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| Titel |
Towards a unified solution of localization failure with mixed finite elements |
| VerfasserIn |
Lorenzo Benedetti, Miguel Cervera, Michele Chiumenti, Antonia Zeidler, Jan-Thomas Fischer |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250108128
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| Publikation (Nr.) |
 EGU/EGU2015-7862.pdf |
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| Zusammenfassung |
| Notwithstanding computational scientists made significant steps in the numerical simulation
of failure in last three decades, the strain localization problem is still an open question.
Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is
necessary to provide correct distribution of displacements, to evaluate the stresses in the
ground and, therefore, to be able to identify the slip lines that brings to progressive collapse
of the slope.
Finite elements are an attractive method of solution thanks to profound mathematical
foundations and the possibility of describing generic geometries. In order to account for the
onset of localization band, the smeared crack approach [1] is introduced, that is the strain
localization is assumed to occur in a band of finite width where the displacements are
continuous and the strains are discontinuous but bounded.
It is well known that this kind of approach poses some challenges. The standard
irreducible formulation of FEM is known to be heavily affected by spurious mesh
dependence when softening behavior occurs and, consequently, slip lines evolution is
biased by the orientation of the mesh. Moreover, in the case of isochoric behavior,
unbounded pressure oscillations arise and the consequent locking of the stresses
pollutes the numerical solution. Both problems can be shown not to be related to the
mathematical statement of the continuous problem but instead to its discrete (FEM)
counterpart.
Mixed finite element formulations represent a suitable alternative to mitigate these
drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in
terms of displacements and pressure not only provides a propitious solution to the problem of
incompressibility, but also it was found to possess the needed robustness in case of strain
concentration.
This presentation introduces a (stabilized) mixed finite element formulation
with continuous linear strain and displacement interpolations. As a fundamental
enhancement of the displacement-pressure formulation above mentioned, this kind
of formulation benefits of the following advantages: it provides enhanced rate of
convergence for the strain (and stress) and it is able to deal with incompressible
situations. The method is completed with constitutive laws from Von Mises and
Drucker-Prager local plasticity models with nonlinear strain softening. Moreover,
global and local error norms are discussed to support the advantages of the proposed
method.
Then, numerical examples of stability analysis of slopes are presented to demonstrate the
capability of the method. It will be shown that not only soil slopes can be modeled but also
snow avalanche release and their weak layer fracture can be similarly treated. Consequently,
this formulation appears to be a general and accurate tool for the solution of mechanical
problem involving failure with localization bands [3,4].
References
[1] Y.R. Rashid, “Ultimate strength analysis of prestressed concrete pressure
vessels”, Nuclear Engineering and Design, Volume 7, Issue 4, April, Pages 334-344,
1968.
[2] M. Cervera, M. Chiumenti, D. Di Capua. “Benchmarking on bifurcation and
localization in J 2 plasticity for plane stress and plane strain conditions.” Computer
Methods in Applied Mechanics and Engineering, Vol. 241-244, Pages 206-224,
2012.
[3] L. Benedetti, M. Cervera, M. Chiumenti. “Stress-accurate mixed FEM for soil failure
under shallow foundations involving strain localization in plasticity” Computers and
Geotechnics, Vol. 64, pp. 32–47, 2015.
[4] Cervera, M., Chiumenti, M., Benedetti, L., Codina, R. “Mixed stabilized finite element
methods in nonlinear solid mechanics. Part III: Compressible and incompressible
plasticity” Computer Methods in Applied Mechanics and Engineering, to appear, 2015. |
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