Journal of Theoretical and Applied Mechanics

Volume 38, Numbers 1-2, 2008


Guest Editor: T. Schanz

Bauhaus- University Weimar, Germany








Lorenzo Sanavia


Dipartimento di Costruzioni e Transporti,

Universitá degli Studi di Padova,

Via Marzolo 9, 35-131 Padova, Italy,



Bertrand François


Soil Mechanics Laboratory, Ecole Polytechnique Fédérale Lausanne,

EPFL, 1015 Lausanne, Switzerland,



Roberto Bortolotto Loris Luison


Dipartimento di Costruzioni e Transporti,

Universitá degli Studi di Padova,

Via Marzolo 9, 35-131 Padova, Italy,



Lyesse Laloui


Soil Mechanics Laboratory, Ecole Polytechnique Fédérale Lausanne,

EPFL, 1015 Lausanne, Switzerland,



Finite element modelling of thermo-elasto-plastic water saturated porous materials


Abstract. The purpose of this paper is to present a new finite element formulation for the hydro-thermo-mechanical analysis of elasto-plastic multiphase materials based on Porous Media Mechanics

To this end, the ACMEG-T thermo-plastic constitutive model for saturated soils has been implemented in the finite element code COMES-GEO.

Validation of the implemented model is made by selected comparison between model simulation and experimental results for different combinations of thermo-hydro-mechanical loading paths. A case of non-isothermal elasto-plastic consolidation is also shown.


Key words: thermo-elastoplasticity, water saturated porous materials, finite element method, isotropic compression test, triaxial test, consolidation.

P. Gerard, R. Charlier


Université de Liège, ArGEnCo, Chemin des Chevreuils,

14000 Liège, Belgium,



J-D. Barnichon, K. Su


Agence nationale pour la gestion des déchets radioactifs (ANDRA), France


J-F. Shao, G. Duveau


Laboratoire de Mécanique de Lille, Université de Lille, France


R. Giot


Laboratoire Environnement, Géomécanique et Ouvrages,

Ecole Nationale Supérieure de Géologie de Nancy, France


C. Chavant


EDF, France


F. Collin


Université de Liège, ArGEnCo, Chemin des Chevreuils,

14000 Liège, Belgium,

FNRS Research Associate,



Numerical modelling of coupled mechanics and gas transfer around radioactive waste in long-term storage


Abstract. During long-term storage of radioactive waste, steel containers will be corroded. This process leads to hydrogen production. A boundary value problem has been proposed to study the numerical modelling of the gas migration and its coupling with the mechanical strains and stresses, under isothermal conditions. Biphasic fluid transfer model (considering water, vapour, gaseous hydrogen and dissolved hydrogen) is defined. A 2D axisymmetric case with simplified geometry close to waste disposal in clay is modelled. Fluid transport problem is first resolved. Then, coupled mechanics and fluid transfers are modelled to determine the coupling effects.


Key words: numerical modelling, gas transfer, radioactive waste, hydro-mechanical coupling, two-phase flow model.

L. Beuth, T. Benz, P. A. Vermeer


Universität Stuttgart,

Pfaffenwaldring 35, 70569 Stuttgart, Germany,



Z. Więckowski


Technical University of Łódź,

6, al. Politechniki, 90-924 Łódź, Poland


Large deformation analysis using a quasi-static Material Point Method


Abstract. The Finite Element Method (FEM) has become the standard tool for the analysis of a wide range of solid mechanics problems. However, the underlying structure of a classical updated Lagrangian FEM is not well suited for the treatment of large deformation problems, since excessive mesh distortions can lead to numerical difficulties. The Material Point Method (MPM) represents an approach in which material points moving through a fixed finite element grid are used to simulate large deformations. As the method makes use of moving material points, it can also be classified as a point-based or meshless method. With no mesh distortions, it is an ideal tool for the analysis of large deformation problems. MPM has its origin in fluid mechanics and has only recently been applied to solid mechanics problems. It has been used successfully for impact analyses where bodies penetrate each other and for silo discharging problems. All existing MPM codes found in literature are dynamic codes with explicit time integration and only recently implicit time integration. In this study a quasi-static MPM formulation and implementation are presented. The paper starts with the description of the quasi-static governing equations and the numerical discretisation. Afterwards, the calculation process of the quasi-static MPM is explained, followed by the presentation of some geotechnical boundary value problems which have been solved with the newly developed quasi-static MPM code. The benchmark problems consist of an oedometer test and a slope. For validation, the results are compared with analytical solutions and FEM results, respectively.


Key words: meshless methods, Material Point Method, large deformations.

Ivo Herle


Institute of Geotechnical Engineering, Technische Universität Dresden,

01062 Dresden, Germany,



On Basic features of constitutive models for geomaterials


Abstract. Constitutive models are inevitable for numerical calculations of the mechanical behaviour. A large amount of proposed models makes it difficult to judge their suitability for particular applications. In the paper, several fundamental properties of the soil behaviour (nonlinearity of stress-strain curves and stress envelopes, proportional stress and strain paths, irreversibility and deformation history) are discussed with respect to commonly used models.


Key words: constitutive models, soil behaviour, nonlinearity, irreversibility, proportional paths, deformation history.

A. Zervos


School of Civil Engineering and the Environment,

University of Southampton,

SO17 1BJ, UK,



P. Papanastasiou


Department of Civil and Environmental Engineering,

University of Cyprus,

P.O.Box 20537 Nicosia, 1678, Cyprus,

e-mail: panospap@


I. Vardoulakis


Section of Mechanics, National Technical University of Athens,

Zografou 157 73, Greece,



Shear localisation in thick-walled cylinders under internal pressure based on gradient elastoplasticity


Abstract. We studied failure of thick-walled cylinders under external confinement and internal pressurisation. The material is assumed to be pressure-sensitive with dilatant and strain-softening response. The analysis was carried out using Gradient Elastoplasticity, a higher order theory developed to regularise the ill-posed problem caused by material strain-softening. In this theory the stress increment is related to both the strain increment and its Laplacian. The gradient terms in the constitutive equations introduce an extra parameter of internal length related to material micro-structure, allowing robust modelling of the post-peak material behaviour. The governing equations were solved numerically with the displacement finite element formulation, using C1-continuity elements. Numerical results show that at a critical loading threshold the initial axisymmetry of deformation breaks spontaneously and an instability of finite wavenumber develops. With increasing pressurisation, a curved shear-band of finite thickness forms and propagates progressively towards the outer boundary. For high confining pressures this mode of shear failure is more critical than the trivial tensile failure mode. Practical applications can be found in wellbore stability and hydraulic fracturing in petroleum engineering, and in pile driving design and the interpretation of pressuremeter and penetrometer tests in geotechnical engineering.


Key words: gradient elastoplasticity, gradient plasticity, cavity expansion, shear localisation, strain softening, finite elements.

Manuel Pastor, José A. Fernández Merodo, Bouchra Haddad,

Diego Manzanal, Pablo Mira, Isabel Herreros, V. Drempetic


Grupo M2i, Dpto. de Matemática e Informática Aplicadas a la Ing Civil, Universidad Politécnica de Madrid,



Manuel Pastor, José A. Fernández Merodo, Pablo Mira,

Isabel Herreros, V. Drempetic


Ingeniería Computacional,

Centro de Estudios y Experimentación de Obras Públicas,


José A. Fernández Merodo, Isabel Herreros


Universidad Rey Juan Carlos,


Laura Tonni


Universitá de Bologna


Modelling of fluidized geomaterials: application to fast landslides


Abstract. Fast catastrophic landslides cause many victims and important economic damage around the world every year. It is therefore important to predict their path, velocity and depth in order to provide adequate mitigation and protection measures. The distance travelled by these fluidized avalanches is large in many cases, such as lahars in volcanoes. Three dimensional models are extremely expensive, and depth integrated models provide a reasonable compromise between computational cost and accuracy. One important aspect to model is the constitutive/rheological behaviour of the materials. This paper describes both from the solid and from the fluid dynamics points of view models which can be used to describe fluidized soil behaviour. Concerning initiation or triggering, we describe generalized plasticity models for liquefaction and collapse of loose metaestable soils, as these mechanisms are found in many fast landslides. Once the soil has fluidized, we shall describe its rheological behaviour, giving details of how to obtain depth integrated rheological models


Key words: liquefaction, collapse of loose soils, fluidization, generalized plasticity, rheological models, Bagnold model, critical state.

Wenqing Wang, Olaf Kolditz


Environmental Informatics, Helmholtz Centre for Environmental Research UFZ, Leipzig, D-04318, Germany,



Numerical analysis of strong discontinuity propagation in dilatant media: Enhanced strain finite elements and tracking strategy


Abstract. In this work a new approach is presented for discontinuity propagation in dilatant media. This model is a combination of enhanced strain finite elements and a specific tracking algorithm for discontinuity propagation. A non-associative flow rule is used until onset of discontinuity for plasticity calculation. For the evolution of the discontinuity (i.e. post localization) an associative flow rule is applied to derive a failure model. The material behaviour is represented by Drucker-Prager plasticity. Quadratic smooth functions are utilized in order to improve the kinematic properties of elements having discontinuities. A new discontinuity tracking technique is developed for 2D problems. This algorithm is efficient because tracking takes place only on neighbouring elements of the last ones where discontinuities have occurred. Three applications are presented which cover typical problems from geomechanics, such as biaxial and shear tests as well as footing problems.


Key words: strong discontinuity, discontinuity propagation, tracking, enhanced strain finite elements.

Stavros A. Savidis, Daniel Aubram, Frank Rackwitz


Soil Mechanics and Geotechnical Engineering Division,

Technical University of Berlin,

Secr. TIB1-B7, Building 13b, Gustav-Meyer-Allee 25,

13355 Berlin, Germany,



Arbitrary Lagrangian-Eulerian Finite Element Formulation for Geotechnical Construction Processes


Abstract. The paper presents a numerical approach to the simulation of geotechnical construction processes involving large local deformation of sandy soil. In contrast to standard Lagrangian and Eulerian formulations of the finite element methods, the chosen simple arbitrary Lagrangian-Eulerian (SALE) formulation succeeds in avoiding entanglement of the finite element mesh without disclaiming free surfaces and moving boundaries, by introducing a reference domain uncoupled with the material and the spatial configuration. In order to produce realistic results, the incorporation of an advanced path- and state-dependent constitutive equation for sand is necessary. Furthermore, the treatment of the convective terms, which enter the governing equations, also plays a crucial role. First results of numerical examples highlight the facilities of the SALE framework compared to the classical Lagrangian solution.


Key words: arbitrary Lagrangian-Eulerian, large deformations, finite element method, penetration, sand, constitutive equation.