Multiscale computational homogenization: review and proposal of a new enhanced-first-order method

This is a copy of the author 's final draft version of an article published in the Archives of computational methods in engineering. The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-016-9205-0The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical boundary value problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. first-order and second-order, in this work an enhanced-first-order computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macro-scale BVP.Peer ReviewedPostprint (author's final draft

Philosophy and citizenship: Analysis of Martha C. Nussbaum’s educational proposal

En el presente Trabajo de Fin de Máster llevaremos a cabo una lectura de la propuesta educativa de Martha C. Nussbaum. La autora defiende que la enseñanza de la filosofía debe estar comprometida con el cultivo de la ciudadanía y de los valores democráticos en los estudiantes. Para este objetivo, Nussbaum elabora tres habilidades o capacidades que el alumno deberá desarrollar en su proceso de formación ciudadana –el autoexamen socrático, la ciudadanía mundial y la imaginación narrativa–. A través de estas habilidades, el estudiante podrá alcanzar una serie de aptitudes –que agrupamos en los bloques de aptitudes políticas, de reconocimiento y cosmopolitismo y de desarrollo personal–, que se consideran fundamentales para la salud democrática de la sociedad. Una vez llevado a cabo la exposición de su propuesta educativa, mostraremos nuestras discrepancias con algunos elementos del análisis realizado por Nussbaum. Concretamente, nos distanciaremos de su diagnóstico sobre el mal del que se adolece la educación, así como de una concepción nouménica del poder que, en algunos puntos –si bien no en todos–, consideramos subyace a la interpretación que Nussbaum hace de la argumentación. Cerraremos nuestro trabajo con una breve propuesta personal –aunque anclada en el valor que Nussbaum concede al teatro– consistente en emplear el teatro del oprimido, de Augusto Boal, como recurso didáctico complementario a la enseñanza teórica del cuestionamiento filosófico a través de grupos de teatro que pueden conformarse en los centros.The current Master’s degree final project will carry out a reading on Martha C. Nussbaum’s educational proposal. The author holds that the teaching of philosphy must be committed with the cultivating of citizenship and democratic values in the students. For this goal, Nussbaum develops three abilities or skills that the student must cultivate in his educational process –socratic self-examination, global citizenship and narrative imagination–. Through these abilities, the student will achieves some aptitudes –which we agroup in politics, of recognizing and cosmopolitism and of personal growth aptitudes–, considered fundamental to keep the democratic health of society. 2 Once done this exposition, we will show our discrepancies with some points of Nussbaum’s analysis. Mainly, we will distance ourselves from her diagnosis of the education disease, and from her conception of noumenal power that, in some placces –but not all of them– we consider that underlies Nussbaum’s interrpretation of argumentation. We will close with a short personal proposal –grounded on the value Nussbaum attaches to the theater–, which consists on use Augusto Boal’s theater of oppressed as a complementary didactic resource to the theoretical teaching of philosophical questioning, from theater groups that can be formed in schools.Fac. de FilosofíaTRUEunpu

Structural analyses of orthogrid fuselage panel for integrated Ku-band SatCom antenna

The aim of this work is to describe the structural analysis of a multifunctional aircraft fuselage panel. The structure of the panel has an embedded antenna tiles. The panel consists of UniDirectional (UD) carbon fibre reinforced composite skin stiffened with ortho-grid ribs, and a transparent skin window made using UD glass fibre reinforced composite. The orthogrid structure is a structural reinforcement but also the antenna tiles support. The presented work proposes a numerical multiscale strategy. The laminate is simulated with solid elements, in order to capture the real kinematics of the material, but several laminas are condensed in a single finite element. The performance of each lamina is obtained using the Serial-Parallel (SP) mixing theory. The specific formulations developed have been very useful to identify and study the mechanical performance of these new structures and the localization of unknown and un-predicted hot-spots in the structure.Postprint (published version

Multi-scale procedure for the mechanical analysis of composite laminate structures considering mixed boundary conditions

This paper presents a multi-scale procedure for the study of flat composite structures with discontinuities. In this procedure, the structure is solved using shell elements while the laminate performance and the structural discontinuities (e.g. connections or change in the laminate thickness) are analysed with a subscale model made with solid 3D elements. The kinematics of both models are coupled following the Kirchhoff–Love theory. This coupling is used during the homogenization procedure where the characteristic behavior of the different micro-models is obtained. Periodical boundary conditions are used for the laminates whereas a combination between periodical and linear boundary conditions are used for the discontinuities. The proposed procedure allows to reproduce accurately the structure elastic behaviour, as well as the stress and strain states in regions with discontinuities, which until now could only be accurately simulated by means of expensive numerical models using volumetric solid elements.This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement № 101006860 (FIBRE4YARDS project) and under grant agreement № 952966 (FIBREGY project). In addition, this research work is framed within an FI doctoral grant awarded by the Generalitat de Catalunya and co-financed jointly with the European Union . These supports are gratefully acknowledged.Peer ReviewedPostprint (published version

Multiscale numerical modelling of microstructured reinforced composites

Most of the existing materials around us can be considered composite materials, since they are composed by several phases or components at certain spatial scale. The physical and chemical properties of composites, as occurs with structures composed by two or more materials, is de¿ned by the response provided by their constituents. Therefore, a good characterization of the composite requires con-sidering the performance of its components. In the last decades, several methods have been proposed with this approach to characterize composite materials, most of them based on multiscale techniques.Peer ReviewedPostprint (published version

Strategy for an efficient material non-linear multiscale analysis

As the internal microstructure of composite materials becomes more complex, multi-scale methods are gaining strength. These allow obtaining the material performance from the analysis of a representative volume element. The use of multiscale procedures is also encouraged by the increase of computational capacity. However, despite of this increase, performing a non-linear multiscale analysis of a real structure is still chimeric due to its computational cost. This work presents a strategy to conduct non-linear multiscale analysis in an efficient way. It is based in the definition of a threshold function, which is developed specifically for each micro-model using its specific strain field. The procedure allows a large reduction of the computational cost, facilitating its use by researchers and engineers without large computational means. The validity of the proposed strategy is shown with the analysis of a pultruded cantilever beam. The results obtained prove the efficiency of the method.Postprint (published version

Cation–π complexes between alkaline cations and molecular bowls related with fullerene: a DFT study

The 14th International Electronic Conference on Synthetic Organic Chemistry session Computational ChemistryThe formation of complexes between alkaline cations and molecular bowls (MBs), curved conjugated systems related with fullerene (C 60 ), is studied using DFT calculations. The series of MBs is constructed starting with benzene and additional hexagonal or pentagonal rings are added symmetrically to complete the C 60 structure. All the MBs studied form stable cation–π complexes by both of its sides: concave and convex. In all cases complexes with the cation in the convex side are more stable than their corresponding partner inside the bowl. The stability of the complexes is determined by the polarizing power of the cation and by the molecular electrostatic potential and the polarizability of the bowl. Additionally, size effects are observed when bulky cations are placed in the concave side of the largest bowl

Influence of the substitution on the inversion barrier of corannulene: a theoretical study.

The 15th International Electronic Conference on Synthetic Organic Chemistry session Computational ChemistryThe lower molecular weight hydrocarbons that can be mapped on the buckminsterfullerene (C60) structure are commonly known as "buckybowls" or "geodesic polyarenes" and have the distinctive characteristics of preserving the curvature and aromaticity of fullerene. These bowl-shaped structures are expected to be quite rigid. Nevertheless, the smaller members of the family, in spite of its substantial curvature are surprisingly flexible undergoing rapid bowl-to-bowl inversion in solution as evidenced by the dynamic NMR behavior of C20H10 (corannulene) and several of its derivatives. With the aim of gaining understanding in the bowl-to-bowl inversion, the present theoretical study has explored the effect that substitution of some of the hydrogen atoms of corannulene has on this process. The model systems studied have the formula C20H10-nRn with R = -Cl, -Br, -C≡CH, -CH3 and n = 0, 2, 4, 5, 6, 8, and 10. It is observed that the bowl depth is reduced only by high substitution levels or by a substitution pattern that conduces to important peri interactions. Full substitution with bulky groups causes a pronounced repulsion and the deformation of the transition structure for bowl inversion that otherwise is planar. The activation barrier for the inversion – bowl depth data fit an empirical quartic/quadratic function used previously in similar systems but the coefficients of the fitting don\'t follow the predicted substituent independenc

Computational Study of the interaction between Sumanene and Cations as a function of the cation–π separation

With the aim of enhancing the comprehension of the cation-π interaction, a computational study of the interaction established between sumanene molecule and various cations was performed. Sumanene is a polycyclic aromatic hydrocarbon with a bowl-shaped structure. The curvature of the molecule causes an asymmetry in the distribution of its molecular electrostatic potential that is more negative in its outer (convex) side. This feature allows testing the role of the electrostatic contribution to cation-π interaction using the same molecule. Five cations with different sizes and shapes were selected for the study: sodium, potassium, ammonium, tetramethylammonium, guanidinium and imidazolium. These are monoatomic cations and models of cationic amino acids side-chains, all of which are known to participate in the formation of cation-π complexes in biological systems. The polyatomic cations were placed in different orientations with respect to the sumanene molecule including the “T-shaped” and “stacked” configurations of the flat cations. The study was accomplished at the RI‑MP2/aug-cc-pVTZ level of calculation, to ensure the correct retrieving of the correlation energy and also that the wavefunction size is appropriate for the modeling of effects more complicated than the electrostatic contribution. The interaction energy (Eint) was computed at different sumanene-cation distances following the C3v symmetry axe of sumanene and exploring it’s both sides: concave and convex. The rigid scans of the potential energy surface indicate that at sumanene-cation distances around the Eint minima, the complexes are more stable with the cation placed by the inner (concave) side of sumanene, with the only exception of the complexes with Na+, the smallest of the cations studied. This result is the opposite of that expected from the pure electrostatic interpretation of the cation-π interaction. As the cation moves away from the sumanene molecule the situation is reversed, and at long distances the outer complexes are more stable than its inner partners. These findings suggest that at long cation-molecule separations the electrostatic contribution dominates because its influence propagates to long distances but at short distances the cation-π interaction is controlled by other stabilizing contributions (induction and dispersion) defining the minimum of the Eint profile. The results obtained contribute to a better understanding the cation-π interaction and emphasize the importance of using the correct level of calculations in its theoretical modelin