Strain localization and bifurcation in a nonlocal continuum

Keywords

Bifurcation, Mathematical analysis, Wavelength, Infinitesimal strain theory, Classical mechanics

References

• SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUMRené de Borst — 1991
• Localization of damage in a nonlocal continuumGilles Pijaudier‐Cabot, Laurent Bodé — 1992
• Localized necking in thin sheetsSigurd Støren, J. R. Rice — 1975
• Nonlocal Continuum Damage, Localization Instability and ConvergenceZdeneˇk P. Bazˇant, Gilles Pijaudier‐Cabot — 1988
• Gradient-dependent plasticity: formulation and algorithmic aspectsRené de Borst, H.‐B. Mühlhaus — 1992
• Wave propagation and localization in a rate-dependent cracked medium-model formulation and one-dimensional examplesL.J. Sluys, René de Borst — 1992
• CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALSJohn W. Rudnicki, J. R. Rice — 1975
• Nonlocal damage theoryGilles Pijaudier‐Cabot, Zdeněk P. Bažant — 1987
• Crack-induced anisotropy and scattering in stressed rocks: Effective elastic moduli and attenuationMonique Piau — 1980
• Localization limiters in transient problemsDavid Lasry, Ted Belytschko — 1988
• Some basic principles in the mechanics of solids without a natural timeR. Hill — 1959
• The thickness of shear bands in granular materialsH.-B. Muhihaus, I. Vardoulakis — 1987
• Analytical Solutions for Nonlinear Strain-Gradient Softening and LocalizationH. L. Schreyer — 1990
• Material rate dependence and mesh sensitivity in localization problemsA. Needleman — 1988
• On nonlocal elasticityA. Cemal Eringen, Dominic G. B. Edelen — 1972
• Dynamic Strain Localization in Fluid‐Saturated Porous MediaBenjamin Loret, Jean H. Prévost — 1991
• Wave propagation in a strain-softening bar: Exact solutionZdeněk P. Bažant, Ted Belytschko — 1985
• Stable States and Paths of Structures with Plasticity or DamageZdeněk P. Bažant — 1988
• Localization limiting properties of nonlocal damage modelsGilles Pijaudier‐Cabot, Zdeněk P. Bažant, Ahmed Benallal — 1992
• The thickness of shear bands in granular materialsH.‐B. Mühlhaus, I. Vardoulakis — 1987

Cited by

• Propagation numérique de zones critiques dans un pneumatique par approches multi-modèlesOlivier Jamond — 2011
• Vers un matériau virtuel pour les composites céramiquesMartin Genet — 2010
• Enhanced damage modelling for fracture and fatigueRhj Ron Peerlings — 1999
• Micro-Crack Clustering, Non Local and Gradient Damage ModelsGilles Pijaudier‐Cabot — 2000
• Mécanique de l'endommagement. Théorie du premier gradient et application au bétonBoumediene Nedjar — 1995
• Prévision objective de la rupture ductile en grandes déformations sous sollicitation dynamique : Modèle d'épuisement plastique à taux limitésGermain Court — 2006
• Construction et analyse de modèles d'endommagement à gradientKim Pham — 2010
• Contribuciones a la simulación numérica del fallo material en deformaciones finitas. Modelos elastoplásticosMaría Dolores Gómez Pulido, J. Oliver — 2007
• Modeling the Macroscopic Behavior of ConcreteJ.M. Reynouard, J.F. Georgin, Khalil Haidar — 2013
• Contribuciones a la simulación numérica del fallo material en deformaciones finitas. Modelos degradablesMaría Dolores Gómez Pulido, J. Oliver — 2006
• Development and Validation of a 3D Computational Tool to describe Damage and Fracture due to Alkali-Silica Reaction in Concrete StructuresI. Peyrot — 2006
• 3d nonlocal simulation of ductile crack growth—a numerical realizationHerbert Baaser, Dietmar Groß — 2001
• Nonlocal modelling of fracture in heterogeneous quasi-brittle materialsD. Xenos — 2015
• Contribuciones a la simulación numérica del fallo material en deformaciones infinitesimales: modelos de degradación y daño continuoMaría Dolores Gómez Pulido, J. Oliver — 2006
• From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage modelsKim Pham, Jean‐Jacques Marigo — 2013
• Analysis of non-local models through energetic formulationsÉric Lorentz, S. Andrieux — 2003
• Rate Dependent Damage Model for Concrete in DynamicsJean‐François Dubé, Gilles Pijaudier‐Cabot, Christian La Borderie — 1996
• An Analytical and Numerical Study to Simulate the Evolution of Dynamic Failure with Local Elastodamage ModelsXiangpeng Xin, Zhen Chen — 2000
• Progressive damage in discrete models and consequences on continuum modellingArnaud Delaplace, Gilles Pijaudier‐Cabot, Stéphane Roux — 1996
• A damage model with evolving nonlocal interactionsGiang D. Nguyen — 2011

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