Stabilized MorteX method for mesh tying along embedded interfaces

We present a unified framework to tie overlapping meshes in solid mechanics applications. This framework is a combination of the X-FEM method and the mortar method, which uses Lagrange multipliers to fulfill the tying constraints. As known, mixed formulations are prone to mesh locking which manifests itself by the emergence of spurious oscillations in the vicinity of the tying interface. To overcome this inherent difficulty, we suggest a new coarse-grained interpolation of Lagrange multipliers. This technique consists in selective assignment of Lagrange multipliers on nodes of the mortar side and in non-local interpolation of the associated traction field. The optimal choice of the coarse-graining spacing is guided solely by the mesh-density contrast between the mesh of the mortar side and the number of blending elements of the host mesh. The method is tested on two patch tests (compression and bending) for different interpolations and element types as well as for different material and mesh contrasts. The optimal mesh convergence and removal of spurious oscillations is also demonstrated on the Eshelby inclusion problem for high contrasts of inclusion/matrix materials. Few additional examples confirm the performance of the elaborated framework

Computational strategies toward the modelling of the intervertebral disc

Lumbar back pain has considerable socio-economical impacts, motivating a recently increasing interest from the research community. Yet, mechanisms triggering pain are not fully understood and this considerably hinders the development of efficient treatments and therapies. The objective of this thesis is to participate to the general understanding of the biomechanics of the spine through the development of computational strategies for the intervertebral disc. The intervertebral disc is a complex structure mainly comprised of the nucleus pulposus and the annulus fibrosus. The nucleus pulposus is the gelatinous core of the disc, which consists of a charged and hydrated extra-cellular matrix and an ionised interstitial fluid. It is enclosed in the annulus fibrosus which is formed by concentric layers of aligned collagen fibre sheets, oriented in an alternating fashion. A biphasic swelling model has been derived using mixture theory for soft, hydrated and charged tissues in order to capture the salient characteristics of the disc's behaviour. The model fully couples the solid matrix under finite deformations with the ionised interstitial fluid. The nucleus is assumed to behave isotropically while the effects of the collagen fibres in the annulus fibrosus are accounted for with a transversely isotropic model. The fixed negative charges of the proteoglycans, which induce an osmotic pressure responsible for the swelling capabilities of the disc, are constitutively modelled under the simplifying Lanir hypothesis. A Newton-Raphson solver was specifically built to solve the resulting nonlinear system of equations, together with a verification procedure to ensure successful implementation of the code. This was first reduced to the one dimensional case in order to demonstrate the appropriateness of the biphasic swelling model. The three dimensional model exhibited numerical instabilities, manifesting in the form of non-physical oscillations in the pressure field near boundaries, when loads and free-draining boundary conditions are simultaneously applied. As an alternative to considerable mesh refinement, these spurious instabilities have been addressed using a Galerkin Least-Square formulation, which has been extended for finite deformations. The performance and limitations of the GLS framework, which drastically reduces the pressure discrepancies and prevents the oscillations from propagating through the continuum, are demonstrated on numerical examples. Finally, the current state of the model's development is assessed, and recommendations for further improvements are proposed

Scénariser les 4 piliers de la pédagogie

International audienceLa scénarisation des activités pédagogiques constitue un domaine de recherche stimulant à la croisée de l'informatique et des sciences humaines. Nous constatons que les activités pédagogiques traditionnelles relèvent de plusieurs niveaux de préoccupation : l'organisation générale de l'activité, les étapes d'apprentissage proprement dit, l'observation des comportements des apprenants et de leur appropriation des enseignements, et enfin de l'évaluation de l'activité autant sur le plan des connaissances acquises ou confortées, que des méthodes de travail mises en jeu pour cela ou de la façon de collaborer pour y parvenir. Nous formulons l'hypothèse que les activités pédagogiques en ligne peuvent être modélisées de façon modulaire selon ces quatre piliers fondamentaux « organisation, apprentissage, observation et évaluation » et qu'en corollaire il est possible d'exprimer ces différents points de vue avec un seul et même langage de modélisation pédagogique, LDL répondant pour sa part à cette proposition

Modélisation de scénarios pédagogiques collaboratifs

Cet article part du besoin d'exprimer des scénarios d'apprentissage collaboratif par les enseignants animant des classes virtuelles afin de favoriser la réutilisation et le partage des pratiques pédagogiques. Il propose une démarche conduite par les modèles conformément aux préconisations du Model Driven Architecture de l'OMG. Il présente un méta-modèle basé sur IMS-LD mais enrichi pas les concepts du modèle de participation afin de capturer la richesse des interactions inhérentes aux activités collaboratives. Un modèle de scénario est exprimé à l'aide de ce méta-modèle hybride. Ce modèle sera instancié et pourra être à terme opérationnalisé sur un Espace Numérique de Travail en ligne

A new arc-length control method based on the rates of the internal and the dissipated energy

Purpose - The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach - In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings - The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value - A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion

Description of the 'Planet Game' Case Study and guidelines to the authors

This paper describes the 'Planet Game' case study, also called the 'Astronomy Game', initially proposed to the participants of the workshop "Comparing Educational Modelling Languages on a Case Study" which was held in Heerlen, The Netherlands, during ICALT 2006. This case study is supposed to facilitate the comparison of approaches (model/tool/...). This is only a « framework » that has been sometimes adapted by the authors of the papers of the special issue. This paper gives also guidelines to structure the paper, again to improve the comparison of the approaches for the reader of the special issue.Editors: Laurence Vignollet (Université de Savoie, France)

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

Recently, phase-field approaches have gained popularity as a versatile tool for simulating fracture in a smeared manner. In this paper we give a numerical assessment of two types of phase-field models. For the case of brittle fracture we focus on the question whether the functional that describes the smeared crack surface approaches the functional for the discrete crack in the limiting case that the internal length scale parameter vanishes. By a one-dimensional example we will show that Γ-convergence is not necessarily attained numerically. Next, we turn attention to cohesive fracture. The necessity to have the crack opening explicitly available as input for the cohesive traction-relative displacement relation requires the independent interpolation of this quantity. The resulting three-field problem can be solved accurately on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crack opening. A simple patch test shows that this observation does not necessarily extend to unstructured meshes

A Transversal Analysis of Different Learning Design Approaches

The goal of the ICALT workshop "Comparing Educational Modelling* Languages on a Case Study" was to compare different Learning Design approaches. Various teams were asked to design and implement a common case study and to answer common given challenges. Then, a special issue on "Comparing Educational Modelling Languages on the "Planet Game Case Study"" was proposed to give the workshop challengers the opportunity to describe their solution in more detail. It is now time to make the comparison. Based on an in-depth analysis and many exchanges with the teams involved, this paper introduces the approaches and highlights current challenges in the Learning Design field in connection with the pitfalls included in the case study and the given challenges.Editors: Laurence Vignollet (Université de Savoie, France)

Fluid flow in fractured and fracturing porous media: A unified view

Fluid flow in fractures that pre-exist or propagate in a porous medium can have a major influence on the deformation and flow characteristics. With the aim of carrying out large-scale calculations at reasonable computing costs, a sub-grid scale model has been developed. While this model was originally embedded in extended finite element methods, thereby exploiting some special properties of the enrichment functions, we will herein show that, using proper micro-macro relations, in particular for the mass balance, sub-grid scale models can be coupled to a range of discretisation methods at the macroscopic scale, from standard interface elements to isogeometric finite element analysis