideXlab platform.
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a fourth order gauge invariant gradient plasticity model for polycrystals based on kroner s incompatibility tensor
Mathematics and Mechanics of Solids, 2020Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:In this paper we derive a novel fourth-order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with Isotropic Hardening and Kroner’s incompatibility tenso...
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A canonical rate-independent model of geometrically linear Isotropic gradient plasticity with Isotropic Hardening and plastic spin accounting for the Burgers vector
Continuum Mechanics and Thermodynamics, 2019Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper, we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor $${{\,\mathrm{Curl}\,}}p$$ Curl p giving rise to a non-symmetric nonlocal backstress, and Isotropic Hardening response only depending on the accumulated equivalent plastic strain. The model is fully Isotropic and satisfies linearized gauge invariance conditions, i.e., only true state variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn’s inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain $$\mathbf \varepsilon _p$$ ε p and standard Isotropic Hardening.
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a fourth order gauge invariant gradient plasticity model for polycrystals based on kr oner s incompatibility tensor
arXiv: Analysis of PDEs, 2017Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:In this paper we derive a novel fourth order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with Isotropic Hardening and Kroner's incompatibility tensor $inc(\epsilon_p):= Curl[(Curl \epsilon_p)^T]$, where $\epsilon_p=sym p$ is the symmetric infinitesimal plastic strain tensor and $p$ is the (non-symmetric) infinitesimal plastic distortion. 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 $inc(\epsilon_p)$ and it contains Isotropic Hardening based on the rate of the symmetric infinitesimal plastic strain tensor $\dot{\epsilon_p}$. 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 infinitesimal plastic distortion $\dot{p}$ to their symmetric counterpart $\dot{\epsilon_p}$. 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.
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a canonical rate independent model of geometrically linear Isotropic gradient plasticity with Isotropic Hardening and plastic spin accounting for the burgers vector
arXiv: Analysis of PDEs, 2016Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl(p) giving rise to a non-symmetric nonlocal backstress, and Isotropic Hardening response only depending on the accumulated equivalent plastic strain. The model is fully Isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain sym(p) and standard Isotropic Hardening.
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existence and uniqueness for rate independent infinitesimal gradient plasticity with Isotropic Hardening and plastic spin
Mathematics and Mechanics of Solids, 2010Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:Existence and uniqueness for infinitesimal dislocation based rate-independent gradient plasticity with linear Isotropic Hardening and plastic spin are shown using convex analysis and variational inequality methods. The dissipation potential is extended non-uniquely from symmetric plastic rates to non-symmetric plastic rates and three qualitatively different formats for the dissipation potential are distinguished.
A Meyers - One of the best experts on this subject based on the ideXlab platform.
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Large-strain response of Isotropic-Hardening elastoplasticity with logarithmic rate: Swift effect in torsion
Archive of Applied Mechanics, 2001Co-Authors: O. T. Bruhns, H. Xiao, A MeyersAbstract:Recently, a new Eulerian rate-type Isotropic-Hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all Isotropic Hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular, the second-order effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the Runge–Kutta method. It is shown that the prediction of this model for the shear stress is in good accord with experimental data, but the predicted axial length change is negligibly small and much less than experimental data. This suggests that the strain-induced anisotropy may be the main cause of the Swift effect.
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self consistent eulerian rate type elasto plasticity models based upon the logarithmic stress rate
International Journal of Plasticity, 1999Co-Authors: O. T. Bruhns, H. Xiao, A MeyersAbstract:Abstract The objective of this article is to suggest new Eulerian rate type constitutive models for Isotropic finite deformation elastoplasticity with Isotropic Hardening, kinematic Hardening and combined Isotropic-kinematic Hardening etc. The main novelty of the suggested models is the use of the newly discovered logarithmic stress rate and the incorporation of a simple, natural explicit integrable-exactly rate type formulation of general hyperelasticity. Each new model is thus subjected to no incompatibility of rate type formulation for elastic behaviour with the notion of elasticity, as encountered by any other existing Eulerian rate type model for elastoplasticity or hypoelasticity. As particular cases, new Prandtl-Reuss equations for elastic-perfect plasticity and elastoplasticity with Isotropic Hardening, kinematic Hardening and combined Isotropic-kinematic Hardening, respectively, are presented for computational and practical purposes. Of them, the equations for kinematic Hardening and combined Isotropic–kinematic Hardening are, respectively, reduced to three uncoupled equations with respect to the spherical stress component, the shifted stress and the back-stress. The effects of finite rotation on the current strain and stress and Hardening behaviour are indicated in a clear and direct manner. As illustrations, finite simple shear responses for the proposed models are studied by means of numerical integration. Further, it is proved that, among all possible (infinitely many) objective Eulerian rate type models, the proposed models are not only the first, but unique, self-consistent models of their kinds, in the sense that the rate type equation used to represent elastic behaviour is exactly integrable to really deliver an elastic relation. ©
Issam Doghri - One of the best experts on this subject based on the ideXlab platform.
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numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage
International Journal for Numerical Methods in Engineering, 1995Co-Authors: Issam DoghriAbstract:This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear Isotropic Hardening, non-linear kinematic Hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented acid discussed.
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fully implicit integration and consistent tangent modulus in elasto plasticity
International Journal for Numerical Methods in Engineering, 1993Co-Authors: Issam DoghriAbstract:This paper deals with the numerical integration of a class of rate-independent elasto-plastic models. The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent modulus is obtained by exact linearization of the algorithm. In the case of J 2 elastoplasticity with non-linear Isotropic Hardening and non-linear kinematic Hardening (Chaboche-Marquis model), explicit formulas are derived, without any approximations
Francois Ebobisse - One of the best experts on this subject based on the ideXlab platform.
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a fourth order gauge invariant gradient plasticity model for polycrystals based on kroner s incompatibility tensor
Mathematics and Mechanics of Solids, 2020Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:In this paper we derive a novel fourth-order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with Isotropic Hardening and Kroner’s incompatibility tenso...
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A canonical rate-independent model of geometrically linear Isotropic gradient plasticity with Isotropic Hardening and plastic spin accounting for the Burgers vector
Continuum Mechanics and Thermodynamics, 2019Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper, we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor $${{\,\mathrm{Curl}\,}}p$$ Curl p giving rise to a non-symmetric nonlocal backstress, and Isotropic Hardening response only depending on the accumulated equivalent plastic strain. The model is fully Isotropic and satisfies linearized gauge invariance conditions, i.e., only true state variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn’s inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain $$\mathbf \varepsilon _p$$ ε p and standard Isotropic Hardening.
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a fourth order gauge invariant gradient plasticity model for polycrystals based on kr oner s incompatibility tensor
arXiv: Analysis of PDEs, 2017Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:In this paper we derive a novel fourth order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with Isotropic Hardening and Kroner's incompatibility tensor $inc(\epsilon_p):= Curl[(Curl \epsilon_p)^T]$, where $\epsilon_p=sym p$ is the symmetric infinitesimal plastic strain tensor and $p$ is the (non-symmetric) infinitesimal plastic distortion. 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 $inc(\epsilon_p)$ and it contains Isotropic Hardening based on the rate of the symmetric infinitesimal plastic strain tensor $\dot{\epsilon_p}$. 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 infinitesimal plastic distortion $\dot{p}$ to their symmetric counterpart $\dot{\epsilon_p}$. 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.
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a canonical rate independent model of geometrically linear Isotropic gradient plasticity with Isotropic Hardening and plastic spin accounting for the burgers vector
arXiv: Analysis of PDEs, 2016Co-Authors: Francois Ebobisse, Klaus Hackl, Patrizio NeffAbstract:In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl(p) giving rise to a non-symmetric nonlocal backstress, and Isotropic Hardening response only depending on the accumulated equivalent plastic strain. The model is fully Isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain sym(p) and standard Isotropic Hardening.
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existence and uniqueness for rate independent infinitesimal gradient plasticity with Isotropic Hardening and plastic spin
Mathematics and Mechanics of Solids, 2010Co-Authors: Francois Ebobisse, Patrizio NeffAbstract:Existence and uniqueness for infinitesimal dislocation based rate-independent gradient plasticity with linear Isotropic Hardening and plastic spin are shown using convex analysis and variational inequality methods. The dissipation potential is extended non-uniquely from symmetric plastic rates to non-symmetric plastic rates and three qualitatively different formats for the dissipation potential are distinguished.
O. T. Bruhns - One of the best experts on this subject based on the ideXlab platform.
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Large-strain response of Isotropic-Hardening elastoplasticity with logarithmic rate: Swift effect in torsion
Archive of Applied Mechanics, 2001Co-Authors: O. T. Bruhns, H. Xiao, A MeyersAbstract:Recently, a new Eulerian rate-type Isotropic-Hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all Isotropic Hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular, the second-order effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the Runge–Kutta method. It is shown that the prediction of this model for the shear stress is in good accord with experimental data, but the predicted axial length change is negligibly small and much less than experimental data. This suggests that the strain-induced anisotropy may be the main cause of the Swift effect.
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self consistent eulerian rate type elasto plasticity models based upon the logarithmic stress rate
International Journal of Plasticity, 1999Co-Authors: O. T. Bruhns, H. Xiao, A MeyersAbstract:Abstract The objective of this article is to suggest new Eulerian rate type constitutive models for Isotropic finite deformation elastoplasticity with Isotropic Hardening, kinematic Hardening and combined Isotropic-kinematic Hardening etc. The main novelty of the suggested models is the use of the newly discovered logarithmic stress rate and the incorporation of a simple, natural explicit integrable-exactly rate type formulation of general hyperelasticity. Each new model is thus subjected to no incompatibility of rate type formulation for elastic behaviour with the notion of elasticity, as encountered by any other existing Eulerian rate type model for elastoplasticity or hypoelasticity. As particular cases, new Prandtl-Reuss equations for elastic-perfect plasticity and elastoplasticity with Isotropic Hardening, kinematic Hardening and combined Isotropic-kinematic Hardening, respectively, are presented for computational and practical purposes. Of them, the equations for kinematic Hardening and combined Isotropic–kinematic Hardening are, respectively, reduced to three uncoupled equations with respect to the spherical stress component, the shifted stress and the back-stress. The effects of finite rotation on the current strain and stress and Hardening behaviour are indicated in a clear and direct manner. As illustrations, finite simple shear responses for the proposed models are studied by means of numerical integration. Further, it is proved that, among all possible (infinitely many) objective Eulerian rate type models, the proposed models are not only the first, but unique, self-consistent models of their kinds, in the sense that the rate type equation used to represent elastic behaviour is exactly integrable to really deliver an elastic relation. ©
