Numerical simulation of a synthetic jet with OpenFoam

Numerical simulations of flow surrounding a synthetic jet actuating device are presented. By modifying a dynamic mesh technique available in OpenFoam-a well-documented open-source solver for fluid dynamics, detailed computations of the sinusoidal motion of the synthetic jet diaphragm were possible. Numerical solutions were obtained by solving the two dimensional incompressible viscous N-S equations, with the use of a second order implicit time marching scheme and a central finite volume method for spatial discretization in both streamwise and crossflow directions. A systematic parametric study is reported here, in which the external Reynolds number, the diaphragm amplitude and frequency, and the slot dimensions are varied.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.

Physically-sound simulation of low-velocity impact on fiber reinforced laminates

A high-fidelity virtual tool for the numerical simulation of low-velocity impact damage in unidirectional composite laminates is proposed. A continuum material model for the simulation of intraply damage phenomena is implemented in a numerical scheme as a user subroutine of the commercially available Abaqus finite element package. Delaminations are simulated using of cohesive surfaces. The use of structured meshes, aligned with fiber directions allows the physically-sound simulation of matrix cracks parallel to fiber directions, and their interaction with the development of delaminations. The implementation of element erosion criteria and the application of intraply and interlaminar friction allow for the simulation of fiber splits and their entanglement, which in turn results in permanent indentation in the impacted laminate. It is shown that this simulation strategy gives sound results for impact energies bellow and above the Barely Visible Impact Damage threshold, up to laminate perforation conditions

Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates

Open Access funded by European Research Council Acknowledgements RB thanks GRADUS, Faculty 8.4. Natural Sciences, of Saarland University for partially funding his research visit to the University of California, Santa Barbara. RB would also thank to Dr. S. Khaderi for his help in setting up the model. He also thanks Dr. R. Hensel and Dr. N. Guimard for fruitful discussions and for their continuous support. EA acknowledges funding from the European Research Council under the European Union's Seventh Framework Program (FP/2007-2013)/ERC Advanced Grant no. 340929.

A general additive distance with time-reversibility and rate variation among nucleotide sites.

As additivity is a very useful property for a distance measure, a general additive distance is proposed under the stationary time-reversible (SR) model of nucleotide substitution or, more generally, under the stationary, time-reversible, and rate variable (SRV) model, which allows rate variation among nucleotide sites. A method for estimating the mean distance and the sampling variance is developed. In addition, a method is developed for estimating the variance-covariance matrix of distances, which is useful for the statistical test of phylogenies and molecular clocks. Computer simulation shows (i) if the sequences are longer than, say, 1000 bp, the SR method is preferable to simpler methods; (ii) the SR method is robust against deviations from time-reversibility; (iii) when the rate varies among sites, the SRV method is much better than the SR method because the distance is seriously underestimated by the SR method; and (iv) our method for estimating the sampling variance is accurate for sequences longer than 500 bp. Finally, a test is constructed for testing whether DNA evolution follows a general Markovian model.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.

Refinement of finite element analysis of automobile structures under crash loading. Volume I. Summary final report.

National Highway Traffic Safety Administration, Washington, D.C.

Development of a passenger vehicle finite element model.

Transportation Department, Washington, D.C.

Finite element modeling of motor vehicles. Protocol for developing INGRID data input desks for DYNA3D computer code. Final report.

Federal Highway Administration, Office of Safety and Traffic Operations Research Development, McLean, Va.

Refinement of finite element analysis of automobile structures under crash loading. Volume II. Final technical report.

National Highway Traffic Safety Administration, Washington, D.C.

A finite element head injury model. Volume II: computer program documentation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Validation and application of the WRECKER nonlinear finite element program in analyzing vehicle side structures. Vol. I - summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Validation and application of the WRECKER nonlinear finite element program in analyzing vehicle side structures. Vol. II - technical report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.