FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-yWe present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.Peer ReviewedPostprint (author's final draft

Continuum modelling using the discrete element method. theory and implementation in an object-oriented software platform

The Discrete Element Method is a relatively new technique that has nowadays and intense research in the field of numerical methods. In its first conception, the method was designed for simulations of dynamic system of particles where each element is considered to be an independent and non-deformable entity that interacts with other particles by the laws of the contact mechanics and moves following the second Newton’s law. This first approach for the DEM has obtained excellent results for granular media simulations or another discontinuouslike case. The existing challenge nowadays for the DEM is to be able to simulate the behaviour on a continuous media discretized by a mesh of particles ruled by the equations of the DEM. Although there exist more adequate methods to solve the continuous problem as they are the different variants of the Finite Element Method, the DEM is expected to have a better behaviour when the failure of the media occurs; in terms of tracking the evolution of the fracture locally between the elements of the discretization and also the post-fractural behaviour of the material. Nowadays, there are several DEM codes that try to solve this problem although there is no one which can assure an accurate solution applicable universally to any case. The objective of the present work is to develop calculation software for the Discrete Element Method included in the platform for numerical methods KRATOS, which is developed in CIMNE. One of the goals of the so-called DEM-Application is to be able to reproduce a wide set of engineering problems; not only the discrete ones such as the excavation or agroalimentary applications but also to reproduce the continuous media, simulating compression test for concrete or asphalt samples for instance. In addition it is desired that the application permits the coupling with another methods, particularly the Finite Element Method. In order to do this, the present work includes the study of all the advances and ideas that, globally in the numerical method field and particularly in CIMNE, have been discussed to give other approaches and to keep improving and developing the to the Discrete Element Method

On the theory of cell migration: durotaxis and chemotaxis

Cell migration is a fundamental element in a variety of physiological and pathological processes. Alteration of its regulatory mechanisms leads to loss of cellular adhesion and increased motility, which are critical steps in the initial stages of metastasis, before a malignant cell colonizes a distant tissue or organ. Consequently, cell migration has become the focus of intensive experimental and theoretical studies; however the understanding of many of its mechanism remains elusive. Cell migration is the result of a periodic sequence of protrusion, adhesion remodeling and contraction stages that leads to directed movement of cells towards external stimuli. The spatio-temporal coordination of these processes depends on the di erential activation of the signaling networks that regulate them at specific subcellular locations. Particularly, proteins from the family of small RhoGTPases play a central role in establishing cell polarization, setting the direction of migration, regulating the formation of adhesion sites and the generation of the forces that drive motion. Theoretical models based on an independent description of these processes have a limited capacity to predict cellular behavior observed in vitro, since their functionality depends intrinsically on the cross-regulation between their signaling pathways. This thesis presents a model of cell migration that integrates a description of force generation and cell deformation, adhesion site dynamics and RhoGTPases activation. The cell is modeled as a viscoelastic body capable of developing active traction and protrusion forces. The magnitude of stresses is determined by the activation level of the RhoGTPases, whose distribution in the cell body is described by a set of reaction-di usion equations. Adhesion sites are modeled as punctual clusters of transmembrane receptors that dynamically bind and unbind the extracellular matrix depending on the force transmitted to them and the distance with ligands on the substrate. Onthe theoretical level, the major findings concern the relationship between the topology of a crosstalk scheme and the properties, as defined in [1], inherited by the associated reaction network as a gradient sensing and regulatory system: persistent and transient polarization triggered by external gradients, adaptation to uniform stimulus, reversible polarization, multi-stimuli response and amplification. This leads to models that remain functional against the biological diversity associated to di erent cell types and matches the observed cell behaviour in Chemotaxis essays [2, 3, 4, 5]: the capacity of cells to amplify gradients, polarize without featuring Turing patterns of activation, and switch the polarization axis and the direction of migration after the source of the external stimulus is changed. The RhoGTPase model, derived on theoretical premises, challenges a long held view on the mechanisms of RhoGTPase crosstalk and suggests that the role of GDIs, GEFs and GAPs has to be revised. Recent experimental evidence supports this idea[6]. In addition, the model allows to recapitulate a continuous transition between the tear-like shape adopted by neutrophiles and the fan-like shape of keratocytes during migration [7] by varying the relative magnitudes of protrusion and contraction forces or, alternatively, the strength of RhoGTPase Crosstalk. The second mechanism represents a novel explanation of the di erent morphologies observed in migrating cells. Di erences in RhoGTPase crosstalk strength could be mediated by di erences between the activity or concentration of GEFs, GAPs and GDIs in di erent cell types; an idea that can be explored experimentally. On cell mechanosensing, a new hypothesis based on a simple physical principle is proposed as the mechanism that might explain the universal preference of cells (bar neurons) to migrate along sti ness gradients. The theory provides a simple unifying explanation to a number of recent observations on force development and growth in real time at cell Focal adhesions [8, 9, 10, 11]. The apparently conflicting results have been attributed to the di erences in experimental set-ups and cell types used, and have fueled a longstanding controversy on how cells prove the mechanical properties of the extra-cellular matrix. The predictions of the theory recapitulate these experimental observations, and its founding hypothesis can be tested experimentally. This hypothesis directly suggests the mechanism that could explain the preference of cells to migrate along sti ness gradients, and for the first time, a plausible biological function for its existence. This phenomenon is known as Durotaxis, and its abnormal regulation has been associated to the malignant behaviour of cancer cells. &nbsp

Simple and efficient numerical tools for the analysis of parachutes

This work describes a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural solver for unsteady simulations of ram-air type parachutes. For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly non-linear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness. An added benefit of the proposed aerodynamic and structural techniques is that they can be easily vectored and thus suitable for use in parallel architectures. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique

A 3D low-order panel method for unsteady aerodynamic problems

An unsteady low-order panel method for three-dimensional subsonic analyses is presented. The method, which is based on well-established techniques in computational aerodynamics, is intended to achieve a cost-effective solution of unsteady flows around arbitrary aerodynamic configurations. This work has two main objectives. First, to relax geometry discretization requirements and, second, to simplify the treatment of problems in which the analysis configuration moves along specified flight paths and/or changes its geometry during the simulation. Following this aim, a time-marching solution procedure is adopted in conjunction with a free-wake model which avoids iterative solutions for wake shape and position. The suitability of the present approach for solving typical aerodynamic problems is illustrated by means of several numerical examples

Application of explicit FE codes to simulation of sheet and bulk metal forming processes

This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences reported here have been gained during the development and use of our own explicit program Stampack. An original formulation of a triangular shell element without rotational degrees of freedom is reviewed combining the explicit sheet forming simulation with the implicit springback analysis as well as the parallelization of the explicit program described. An extension of a finite element code for coupled thermomechanical analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. Numerical examples illustrate some of the possibilities of the finite element code developed

Tratamiento numérico de los Materiales Compuestos

La principal dificultad que se encuentra en el momento de diseñar estructuras con materiales compuestos es la falta de modelos constitutivos que permitan si- mular su comportamiento.  Las técnicas analíticas convencionales utilizadas para el estudio de materiales simples isótropos no resultan adecuadas para el análisis de materiales compuestos. Tampoco ha resultado satisfactoria la representación de un compuesto mediante un único material ortótropo con propiedades del conjunto. Puede observarse en distintas referencias los intentos que ha habido para modelar el comportamiento de materiales compuestos, utilizando la técnica de elementos fi- nitos para el análisis y diseño de estructuras, donde la correlación entre los análisis y los resultados experimentales no resulta satisfactoria (Ali, 1996) (Klintworth y Macmillian, 1992). El proceso de diseño de componentes en materiales compuestos se ha basado, principalmente, en métodos empíricos, observándose en la literatura la ausencia de análisis o simulaciones del comportamiento de materiales compuestos sometidos a niveles de esfuerzos que sobrepasan el límite elástico. &nbsp

A four-noded quadrilateral element for composite laminated plates/shell using the refined zigzag theory

A new bilinear 4-noded quadrilateral element (called QLRZ) for the analysis of composite laminated and sandwich plates/shells based on the refined zigzag theory (RZT) proposed by Tessler et al. [1] is presented. The element has seven kinematic variables per node. Shear locking is avoided by introducing an assumed linear shear strain field. The performance of the element is studied in several examples where the reference solution is the 3D finite element analysis using 20-noded hexahedral elements. Finally, the capability for capturing delamination effects is analyzed