This book presents numerical simulations of shear localization in granular materials using a hypoplastic constitutive model enhanced by a characteristic length of the micro-structure in the form of a mean grain diameter. Due to the presence of the characteristic length, the boundary value problems are well-posed, the numerical results are mesh-independent (load-displacement diagrams, spacing and thickness of shear zones), and a deterministic size effect related to the ratio between a mean grain diameter and specimen size is captured.

A comprehensive exposition of the hypoplastic constitutive equation and its extension within the framework of the micro-polar continuum are provided. Problems simulated include: plane strain compression, monotonic and cyclic shearing of an infinite long layer, direct and simple shearing, direct shearing along structure wall, sandpile, strip foundation and earth pressure. Some challenging problems are discussed, e.g. wall boundary conditions, non-coaxiality and stress-dilatancy rule, and textural anisotropy. Moreover, deterministic and statistical size effects are investigated.

Zusammenfassung
This book includes a numerical investigation of shear localization in granular materials within micro-polar hypoplasticity, which was carried out during my long research stay at the Institute of Soil and Rock Mechanics at Karlsruhe University from 1985 to 1996. I dedicate my book to Prof. Gerd Gudehus from Germany, the former head of the Institute of Rock and Soil Mechanics at Karlsruhe University and the supervisor of my scientific research during my stay in Karlsruhe, who encouraged me to deal with shear localization in granular bodies within micro-polar hypoplasticity. I greatly - preciate his profound knowledge, kind help constructive discussions, and collegial attitude to his co-workers. I am thankful to the both series editors: Prof. Wei Wu from Universität für Bodenkultur in Austria and Prof. Ronaldo Borja from Stanford University in USA for their helpful suggestions with respect to the contents and structure of the book. I am also grateful to Dr. Thomas Ditzinger and Mrs. Heather King from the Springer Publishing Company and SPS data processing team for their help in editing this book. Gdansk, Jacek Tejchman June 2008 Contents 1 Introduction......................................................................... 1 2 Literature Overview on Experiments........................................... 11 3 Theoretical Model.................................................................. 47 3.1 Hypoplastic Constitutive Model............................................. 47 3.2 Calibration of Hypoplastic Material Parameters........................... 60 3.3 Micro-polar Continuum.. 67 3.4 Micro-polar Hypoplastic Constitutive Model 72 3.5 Finite ElementImplementation...... 75 4 Finite Element Calculations: Preliminary Results.

Inhalt
Literature Overview on Experiments.- Theoretical Model.- Finite Element Calculations: Preliminary Results.- Finite Element Calculations: Advanced Results.- Epilogue.