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A finite strain model of combined viscoplasticity and rate-independent plasticity without a yield surface

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Abstract

A new internal variable formulation dealing with mechanisms with different characteristic times in solid materials is proposed within a finite deformation framework. The framework relies crucially on the consistent combination of a general viscoplastic theory and a rate-independent theory (generalized plasticity) which does not involve the yield surface concept as a basic ingredient. The formulation is developed initially in a material setting and then is extended to a covariant one by applying some basic elements and results from the tensor analysis on manifolds. The covariant balance of energy is systematically employed for the derivation of the mechanical state equations. It is shown that unlike the case of finite elasticity, for the proposed formulation the covariant balance of energy does not yield the Doyle–Ericksen formula, unless a further assumption is made. As an application, by considering the material (intrinsic) metric as a primary internal variable accounting for both elastic and viscoplastic (dissipative) phenomena within the body, a constitutive model is proposed. The ability of the model in simulating several patterns of the complex response of metals under quasi-static and dynamic loadings is assessed by representative numerical examples.

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Authors and Affiliations

  1. Department of Civil Engineering, Demokritos University of Thrace, 12 Vassilissis Sofias Street, 67100, Xanthi, Greece

    V. P. Panoskaltsis & D. Soldatos

  2. Autonomic and Grid Computing, Athens Information Technology, 19002, Peania, Greece

    L. C. Polymenakos

Authors
  1. V. P. Panoskaltsis
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  2. L. C. Polymenakos
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  3. D. Soldatos
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Correspondence to V. P. Panoskaltsis.

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Panoskaltsis, V.P., Polymenakos, L.C. & Soldatos, D. A finite strain model of combined viscoplasticity and rate-independent plasticity without a yield surface. Acta Mech 224, 2107–2125 (2013). https://doi.org/10.1007/s00707-012-0767-0

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  • DOI: https://doi.org/10.1007/s00707-012-0767-0

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