Numerical Model Reduction and Error Control for Computational Homogenization of Transient Problems

Multiscale modeling is a class of methods useful for numerical simulation of mechanics, in particular, when the microstructure of a material is of importance. The main advantage is the ability to capture the overall response, and, at the same time, account for processes and structures on the underlying fine scales. The FE2 procedure, "finite element squared", is one standard multiscale approach in which the constitutive relation is replaced with a boundary value problem defined on an Representative Volume Element (RVE) which contains the microscale features. The procedure thus involves the solution of finite element problems on two scales: one macroscopic problem and multiple RVE problems, typically one for each quadrature point in the macroscale mesh. While the solution of the independent RVE problems can be trivially parallelized it can still be computationally impractical to solve the two-scale problem, in particular for fine macroscale meshes. It is, therefore, of interest to investigate methods for reducing the computational cost of solving the individual RVE problems, while still having control of the accuracy.In this thesis the concept of Numerical Model Reduction (NMR) is applied for reducing the RVE problems by constructing a reduced spatial basis using Spectral Decomposition (SD) and Proper Orthogonal Decomposition. Computational homogenization of two different transient model problems have been studied: heat flow and consolidation. In both cases the RVE problem reduces to a system of ordinary differential equations, with dimension much smaller than of the finite element system.With the reduced basis and decreased computational time comes also loss of accuracy. Thus, in order to assess results from a reduced computation, it is useful to quantify the error. This thesis focuses solely on estimation of the error stemming from the reduced basis by assuming the fully resolved finite element solution to be exact, thereby ignoring e.g. time- and space-discretization errors. For the linear model problems guaranteed, fully computable, bounds are derived for the error in (i) a constructed "energy" norm and (ii) a user-defined quantity of interest within the realm of goal-oriented error estimation. In the non-linear case approximate, fully computable, bounds are derived based on the linearized error equation.In all cases an associated (non-physical) symmetrized variational problem in space-time is introduced as a "driver" for the estimate. From this residual-based estimates with low computational cost are obtained. In particular, no extra modes than the ones used for the reduced basis approximation are required. The performance of the estimator is demonstrated with numerical examples, and, for both the heat flow problem and the poroelastic problem, the error is overestimated by an order of magnitude, which is deemed acceptable given that the estimate is fully explicit and the extra cost is negligible

Effects of biodiesel fuel temperature on performance and emissions of a compression ignition (CI) engine

Diesel engines are still widely needed and applicable to light duty passenger car and heavy duty vehicles. In recent years, limited supply of fossil fuel makes alternative sources of fuel especially biodiesel receiving a lot of attention in the automotive industry. However, in using biodiesel as fuel had created poor fuel-air mixing that generally will produce lower performance and higher emissions than diesel fuel. This is associated with the fuel properties especially viscosity that higher compared to diesel fuel. The aim of this present research was to investigate the effects of preheated biodiesel based crude palm oil (B5, B10 and B15) at 40oC, 50oC and 60oC on performance and emissions of diesel engine at three different load conditions, which are 0% load, 50% load and 100% load. A four-cylinder four strokes cycle, water cooled, direct injection engine was used for the experiments. The results showed that the maximum performance produced was at 0% load condition with the 60oC of heating temperature by B10 where the torque, flywheel torque and brake power increased by 11.55%, 11.42% and 4.16% respectively compared to diesel fuel. While for the emissions, the preheat temperature results on the decrement of CO emission for all load conditions and the maximum reduction recorded was 41.2%. However, the increment of fuel temperature promotes to the higher NOx emissions produced and the maximum increment recorded was 51.7%

Computational homogenization of higher-order electro-mechanical materials with built-in generalized periodicity conditions

We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying periodic architected metamaterials. Such theory results in fourth-order governing partial differential equations, and the periodicity conditions involve continuity across the periodic boundary of primal fields (displacement and electric potential) and their normal derivatives, continuity of the corresponding dual generalized forces (tractions, double tractions, surface charge density and double surface charge density). Rather than imposing these conditions numerically as explicit constraints, we develop an approximation space which fulfils generalized periodicity by construction. Our method naturally allows us to impose general macroscopic fields (strains/stresses and electric fields/electric displacements) along arbitrary directions, enabling the characterization of the material anisotropy. We apply the proposed method to study periodic architected metamaterials with apparent piezoelectricity. We first verify the method by directly comparing the results with a large periodic structure, then apply it to evaluate the anisotropic apparently piezoelectricity of a geometrically polarized 2D lattice, and finally demonstrate the application of the method in a 3D architected metamaterial

Efficient computational homogenisation of 2D beams of heterogeneous elasticity using the patch scheme

Modern 'smart' materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science. The multiscale Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately predict the large scale, system level, solutions through computations on only small sparse patches of the given detailed microscale system. Here the microscale system is that of a 2D beam of heterogeneous elasticity, with either fixed fixed, fixed-free, or periodic boundary conditions. We demonstrate that the described multiscale Patch Scheme simply, efficiently, and stably predicts the beam's macroscale, with a controllable accuracy, at finite scale separation. Dynamical systems theory supports the scheme. This article points the way for others to use this systematic non-intrusive approach, via a developing toolbox of functions, to model and compute accurately macroscale system-levels of general complex physical and engineering systems

Caracterización de propiedades mecánicas de un material compuesto de harina de madera-pet mediante homogeneización computacional y pruebas experimentales

52 p.Un compuesto de madera y plástico (WPC) se refiere a una matriz de polímero reforzada con partículas de madera. La madera es atractiva porque tiene una alta relación resistencia-peso, se integra fácilmente en las líneas de producción de plástico existentes y es un recurso renovable. Estos compuestos pueden ser más amigables con el medio ambiente si la matriz y los rellenos provienen de residuos de reciclaje, como el tereftalato de polietileno (PET) y la harina de madera – partículas finas de madera de las industrias de la madera. Debido a que la homogeneización computacional puede reducir los costos de procesamiento y experimentación, este trabajo propone estudiar las propiedades elásticas efectivas (EEP) de un compuesto elaborado a partir de PET y harina de madera de pino Radiata de Chile, utilizando simulaciones de elementos finitos de un volumen elemental representativo (RVE) con condiciones de borde periódicas. Las simulaciones se validan mediante ensayos de flexión estática de 3 puntos, con probetas obtenidas por extrusión e inyección. Aquí se examina el efecto de diferentes fracciones de peso, orientación en el espacio y tamaños de harina de madera. Las predicciones numéricas se confirman empíricamente en el sentido de que los compuestos con mayor contenido de harina de madera y mayor tamaño tienen un módulo de elasticidad más alto. Sin embargo, estos resultados son muy sensibles a la orientación de las partículas. Los enfoques de homogeneización de campo medio de Voigt y Reuss también se dan como límites superior e inferior. Las pruebas experimentales evidencian que las resistencias a la flexión del WPC disminuyen con respecto a las muestras de PET al 100 %, pero estas propiedades se pueden mejorar considerando distribuciones de tamaño de partícula en lugar de un tamaño fijo de harina de madera. //ABSTRACT: A wood-plastic composite (WPC) refers to a polymer matrix reinforced with wood particles. Timber is attractive because it has a high strength to weight ratio, is easily integrated into existing plastic production lines and is a renewable resource. These composites can be further environment-friendly if the matrix and fillers are from recycling waste, such as polyethylene terephthalate (PET) and wood flour – fine particles of wood from woodworking industries. Because computational homogenisation can reduce processing and experimentation costs, this work proposes to study the effective elastic properties (EEP) of a composite made from PET and Chilean Radiate pine’s wood flour, using finite element simulations of a representative volume element (RVE) with periodic boundary conditions. Simulations are validated through a static 3-point bending test, with specimens obtained by extruding and injection. The effect of different weight fractions, orientation space and sizes of wood flour are here examined. Numerical predictions are empirically confirmed in the sense that composites with more wood flour content and bigger size, have higher elastic modulus. However, these results are very sensitive to the orientation of particles. Voigt and Reuss mean-field homogenisation approaches are also given as upper and lower limits. Experimental tests evidence that flexural strengths of WPC decrease respect to 100 % PET specimens, but these properties can be enhanced considering particle-size distributions instead of a fixed size of wood flour

Intelligent active torque control for vibration reduction of a sprayer boom suspension system

The most usual way of protecting crop from diseases is by using chemical method whereby mixture of chemicals and water are sprayed onto crop via nozzles. These nozzles are located consistently along a boom structure oriented perpendicular to the direction of motion to cover large areas. The most important factor on spray distribution pattern is spray boom vibration. Thus, suspension control aims to attenuate the unwanted vibration and should provide improvements in term of distribution uniformity. In this study, a combination of passive and active suspension was considered to create superior performance. A passive suspension was employed to control undesired vertical motion of sprayer boom structure while the roll movement of spray boom was reduced via active suspension. The active suspension system of sprayer was implemented by applying robust active torque control (ATC) scheme that integrates artificial intelligence (AI) methods plus another feedback control technique utilizing proportional-integral-derivative (PID) control. The proposed control system basically comprises of two feedback control loops; an innermost loop for compensation of the disturbances using ATC strategy and an outermost loop for the computation of the desired torque for the actuator using a PID controller. Two AI methods employing artificial neural network (ANN) and iterative learning (IL) were proposed and utilized to compute the estimated inertial parameter of the system through the ATC loop. The research proposes two main control schemes; the first is a combination of ATC and ANN (ATCANN) while the other is ATC and IL (ATCAIL). The suspension system was first modeled and a number of farmland terrains were simulated as the main disturbance components to verify the robustness of the system and sprayer boom dynamic performance related to distribution uniformity. The simulation results both in frequency and time domains show the effectiveness of the proposed ATC schemes in reducing the disturbances and other loading conditions. The control schemes were further implemented experimentally on a developed laboratory spray boom suspension test rig

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements