On the treatment of non-reciprocal rate-independent kinetics via thermodynamic extremal principles

Hackl, Klaus; Fischer, F.D.; Svoboda, Jiřı́

doi:10.1016/j.jmps.2020.104149

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…The flow rule as a consequence of energy balance. Using the equilibrium conditions (32), the free energy (50) and the dissipation potential (66) in the power balance (40) gives the bulk condition…”

Section: Energetic Formulationmentioning

confidence: 99%

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On the variational modeling of non-associative plasticity

Ulloa

Alessi

Wambacq

et al. 2021

International Journal of Solids and Structures

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In this work, the energetic formulation for rate-independent dissipative materials is extended to consider non-associative plasticity models. In associative models, the fulfilment of the principle of maximum dissipation naturally leads to a variational formulation of the evolution problem. This is no longer true for non-associative models, which are generally presented in the literature in a non-variational form. However, recent studies have unveiled the possibility to recover a variational structure in non-associative plasticity by relying on a suitable state-dependent dissipation potential. Here, this idea is further elaborated in the framework of the energetic formulation, providing a systematic variational approach to non-associative plasticity. A clear link between the classical governing equations of non-associative plasticity and the energetic formulation is established, for which a state-dependent dissipation potential is derived from a generalization of the principle of maximum dissipation. The proposed methodology is then applied to recast specific non-associative plasticity models in variational form, highlighting the flexibility of the formulation. The examples include a Drucker-Prager model with combined isotropic-kinematic hardening and a ratcheting plasticity model. Several thermomechanical insights are provided for both examples. Moreover, exploiting the flexibility of the energetic formulation, extensions to gradient plasticity are devised, leading to representative finite element simulations.

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Section: Energetic Formulationmentioning

confidence: 99%

“…In the latter work, the authors introduce state-dependence by considering certain constraints depending on the thermodynamic driving force. The proposed framework was recently applied to non-associative plasticity in Hackl et al [50].…”

Section: Introductionmentioning

confidence: 99%

On the variational modeling of non-associative plasticity

Ulloa

Alessi

Wambacq

et al. 2021

International Journal of Solids and Structures

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“…Nonassociative plasticity (cf. Reference 13) is included in the variational formulations recently proposed in References 1 and 14 for rate‐independent thermodynamic systems. Variational formulations and slip‐system selection in the gradient‐enhanced crystal plasticity represent another topic, see References 15‐22, which is not addressed here.…”

Section: Introductionmentioning

confidence: 99%

Crystal plasticity algorithm based on the quasi‐extremal energy principle

Petryk

Kursa

2022

Numerical Meth Engineering

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The direct incremental energy minimization in rate‐independent plasticity does not account for the skew‐symmetric part of the tangent stiffness matrix. In crystal plasticity, this corresponds to neglecting the asymmetry of the matrix of interaction moduli for active slip‐systems. This limitation has been overcome in the recently proposed quasi‐extremal energy principle (QEP) applicable to nonpotential problems. In the present article it is shown how to extend QEP to finite increments in the backward‐Euler computational scheme. A related constitutive algorithm is proposed which enables automatic selection of active slip systems using an energetic criterion, along any path of large deformation of a rate‐independent single crystal with a nonsymmetric slip‐system interaction matrix. Numerical examples have been calculated for a fcc single crystal subjected to simple shear or uniaxial tension. The slip system activity predicted by using the QEP algorithm has been found to be more reliable in describing the actual plastic response of metal crystals than conventional rate‐dependent modeling in cases where the selection of active slip‐systems is essential.

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