Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Soil Behaviour and Critical State Soil Mechanics

Discrete particle simulation of particulate systems: Theoretical developments

With reference to practical engineering problems it is shown that considerable differences may be encountered between the results from associated and those from nonassociated plasticity theories. Next, the need for a non-associated plasticity theory is demonstrated by considering test results for sand, concrete and rock. Elementary material parameters are discussed such as Young's modulus and Poisson's ratio for the description of the elastic properties; and a cohesion and a friction angle for the determination of the strength. The salient difference from associated plasticity theory concerns the introduction of a dilatancy angle which controls the inelastic (plastic) volume changes. This dilatancy angle is not only a suitable parameter for the description of soils, but also appears to be useful for concrete and rock. Basically, the paper consists of three parts as we consider three types of models of increasing complexity. The first model is a perfectly-plastic model, which employs the five aforementioned parameters. It is based on test data rather than on Drucker's hypothesis of material stability. The consequences thereof are examined. The second model is a straightforward extension of the first model by augmenting it with friction hardening and cohesion softening. This novel idea is introduced to account for the degradation of the cohesion of cemented granular materials with increasing inelastic deformation. The model is employed in an analysis which shows that plastic deformations tend to localize in thin shear bands, which may occur even before peak strength is reached. Finally, a review is given of concepts for modelling hysteresis and strain accumulation in cyclic loading. The concept of a bounding surface in addition to a yield surface is discussed and is adapted for use in a sophisticated model for loose and cemented granular materials under cyclic loading.

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Non-Associated Plasticity for Soils, Concrete and Rock

Assessment of rolling resistance models in discrete element simulations

A new constitutive model is introduced which is formulated in the framework of classical theory of plasticity. In the model the total strains are calculated using a stress-dependent stiffness, different for both virgin loading and un-/reloading. The plastic strains are calculated by introducing a multi-surface yield criterion. Hardening is assumed to be isotropic depending on both the plastic shear and volumetric strain. For the frictional hardening a non-associated and for the cap hardening an associated flow rule is assumed.
 First the model is written in its rate form. Therefor the essential equations for the stiffness modules, the yield-, failure- and plastic potential surfaces are given.
 In the next part some remarks are given on the models incremental implementation in the Plaxis computer code. The parameters used in the model are summarized, their physical interpretation and determination are explained in detail.
 The model is calibrated for a loose sand for which a lot of experimental data is available. With the so calibrated model undrained shear tests and pressuremeter tests are back-calculated.
 The paper ends with some remarks on the limitations of the model and an outlook on further developments.

The hardening soil model: Formulation and verification

Finite element solutions of consolidation problems often exhibit oscillating pore pressures, which tend to increase when the time steps are reduced. This phenomenon is investigated and a lower limit for the time steps is derived, in terms of the mesh size and the coefficient of consolidation near the draining boundary.

An accuracy condition for consolidation by finite elements

Freeze-thaw cycling affects the geotechnical properties of soils and must be taken into account when selecting soil parameters for stability and deformation analysis of slopes, embankments and cuts in cold regions, especially those underlain by permafrost. This review examines methods of investigation, testing techniques and the impact of freeze-thaw processes on the physical and mechanical properties of soils. Copyright © 2006 John Wiley & Sons, Ltd.

A review of the influence of freeze-thaw cycles on soil geotechnical properties

An elastoplastic model is established for the initial loading, unloading and reloading of sand. The plastic strains are described as the sum of two independent parts. The most important part of the plastic strains is described by means of a shear yield surface and a non-associated flow rule in which Rowe’s stress-dilatancy equation is incorporated. During continued deformation the shear yield surface changes not only in size but also in shape. Close agreement is obtained with experimental data on yield surfaces. The other part of the plastic strains is purely volumetric. This part accounts for the plastic volume strain in isotropic compression. It cannot be disregarded, particularly in the case of loose sands. Un modele elastoplastique est etabli pour le chargement initial, le dechargement et le rechargement de sable. Les deformations plastiques sont decrites comme la somme de deux parties independantes. La partie la plus importante des deformations plastiques est derite a l'aide d'une surface de cisaille...

Pieter A. Vermeer

Papers

Non-Associated Plasticity for Soils, Concrete and Rock

The hardening soil model: Formulation and verification

An accuracy condition for consolidation by finite elements

A review of the influence of freeze-thaw cycles on soil geotechnical properties

A double hardening model for sand