Simulación numérica de procesos de compactación de pubimateriales

En esta tesis se presenta un modelo numérico para simular la fase de compactación de pulvimateriales y su implementación en ordenadores de cálculo paralelo, con el ánimo de facilitar y mejorar el diseño de los procesos de fabricación por compactación de polvos metálicos. El estudio se inicia llevando a cabo una breve descripción fenomenologica del proceso de compactación, se estudian las principales propiedades y métodos de producción del material en polvo y su efecto sobre las propiedades finales del compacto, se analizan cada una de las operaciones que intervienen en el proceso y se estudian las modificaciones de las propiedades físicas a medida que avanza la compactación. El estudio continua con una breve descripción del estado del arte de los modelos constitutivos empleados hasta ahora y las diferentes técnicas numéricas propuestas para la solución del sistema de ecuaciones asociado a la modelizacion.En el núcleo de la tesis se presenta la formulación matemática del modelo numérico. Se describen las variables básicas y su interpretación física, se formulan las ecuaciones básicas necesarias para la simulación numérica: ecuaciones cinemáticas, ecuación constitutiva, función de fluencia, reglas de flujo y disipación. Se formula el algoritmo de integración de la ecuación constitutiva y el cálculo del tensor constitutivo tangente. Adicionalmente, se describen los modelos numéricos de contacto y de fricción, que permiten simular los efectos que producen las paredes tanto del molde como de los punzones, sobre el material en polvo y en general sobre las propiedades mecánicas finales del compacto.El estudio del comportamiento del modelo numérico propuesto, se lleva a cabo mediante dos grupos de ejemplos.En el primer grupo se calibra y compara el modelo frente a una campaña de resultados experimentales. El segundo grupo, muestra la utilidad que tiene la herramienta numérica en el diseño de piezas complejas

Simulación numérica de procesos de compactación de pubimateriales

En esta tesis se presenta un modelo numérico para simular la fase de compactación de pulvimateriales y su implementación en ordenadores de cálculo paralelo, con el ánimo de facilitar y mejorar el diseño de los procesos de fabricación por compactación de polvos metálicos. El estudio se inicia llevando a cabo una breve descripción fenomenologica del proceso de compactación, se estudian las principales propiedades y métodos de producción del material en polvo y su efecto sobre las propiedades finales del compacto, se analizan cada una de las operaciones que intervienen en el proceso y se estudian las modificaciones de las propiedades físicas a medida que avanza la compactación. El estudio continua con una breve descripción del estado del arte de los modelos constitutivos empleados hasta ahora y las diferentes técnicas numéricas propuestas para la solución del sistema de ecuaciones asociado a la modelizacion.En el núcleo de la tesis se presenta la formulación matemática del modelo numérico. Se describen las variables básicas y su interpretación física, se formulan las ecuaciones básicas necesarias para la simulación numérica: ecuaciones cinemáticas, ecuación constitutiva, función de fluencia, reglas de flujo y disipación. Se formula el algoritmo de integración de la ecuación constitutiva y el cálculo del tensor constitutivo tangente. Adicionalmente, se describen los modelos numéricos de contacto y de fricción, que permiten simular los efectos que producen las paredes tanto del molde como de los punzones, sobre el material en polvo y en general sobre las propiedades mecánicas finales del compacto.El estudio del comportamiento del modelo numérico propuesto, se lleva a cabo mediante dos grupos de ejemplos.En el primer grupo se calibra y compara el modelo frente a una campaña de resultados experimentales. El segundo grupo, muestra la utilidad que tiene la herramienta numérica en el diseño de piezas complejas.Postprint (published version

Simulación numérica de procesos de compactación de pulvimateriales. Parte 2: Validación y aplicaciones industriales

En la primera parte de este trabajo se describió el modelo numérico propuesto para la simuación del proceso de compactación de pulvimateriales. En esta segunda parte se estudia el comportamiento del modelo mediante la comparación de resultados experimentales con resultados numéricos. Se desarrollan también una serie de ejemplos axisimétricos, que muestran la robustez del modelo numérico, y su utilidad como herramienta de diseño de procesos de compactación de piezas de uso industrial.In Part 1 of this work a numerical model to simulate the compaction of powder materials was proposed. In this second part, the behaviour of the model is studied by means of the comparison between experimental and numerical results. Robustness and usefullness of the numericd model as a design tool are shown through the simulation of the compaction of severa1 axisymmetric industrial parts.Peer Reviewe

Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the workPeer ReviewedPostprint (author's final draft

Numerical modeling of crack formation in power compaction processes

Powder metallurgy (P/M) is an important technique of manufacturing metal parts from metal in powdered form. Traditionally, P/M processes and products have been designed and developed on the basis of practical rules and trial-and-error experience. However, this trend is progressively changing. In recent years, the growing efficiencies of computers, together with the recognition of numerical simulation techniques, and more specifically, the finite element method , as powerful alternatives to these costly trial-and-error procedures, have fueled the interest of the P/M industry in this modeling technology. Research efforts have been devoted mainly to the analysis of the pressing stage and, as a result, considerable progress has been made in the field of density predictions. However, the numerical simulation of the ejection stage, and in particular, the study of the formation of cracks caused by elastic expansion and/or interaction with the tool set during this phase, has received less attention, notwithstanding its extreme relevance in the quality of the final product. The primary objective of this work is precisely to fill this gap by developing a constitutive model that attempts to describe the mechanical behavior of the powder during both pressing and ejection phases, with special emphasis on the representation of the cracking phenomenon. The constitutive relationships are derived within the general framework of rate-independent, isotropic, finite strain elastoplasticity. The yield function is defined in stress space by three surfaces intersecting nonsmoothly, namely, an elliptical cap and two classical Von Mises and Drucker-Prager yield surfaces. The distinct irreversible processes occurring at the microscopic level are macroscopically described in terms of two internal variables: an internal hardening variable, associated with accumulated compressive (plastic) strains, and an internal softening variable, linked with accumulated (plastic) shear strains. The innovative part of our modeling approach is connected mainly with the characterization of the latter phenomenological aspect: strain softening. Incorporation of a softening law permits the representation of macroscopic cracks as high gradients of inelastic strains (strain localization). Motivated by both numerical and physical reasons, a parabolic plastic potential function is introduced to describe the plastic flow on the linear Drucker-Prager failure surface. A thermodynamically consistent calibration procedure is employed to relate material parameters involved in the softening law to fracture energy values obtained experimentally on Distaloy AE specimens. The discussion of the algorithmic implementation of the model is confined exclusively to the time integration of the constitutive equations. Motivated by computational robustness considerations, a non-conventional integration scheme that combines advantageous features of both implicit and explicit method is employed. The basic ideas and assumptions underlying this method are presented, and the stress update and the closed-form expression of the algorithmic tangent moduli stemming from this method are derived. This integration scheme involves, in turn, the solution at each time increment of the system of equations stemming from a classical, implicit backward-Euler difference scheme. An iterative procedure based on the decoupling of the evolution equations for the plastic strains and the internal variables is proposed for solving these return-mapping equations. It is proved that this apparently novel method converges unconditionally to the solution regardless of the value of the material properties. To validate the proposed model, a comparison between experimental results of diametral compression tests and finite element predictions is carried out. The validation is completed with the study of the formation of cracks due to elastic expansion during ejection of an overdensified thin cylindrical part. Both simulations demonstrate the ability of the model to detect evidence of macroscopic cracks, clarify and provide reasons for the formation of such cracks, and evaluate qualitatively the influence of variations in the input variables on their propagation. Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of P/M uniaxial die compaction (including ejection) processes, a detailed case study of the compaction of an axially symmetric multilevel part in an advanced CNC press machine is performed. Special importance is given in this study to the accurate modeling of the geometry of the tool set and the external actions acting on it (punch platen motions). Finally, the potential areas for future research are identified.Postprint (published version

Vademecum-based approach to multi-scale topological material design

The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques. The goal is then to minimize the structural (macro-scale) compliance by appropriately designing the material distribution (microstructure) at a lower scale (micro-scale), which, in turn, rules the mechanical properties of the material. The specific features of the proposed approach are: (1) The cost function to be optimized (structural stiffness) is defined at the macro-scale, whereas the design variables defining the micro-structural topology lie on the low scale. Therefore a coupled, two-scale (macro/micro), optimization problem is solved unlike the classical, single-scale, topological optimization problems. (2) To overcome the exorbitant computational cost stemming from the multiplicative character of the aforementioned multiscale approach, a specific strategy, based on the consultation of a discrete material catalog of micro-scale optimized topologies (Computational Vademecum) is used. The Computational Vademecum is computed in an offline process, which is performed only once for every constitutive-material, and it can be subsequently consulted as many times as desired in the online design process. This results into a large diminution of the resulting computational costs, which make affordable the proposed methodology for multiscale computational material design. Some representative examples assess the performance of the considered approach.Peer ReviewedPostprint (published version

A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling

A framework, based on an extended Hill–Mandel principle accounting for inertial effects (Multiscale Virtual Work principle), is developed for application to acoustic problems in the context of metamaterials modelling. The classical restrictions in the mean values of the micro-displacement fluctuations and their gradients are then accounted for in a saddle-point formulation of that variational principle in terms of Lagrange functionals. A physical interpretation of the involved Lagrange multipliers can then be readily obtained. The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation.Peer ReviewedPostprint (author's final draft

Topology optimization using the unsmooth variational topology optimization (UNVARTOP) method: an educational implementation in MATLAB

The final publication is available at Springer via http://dx.doi.org/10.1007/s00158-020-02722-0This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis, and multi-load compliance problems. The unsmooth variational topology optimization (UNVARTOP) method, developed by Oliver et al. (Comput Methods Appl Mech Eng 355:779–819, 2019), is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems, and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (Appendix A) and it can be downloaded from https://github.com/DanielYago/UNVARTOP together with supplementary material.This research has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Proof of Concept Grant agreement n 874481) through the project \Computational design and prototyping of acoustic metamaterials for target ambient noise reduction" (METACOUSTIC). The authors also acknowledge nancial support from the Spanish Ministry of Economy and Competitiveness, through the research grant DPI2017-85521-P for the project \Computational design of Acoustic and Mechanical Metamaterials" (METAMAT) and through the \Severo Ochoa Programme for Centres of Excellence in R&D" (CEX2018-000797-S). D. Yago acknowledges the support received from the Spanish Ministry of Education through the FPU program for PhD grants.Peer ReviewedPostprint (author's final draft

Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM)

This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools.Peer ReviewedPostprint (published version

Experimental and numerical assessment of local resonance phenomena in 3D-printed acoustic metamaterials

The so called Locally Resonant Acoustic Metamaterials (LRAM) are a new kind of artificially engineered materials capable of attenuating acoustic waves. As the name suggests, this phenomenon occurs in the vicinity of internal frequencies of the material structure, and can give rise to acoustic bandgaps. One possible way to achieve this is by considering periodic arrangements of a certain topology (unit cell), smaller in size than the characteristic wavelength. In this context, a computational model based on a homogenization framework has been developed from which one can obtain the aforementioned resonance frequencies for a given LRAM unit cell design in the sub-wavelength regime, which is suitable for low-frequency applications. Aiming at validating both the proposed numerical model and the local resonance phenomena responsible for the attenuation capabilities of such materials, a 3D-printed prototype consisting of a plate with a well selected LRAM unit cell design has been built and its acoustic response to normal incident waves in the range between 500 and 2000 Hz has been tested in an impedance tube. The results demonstrate the attenuating capabilities of the proposed design in the targeted frequency range for normal incident sound pressure waves and also establish the proposed formulation as the fundamental base for the computational design of 3D-printed LRAM-based structures.Peer ReviewedPostprint (author's final draft