Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

This is the peer reviewed version of the following article: [Aliguer, I., Carol, I., and Sture, S. (2017) Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces. Int. J. Numer. Anal. Meth. Geomech., 41: 918–939. doi: 10.1002/nag.2654.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2654/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed.Peer ReviewedPostprint (author's final draft

Some numerical verification examples for plane stress elasto-viscoplasticity

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This paper will highlight the influence of the strain rate effect occurring during pulse loading on dynamic stability of aluminium profiles. Current work is the development of the analysis carried in [1]. The C–channel cross–section beams/columns are made of 6060 T4, T5, T6 and T66 aluminium alloy. The rectangular–shape compressing pulse is analysed. The static material characteristics had been obtained from the experimental tensile tests and afterwards modified for dynamic response according to Perzyna viscoplastic model. The results of the numerical computations are presented whereas the critical load and DLF (Dynamic Load Factor) basing on the selected dynamic buckling criterion is determined

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Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium thermodynamics, GENERIC, Lie groups, Reference state

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