Justification for non-local and gradient constitutive models

[PerennialII]

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 ?

[Astronuc]

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

"Nonlocal approach is recognized as a powerful localization limiter, which is necessary to capture the localized character of a solution, for example in tension regime of quasi-brittle materials. Due to the non-local character (local response depends on material state in the neighborhood), these models require special data exchange algorithms to be developed in order to efficiently handle the non-local dependency between partitions." 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

Standard local constitutive models are inappropriate for materials which exhibit strain-softening behaviour. (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
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2003; 57:103-116

The local formulation is shown to exhibit spurious sensitivity to cell mesh refinements, localization of softening damage into a band of single-cell width, and excessive dependence of energy dissipation on the cellsize. By contrast, the results for the non-local theory are shown to be free of these physically incorrect features. Compared to the classical non-local finite element approach, an additional advantage is that the internal cells need to be introduced only within the small zone (or band) in which the strain-softening damage tends to localize within the structure.

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.

[PerennialII]

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.