Homogenization of a Multiscale Viscoelastic Model with Nonlocal Damping, Application to the Human Lungs

International audienceWe are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam–like elastic material containing millions of air–filled alveoli connected by a tree– shaped network of airways. In this study, the parenchyma is governed by the linearized elasticity equations and the air movement in the tree by the Poiseuille law in each airway. The geometric arrangement of the alveoli is assumed to be periodic with a small period ε > 0. We use the two–scale convergence theory to study the asymptotic behavior as ε goes to zero. The effect of the network of airways is described by a nonlocal operator and we propose a simple geometrical setting for which we show that this operator converges as ε goes to zero. We identify in the limit the equations modeling the homogenized behavior under an abstract convergence condition on this nonlocal operator. We derive some mechanical properties of the limit material by studying the homogenized equations: the limit model is nonlocal both in space and time if the parenchyma material is considered compressible, but only in space if it is incompressible. Finally, we propose a numerical method to solve the homogenized equations and we study numerically a few properties of the homogenized parenchyma model

Additive Photonic Colors in the Brazilian Diamond Weevil, Entimus imperialis

Structurally colored nano-architectures found in living organisms are complex optical materials, giving rise to multi-scale visual effects. In arthropods, these structures often consist of porous biopolymers and form natural photonic crystals. A signature of the structural origin of coloration in insects is iridescence, i.e., color changes with the viewing angle. In the scales located on the elytra of the Brazilian weevil Entimus imperialis (Curculionidae), three-dimensional photonic crystals are observed. On one hand, each of them interacts independently with light, producing a single color which is observed by optical microscopy and ranges from blue to orange. On the other hand, the color perceived by the naked eye is due to multi-length-scale light effects involving different orientations of a single photonic crystal. This disorder in crystal orientations alters the light propagation in such a way that the crystal iridescence is removed. Entimus imperialis is therefore a remarkable example of additive photonic colors produced by a complex multi-scale organic architecture. In order to study this specific natural photonic structure, electron microscopy is used. The structure turns out to be formed of a single type of photonic crystal with different orientations within each scale on the elytra. Our modeling approach takes into account the disorder in the photonic crystals and explains why the structure displays bright colors at the level of individual scales and a non-iridescent green color in the far-field.Structurally colored nano-architectures found in living organisms are complex optical materials, giving rise to multi-scale visual effects. In arthropods, these structures often consist of porous biopolymers and form natural photonic crystals. A signature of the structural origin of coloration in insects is iridescence, i.e., color changes with the viewing angle. In the scales located on the elytra of the Brazilian weevil Entimus imperialis (Curculionidae), three-dimensional photonic crystals are observed. On one hand, each of them interacts independently with light, producing a single color which is observed by optical microscopy and ranges from blue to orange. On the other hand, the color perceived by the naked eye is due to multi-length-scale light effects involving different orientations of a single photonic crystal. This disorder in crystal orientations alters the light propagation in such a way that the crystal iridescence is removed. Entimus imperialis is therefore a remarkable example of additive photonic colors produced by a complex multi-scale organic architecture. In order to study this specific natural photonic structure, electron microscopy is used. The structure turns out to be formed of a single type of photonic crystal with different orientations within each scale on the elytra. Our modeling approach takes into account the disorder in the photonic crystals and explains why the structure displays bright colors at the level of individual scales and a non-iridescent green color in the far-field

Acoustic Properties of Absorbing Materials

Thanks to the progress made in materials research and to the introduction of innovative manufacturing technologies, a wide range of sound-absorbing elements are currently available to adjust the acoustic features of an environment. Nowadays, performance is only one of the required specifications, together with environmental compatibility, longevity, and affordable cost. This book collects the most recent advances in the broad-spectrum characterization of sound-absorbing materials used in civil, industrial, and tertiary applications, by means of experimental, numerical, or theoretical studies

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling

There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed. Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus

Spectral gaps in a double-periodic perforated Neumann waveguide

We examine the band-gap structure of the spectrum of the Neumann problem for the Laplace operator in a strip with periodic dense transversal perforation by identical holes of a small diameter ε>0. The periodicity cell itself contains a string of holes at a distance O(ε) between them. Under assumptions on the symmetry of the holes, we derive and justify asymptotic formulas for the endpoints of the spectral bands in the low-frequency range of the spectrum as ε→0. We demonstrate that, for ε small enough, some spectral gaps are open. The position and size of the opened gaps depend on the strip width, the perforation period, and certain integral characteristics of the holes. The asymptotic behavior of the dispersion curves near the band edges is described by means of a 'fast Floquet variable' and involves boundary layers in the vicinity of the perforation string of holes. The dependence on the Floquet parameter of the model problem in the periodicity cell requires a serious modification of the standard justification scheme in homogenization of spectral problems. Some open questions and possible generalizations are listed.The work has been partially supported by MICINN through PGC2018-098178-B-I00, PID2020-114703GB-I00 and Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S)

Finite element simulation of additive manufacturing with enhanced accuracy

Tesi en modalitat de compendi de publicacionsThis thesis develops numerical methods to improve the accuracy and computational efficiency of the part-scale simulation of Additive Manufacturing (AM) (or 3D printing) metal processes. AM is characterized by multiple scales in space and time, as well as multiple complex physics that occur in three-dimensional growing-in-time geometries, making its simulation a remarkable computational challenge. To this end, the computational framework is built by addressing four key topics: (1) a Finite Element technology with enhanced stress/strain accuracy including the incompressible limit; (2) an Adaptive Mesh Refinement (AMR) strategy accounting for geometric and solution accuracies; (3) a coarsening correction strategy to avoid loss of information in the coarsening AMR procedure, and (4) a GCodebased simulation tool that uses the exact geometric and process parameters data provided to the actual AM machinery. In this context, the mixed displacement/deviatoric-strain/pressure u/e/p FE formulation in (1) is adopted to solve incompressible problems resulting from the isochoric plastic flow in the Von Mises criterion typical of metals. The enhanced stress/strain accuracy of the u/e/p over the standard and u/p FE formulations is verified in a set of numerical benchmarks in iso-thermal and non-isothermal conditions. A multi-criteria AMR strategy in (2) is used to improve computational efficiency while keeping the number of FEs controlled and without the strictness of imposing the commonly adopted 2:1 balance scheme. Avoiding this enables to use high jumps on the refinement level between adjacent FEs; this improves the mesh resolution on the region of interest and keeps the mesh coarse elsewhere. Moving the FE solution from a fine mesh to a coarse mesh introduces loss of information. To prevent this, a coarsening correction strategy presented in (3) restores the fine solution in the coarse mesh, providing computational cost reduction and keeping the accuracy of the fine mesh solution accuracy. Lastly, design flexibility is one of the main advantages of AM over traditional manufacturing processes. This flexibility is observed in the design of complex components and the possibility to change the process parameters, i.e. power input, speed, waiting pauses, among others, throughout the process. In (4) a GCode-based simulation tool that replicates the exact path travelled and process parameters delivered to the AM machiney is developed. Furthermore, the GCode-based tool together with the AMR strategy allows to automatically generate an embedded fitted cartesian FE mesh for the evolving domain and removes the challenging task of mesh manipulation by the end-user. The FE framework is built on a high-performance computing environment. This framework enables to accelerate the process-to-performance understanding and to minimize the number of trial-and-error experiments, two key aspects to exploit the technology in the industrial environment.Esta tesis tiene como objetivo desarrollar métodos numéricos para mejorar la precisión y eficiencia computacionales en simulaciones de piezas fabricadas mediante Manufactura Aditiva (MA), también conocida como Impresión 3D. La manufactura aditiva es un problema complejo que involucra múltiples fenómenos físicos, que se desarolla en múltiples escalas, y cuya geometría evoluciona en el tiempo. Para tal fin, se plantean cuatro objetivos: (1) Desarrollo de una tecnología de elementos finitos para capturar con mayor precisión tanto tensiones como deformaciones en casos en el que el material tiene comportamiento isocórico; (2) Una estrategia de adaptividad de malla (AMR), que busca modificar la malla teniendo en cuenta la geometría y los errores en la solución numérica; (3) Una estrategia para minimizar la aproximación numérica durante el engrosamiento (coarsening) de la malla, crucial en la reducción de tiempos de cómputo en casos de piezas de grandes dimensiones; y (4) Un marco de simulación basado en la lectura de ficheros GCode, ampliamente usado por maquinaria de impresión en procesos de manufactura aditiva, un formato que no sólo proporciona los datos asociados a la geometría, sino también los parámetros de proceso. Con respecto a (1), esta tesis propone el uso de una formulación mixta en desplazamientos /deformación-desviadora / presión (u/e/p), para simular la deposición de materiales con deformación inelástica isocórica, como ocurre en los metales. En cuanto a la medición de la precisión en el cálculo de las tensiones y las deformaciones, en esta tesis se realiza un amplio número de experimentos tanto en condiciones isotérmicas como no isotérmicas para establecer una comparativa entre las dos formulaciones mixtas, u/e/p y u/p. Con respecto a (2), para mejorar la eficiencia computacional manteniendo acotado el número total de elementos finitos, se desarrolla una novedosa estrategia multicriterio de refinamiento adaptativo. Esta estrategia no se restringe a mallas con balance 2:1, permitiendo así tener saltos de nivel mayores entre elementos adyacentes. Por otra parte, para evitar la pérdida de información al proyectar la solución a mallas más gruesas, se plantee una corrección en (3), que tiene como objetivo recuperar la solución de la malla fina, garantizando así que la malla gruesa conserve la precisión obtenida en la malla fina. El proceso de manufactura aditiva se distingue por su gran flexibilidad comparándolo con otros métodos tradicionales de manufactura. Esta flexibilidad se observa en la posibilidad de construir piezas de gran complejidad geométrica, optimizando propiedades mecánicas durante el proceso de deposición. Por ese motivo, (4) se propone la lectura de ficheros en formato GCode que replica la ruta exacta del recorrido del láser que realiza la deposición del material. Los ingredientes lectura de comandos escritos en lenguaje Gcode, multicriterio de adaptividad de malla y el uso de mallas estructuradas basadas en octrees, permiten capturar con gran precisión el dominio discreto eliminando así la engorrosa tarea de generar un dominio discreto ad-hoc para la pieza a modelar. Los desarrollos de esta tesis se realizan en un entorno de computación de altas prestaciones (HPC) que permite acelerar el estudio de la ejecución del proceso de impresión y por ende reducir el número de experimentos destructivos, dos aspectos clave que permiten explorar y desarrollar nuevas técnicas en manufactura aditiva de piezas industriales.Postprint (published version

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully