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Strain gradient plasticity modeling and finite element simulation of Lüders band formation and propagation

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Abstract

An analytical solution of the problem of the propagation of a Lüders band in an isotropic strain gradient plasticity medium is provided based on a softening–hardening constitutive law. A detailed description is given of the plastic strain distribution in the finite size band front. The solution is shown to be harmonic in the band front and exponential in the band tail. Particular attention is paid to the conditions to be applied at the interface between both regions. This solution is then used to validate finite element simulations of the Lüders band formation and propagation in a plate in tension. The approach is shown to suppress the spurious mesh dependence exhibited by conventional finite element simulations of the Lüders behavior and to provide a finite width band front in agreement with the experimental observations from strain field measurements.

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  1. MINES ParisTech, Centre des Matériaux CNRS UMR 7633, BP 87, 91003, Evry Cedex, France

    Matthieu Mazière & Samuel Forest

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  1. Matthieu Mazière
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  2. Samuel Forest
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Correspondence to Samuel Forest.

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Communicated by Andreas Öchsner.

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Mazière, M., Forest, S. Strain gradient plasticity modeling and finite element simulation of Lüders band formation and propagation. Continuum Mech. Thermodyn. 27, 83–104 (2015). https://doi.org/10.1007/s00161-013-0331-8

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