scholarly journals A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

2019 ◽  
Vol 121 (5) ◽  
pp. 842-866 ◽  
Author(s):  
Moubine Kotob ◽  
Christelle Combescure ◽  
Matthieu Mazière ◽  
Tonya Rose ◽  
Samuel Forest
Keyword(s):  
Loss Of Ellipticity

scholarly journals Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube

2017 ◽  
Vol 109 (1) ◽  
pp. 31-45 ◽  
Author(s):  
Mustapha El Hamdaoui ◽  
José Merodio ◽  
Ray W. Ogden
Keyword(s):  
Cylindrical Tube ◽  
Loss Of Ellipticity ◽  
Circular Cylindrical Tube

Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part II: Failure Mechanisms

1997 ◽  
Vol 64 (4) ◽  
pp. 763-771 ◽  
Author(s):  
M. W. Schraad ◽  
N. Triantafyllidis
Keyword(s):  
Failure Modes ◽  
Scale Effects ◽  
Unit Cell ◽  
Equilibrium Path ◽  
Planar Lattice ◽  
Loss Of Ellipticity ◽  
Finite Models ◽  
Load Paths ◽  
Periodic Microstructures ◽  
Strain Space

Using the nonlinearly elastic planar lattice model presented in Part I, the influence of scale (i.e., the size of the representative volume, relative to the size of the unit cell) on the onset of failure in periodic and nearly periodic media is investigated. For this study, the concept of a microfailure surface is introduced—this surface being defined as the locus of first instability points found along radial load paths through macroscopic strain space. The influence of specimen size and microstructural imperfections (both geometric and constitutive) on these failure surfaces is investigated. The microfailure surface determined for the infinite model with perfectly periodic microstructure, is found to be a lower bound for the failure surfaces of perfectly periodic, finite models, and an upper bound for the failure surfaces of finite models with microstructural imperfections. The concept of a macrofailure surface is also introduced—this surface being defined as the locus of points corresponding to the loss of ellipticity in the macroscopic (homogenized) moduli of the model. The macrofailure surface is easier to construct than the microfailure surface, because it only requires calculation of the macroscopic properties for the unit cell, at each loading state along the principal equilibrium path. The relation between these two failure surfaces is explored in detail, with attention focused on their regions of coincidence, which are of particular interest due to the possible development of macroscopically localized failure modes.

scholarly journals A Finite Points Method Approach for Strain Localization Using the Gradient Plasticity Formulation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Luis Pérez Pozo ◽  
Andy Campos ◽  
Sheila Lascano ◽  
Sergio Oller ◽  
Antonio Rodríguez-Ferran
Keyword(s):  
Strain Localization ◽  
Scale Parameter ◽  
Material Model ◽  
Gradient Plasticity ◽  
Governing Equations ◽  
Internal Length ◽  
Loss Of Ellipticity ◽  
Internal Length Scale ◽  
Discretization Technique ◽  
Method Approach

The softening elastoplastic models present an unsuitable behavior after reaching the yield strength: unbounded strain localization. Because of the material instability, which is reflected in the loss of ellipticity of the governing partial differential equations, the solution depends on the discretization. The present work proposes to solve this dependency using the meshless Finite Points Method. This meshfree spatial discretization technique allows enriching the governing equations using gradient’s plasticity and introducing an internal length scale parameter at the material model in order to objectify the solution.

Loss of ellipticity and structural transformations in planar simple crystal lattices

2015 ◽  
Vol 227 (1) ◽  
pp. 185-201 ◽  
Author(s):  
E. A. Podolskaya ◽  
A. Yu. Panchenko ◽  
A. B. Freidin ◽  
A. M. Krivtsov
Keyword(s):  
Structural Transformations ◽  
Crystal Lattices ◽  
Loss Of Ellipticity
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