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Justification for non-local and gradient constitutive models

  1. Jan 1, 2005 #1


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    What do you see as the best explanations for validity of non-local & gradient constitutive models (considering metal plasticity and damage)? On many occations they naturally work much better than traditional models, but I'm looking for other directly physical phenomena based information, not that much one based on validation and verification by experimental results. Identification of characteristics measures by material microstructure etc. is often the taken course, but anything beyond and other than that ?
  2. jcsd
  3. Jan 1, 2005 #2


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    Non-local and gradient vs traditional local CM

    PerenialII, you address an important matter in the modelling of large and small structures.

    The motivation for non-local or gradient constitutive model comes from trying to accurately model systems and predict failures with an approach such as leak-before-break (LBB), or modeling something with a high degree of local plastic deformation, with or without failure (e.g. modeling hot and cold metal forming operations). I came across a few potentially useful references in the public domain.

    1) Parallel and Distributed Computations - http://ksm.fsv.cvut.cz/~dr/papers/Vienna01b/keynote.html
    for Structural Mechanics - A Review
    Zdenek Bittnar, Jaroslav Kruis, Jirí Nemecek, Borek Patzák, Daniel Rypl

    Department of Structural Mechanics
    Faculty of Civil Engineering
    Czech Technical University in Prague
    Thákurova 7, 166 29 Prague, Czech Republic

    from ( http://ksm.fsv.cvut.cz/~dr/papers/Vienna01b/node4.html )

    2) Parallel Explicit Finite Element Dynamics - http://ksm.fsv.cvut.cz/~dr/papers/Poofem/poofem.html
    with Nonlocal Constitutive Models
    Borek Patzák, Daniel Rypl, Zdenek Bittnar

    Czech Technical University in Prague
    Faculty of Civil Engineering
    Thákurova 7, 166 29, Prague

    (from http://ksm.fsv.cvut.cz/~dr/papers/Poofem/node3.html)

    3)Non-local boundary integral formulation for softening damage
    www.civil.northwestern.edu/ people/bazant/PDFs/Upto2003/424.pdf
    Ján Sládek, Vladimír Sládek and Zdeněk P. Bažant
    Int. J. Numer. Meth. Engng 2003; 57:103-116

    I can definitely vouch for the issue of "spurious sensitivity to cell mesh refinements". I work with problems involving large deformations (large strains), severe thermal gradients (~1200°C/mm), high strain rates, and considerable variation in metallurgical properties. On top of that, the loading can be strain-controlled or pressure-loaded, the latter being potentially uncontrolled.

    Thanks for calling this to my attention.
  4. Jan 2, 2005 #3


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    You found some really interesting material ... thanks !

    Non-local etc. methods are something I think we're going to be spending quite a bit of time in the near future (well, already are). Since the borders between discrete & continuous descriptions e.g. in material modeling are becoming ever more vague and new information needs to be poured into material models, these sorts of issues are bounds to arise and need to be addressed.

    Gonna read those refs carefully, some interesting implementations of localization limiters ... the problems that actually made me put up this thread are the instances when you e.g. in FEA introduce a localization limiter within an element implementation, how do you search for valid theoretical descriptions for the implementation and how do you verify and argue that what you got has some merit. For example in strain-softening localization problems this is quite a challenge, qualitative agreement can be attained with some "ease", but trying to find generally valid methods is quite an endeavour (since your localization limiter does present also postulates back to the constitutive model).

    Extremely interesting.
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