SWITCHING DEFORMATION MODES IN POST-LOCALIZATION SOLUTIONS WITH A QUASIBRITTLE MATERIAL

Localization in a quasibrittle material is studied using a local second-gradient model. Since localization takes place in a medium assumed to be initially homogeneous, nonuniqueness of the solutions of an initial boundary value problem is then also studied. Using enhanced models generalizes the classical localization analysis. In particular, it is necessary to study solutions more continuous (that is, continuous up to the degree one) than the ones used in analysis involving classical constitutive equations. Within the assumptions done, it appears that localization is possible in the second-gradient model if it is possible in the underlying classical model. Then the study of nonuniqueness is conducted for the numerical problem, using different first guesses in the full Newton‐Raphson procedure solving the incremental nonlinear equations. Thanks to this method, we are able to simulate qualitatively the nonreproducibility of usual experiment in the postpeak regime.

[1]  Robert Charlier,et al.  An algorithm and a method to search bifurcation points in non‐linear problems , 2001 .

[2]  Kazuo Murota,et al.  Imperfect Bifurcation in Structures and Materials , 2002 .

[3]  René Chambon,et al.  Localization criteria for non‐linear constitutive equations of geomaterials , 2000 .

[4]  Jacques Desrues.  La localisation de la déformation dans les milieux granulaires , 1984 .

[5]  S. Sloan,et al.  Bifurcation analysis for shear localization in non-polar and micro-polar hypoplastic continua , 2005 .

[6]  Huajian Gao,et al.  Strain gradient plasticity , 2001 .

[7]  Kaspar Willam,et al.  Localized failure analysis in elastoplastic Cosserat continua , 1998 .

[8]  R. Toupin.  Elastic materials with couple-stresses , 1962 .

[9]  René Chambon,et al.  A second gradient elastoplastic cohesive-frictional model for geomaterials , 2001 .

[10]  René Chambon,et al.  Uniqueness studies in boundary value problems involving some second gradient models , 2004 .

[11]  J. Rice.  Localization of plastic deformation , 1976 .

[12]  René Chambon,et al.  Plastic continuum with microstructure, Local Second Gradient Theories for Geomaterials : Localization Studies , 2001 .

[13]  Paul Steinmann,et al.  On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities , 1997 .

[14]  G. Viggiani,et al.  An experimental investigation of the relationships between grain size distribution and shear banding in sand , 2001 .

[15]  Nada El-Hassan Assoum.  Modélisation théorique et numérique de la localisation de la déformation dans les géomatériaux , 1997 .

[16]  R. de Borst,et al.  Non-linear analysis of frictional materials , 1986 .

[17]  Kazuo Murota,et al.  Mode switching and recursive bifurcation in granular materials , 1997 .

[18]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[19]  Ronaldo I. Borja,et al.  Bifurcation of elastoplastic solids to shear band mode at finite strain , 2001 .

[20]  Robert Charlier,et al.  A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models , 2006 .

[21]  R. Chambon,et al.  Modeling the Post-localization Regime with Local Second Gradient Models: Non-uniqueness of Solutions and Nonpersistent Shear Bands , 2006 .

[22]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[23]  D. Caillerie,et al.  One-dimensional localisation studied with a second grade model , 1998 .

[24]  J. Rudnicki,et al.  Chapter 5 Localization: Shear bands and compaction bands , 2004 .

[25]  Wenxiong Huang,et al.  A study of localized deformation pattern in granular media , 2004 .

[26]  Gioacchino Viggiani,et al.  Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry , 2004 .

[27]  Yuki Yamakawa,et al.  Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids , 2003 .

[28]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[29]  N. Challamel,et al.  Non-local behavior of plastic softening beams , 2005 .

[30]  René Chambon,et al.  A strain space gradient plasticity theory for finite strain , 2004 .

[31]  René Chambon,et al.  Large strain finite element analysis of a local second gradient model: application to localization , 2002 .

[32]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[33]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[34]  René Chambon,et al.  A finite deformation second gradient theory of plasticity , 2001 .