Topological optimization of periodic materials to enhance anisotropic dispersive effects

International audienceIn the context of waves in periodic media , we propose an iterative algorithm that determines an optimal material distribution to reach target effective dispersive properties. It relies on an homogenized model of this medium, an update procedure based on the topological derivative concept, and on an efficient FFT-accelerated method to solve cell problems

Multiscale optimization of non-conventional composite structures for improved mechanical response

Nowadays, due to governmental requirements to control climate change, there is a great inter- est on the part of the automotive and aerospace industry to design structures as light as possible, without jeopardize their performance, thus increasing their efficiency. Multi-material design is a way to achieve this goal, as will be shown in this work In this work, multi-material design is considered with the goal of improving the structure’s stiffness, strength, and non-linear behaviour when it yields. Firstly, a microstructural topology optimization is carried out seeking for multi-material microstructures with increased stiffness and strength compared to equivalent single-material microstructures. Afterwards, this study is further extended to perform multi-scale topology optimization, where a concurrent optimization of ma- terial and structure is done. Ultimately, the non-linear behaviour of hybrid fibre reinforced com- posites is optimized in order to introduce a so-called “pseudo-ductility”. Two different optimization problems are formulated and solved here. One compliance mini- mization with mass constraint problem and another stress-based problem where the maximal von Mises stress is locally minimized in the unit-cell. The multi-material design is investigated here using two different approaches. On one hand, the two solids coexist being bonded together across sharp interfaces. On the other hand, a functionally graded material is obtained as an extensive smooth variation of material properties on account of varying composition’s volume fractions of both solids throughout the design domain. The compliance-based optimization results show that multi-material microstructures can be stiffer compared to single-material ones for the same mass requirement. Regarding the stress-based problem, lower stress peaks are obtained in bi-material design solutions and, specially, in the case of graded material solutions. As regards multi-scale topology optimization, the results show that a multi-material structure can be stiffer than its single-material counterpart, which is in accordance with the microstructural study performed earlier. Hybrid composites can achieve the so-called “pseudo-ductile” behaviour mimicking the well- known elastic-plastic behaviour. To understand under what circumstances such behaviour is ob- tained, optimization problems are formulated and solved here. Two different types of optimiza- tion problems are considered. Firstly, one finds out the optimal properties of fibres to hybridize and get the pseudo-ductile behaviour. Once an optimal hybridization is found, another optimiza- tion problem is solved in order to understand the influence of the fibre dispersion on the composite response. The optimal results obtained show hybrid composites having a considerable pseudo- ductile behaviour.Atualmente, devido às imposições governamentais para controlar as alterações climáticas, existe um grande interesse por parte da indústria automóvel e aeroespacial para o projeto de es- truturas o mais leves possíveis, sem se comprometer o seu desempenho, aumentando assim a sua eficiência. O projeto multimaterial de estruturas é um dos caminhos para se alcançar este objetivo, conforme será mostrado neste trabalho. Neste trabalho, considera-se o projeto multimaterial de estruturas com o objetivo de se melho- rar a rigidez, resistência, e comportamento não linear após cedência. Primeiro, é feita uma otimi- zação de topologia ao nível da microestrutura procurando-se microestruturas multimateriais com maior rigidez e resistência quando comparadas com microestruturas de material único equivalen- tes. Depois, este estudo é explorado também no contexto de otimização topológica multi-escala, onde é realizada uma otimização concorrente do material e estrutura. Por fim, o comportamento não linear de compósitos híbridos reforçados por fibra é otimizado com vista à introdução de um efeito de “pseudo-ductilidade”. São formulados e resolvidos aqui dois problemas diferentes de otimização. Um problema de minimização de compliance (flexibilidade) sujeito a um constrangimento de massa e outro pro- blema baseado na tensão, onde a tensão máxima de von Mises é localmente minimizada na célula unitária. O projeto multi-material é investigado aqui utilizando duas diferentes abordagens. Numa das abordagens, os dois sólidos coexistem na sua forma discreta originando-se interfaces com uma variação abrupta de propriedades. Na outra abordagem, obtém-se um material de gradiente funcional onde existe uma suave variação das propriedades obtida variando pontualmente a fração volúmica dos sólidos ao longo de todo o domínio de projeto. Os resultados da otimização baseada na compliance mostraram que microestruturas multimateriais podem ser mais rígidas quando comparadas com as de material único para o mesmo requisito de massa. Relativamente ao pro- blema baseado na tensão, são obtidos picos de tensão mais baixos nas soluções constituídas por duas fases discretas de material e, sobretudo, nas soluções de material de gradiente funcional. No que que diz respeito à otimização topológica multi-escala, os resultados mostraram que uma estrutura multimaterial pode ser mais rígida que uma estrutura de material único equivalente, o que está de acordo com o estudo realizado anteriormente ao nível da microestrutura. Os compósitos híbridos conseguem alcançar um comportamento designado de “pseudo-dúc- til”, imitando o conhecido comportamento elasto-plástico. Para melhor se compreender sob que circunstâncias tal comportamento é obtido, são formulados e resolvidos problemas de otimização. São assim considerados dois tipos diferentes de problemas de otimização. Primeiramente, desco- brem-se quais as propriedades ótimas das fibras a hibridizar, obtendo-se o comportamento pseudo-dúctil. Assim que hibridização ótima tenha sido descoberta, outro problema de otimização é resolvido de modo a perceber-se a influência da dispersão das fibras na resposta do compósito. Os resultados ótimos obtidos mostram compósitos híbridos tendo um comportamento pseudo- dúctil considerável

Multiscale structural optimisation with concurrent coupling between scales

A robust three-dimensional multiscale topology optimisation framework with concurrent coupling between scales is presented. Concurrent coupling ensures that only the microscale data required to evaluate the macroscale model during each iteration of optimisation is collected and results in considerable computational savings. This represents the principal novelty of the framework and permits a previously intractable number of design variables to be used in the parametrisation of the microscale geometry, which in turn enables accessibility to a greater range of mechanical point properties during optimisation. Additionally, the microscale data collected during optimisation is stored in a re-usable database, further reducing the computational expense of subsequent iterations or entirely new optimisation problems. Application of this methodology enables structures with precise functionally-graded mechanical properties over two-scales to be derived, which satisfy one or multiple functional objectives. For all applications of the framework presented within this thesis, only a small fraction of the microstructure database is required to derive the optimised multiscale solutions, which demonstrates a significant reduction in the computational expense of optimisation in comparison to contemporary sequential frameworks. The derivation and integration of novel additive manufacturing constraints for open-walled microstructures within the concurrently coupled multiscale topology optimisation framework is also presented. Problematic fabrication features are discouraged through the application of an augmented projection filter and two relaxed binary integral constraints, which prohibit the formation of unsupported members, isolated assemblies of overhanging members and slender members during optimisation. Through the application of these constraints, it is possible to derive self-supporting, hierarchical structures with varying topology, suitable for fabrication through additive manufacturing processes.Open Acces

Empowering Materials Processing and Performance from Data and AI

Third millennium engineering address new challenges in materials sciences and engineering. In particular, the advances in materials engineering combined with the advances in data acquisition, processing and mining as well as artificial intelligence allow for new ways of thinking in designing new materials and products. Additionally, this gives rise to new paradigms in bridging raw material data and processing to the induced properties and performance. This present topical issue is a compilation of contributions on novel ideas and concepts, addressing several key challenges using data and artificial intelligence, such as:- proposing new techniques for data generation and data mining;- proposing new techniques for visualizing, classifying, modeling, extracting knowledge, explaining and certifying data and data-driven models;- processing data to create data-driven models from scratch when other models are absent, too complex or too poor for making valuable predictions;- processing data to enhance existing physic-based models to improve the quality of the prediction capabilities and, at the same time, to enable data to be smarter; and- processing data to create data-driven enrichment of existing models when physics-based models exhibit limits within a hybrid paradigm

Multiscale structural, thermal and thermo-structural optimization towards three-dimensional printable structures

This thesis develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored structural and thermal characteristics. The work exploits the high process flexibility and precision of additive manufacturing to the physical realization of complex microstructure of metamaterials by developing and implementing a multiscale approach. Structures derived from such metamaterials exhibit properties which differ from that of the constituent base material. Inspired by the concept of Free Material Optimization (FMO), a periodic microscale model is developed whose geometric parameterization enables smoothly changing properties and for which the connectivity of neighbouring microstructures in the large-scale domain is guaranteed by slowly changing large-scale descriptions of the lattice parameters. The microscale model is evaluated at full factorial design points to discretely populate material property spaces. A property point is fully defined for a micro-architecture when its elasticity matrix, thermal conductivity matrix and volume fraction is determined. The process of property-space population is facilitated by leveraging the existence of micro-architecture symmetries so that there exists a 95% reduction in the simulations required despite a full-factorial design of experiments. The discrete property evaluations are converted to continuous functions by response surface modelling so that the properties exist as continuous functions of the micro-architecture geometry parameters. A lattice-based functional grading of material is derived using the finite element method. The optimization is driven by a chain-rule combination of sensitivities derived by the adjoint method and sensitivities derived from explicit material property expressions. The novelty of the work lies in the use of multiple geometry-based small-scale design parameters for optimization problems in three-dimensional real space. The approach is demonstrated by solving structural, thermal and thermo-structural optimization problems. The results show designs with improved optimality compared to commonly implemented optimization methodologies. The optimal designs obtained are physically realizable by additive manufacturing techniques.Open Acces

Gradient-based optimization of non-linear structures and materials

Gradient-based optimization is a potent tool in many design processes today. It is particularly useful in industries where weight considerations are crucial, such as aerospace, but can also be exploited in for example civil engineering applications to reduce the material use and thereby the environmental impact. With the advent of advanced manufacture methods, it even possesses the potential to design novel materials with enhanced properties that naturally occurring materials lack. Unfortunately, most research on the subject often limits itself to linear problems, wherefore the optimization's utility in solving intricate non-linear problems is still comparatively rudimentary. The aim of this thesis is therefore to investigate gradient-based optimization of various non-linear structural problems, while addressing their inherent numerical and modeling complexities.This thesis contains an introduction to gradient-based optimization of non-linear structures and materials, involving both shape and topology optimization. To start, the governing equations of the macroscopic and microscopic problems are described. A multi-scale framework which details the transition between the scales is defined. A substantial part of the thesis is dedicated to eigenvalue problems in topology optimization, and the numerical issues that they accompany. Specifically, the effects of finite deformations on the topology optimized design taking into account eigenfrequencies, structural stability or elastic wave propagation are scrutinized. A fictitious domain approach to topology optimization is employed, wherein void regions are modeled via an ersatz material with low stiffness. Unfortunately, this brings about artificial eigenmodes and convergence problems in the finite element analyzes. Two methods which deal with both of the aforementioned problems are proposed, and their efficacy is illustrated via several numerical examples. The use of shape optimization to post-process topology optimized designs is investigated for problems where accurate boundary descriptions are crucial to capture the physics, as is the case in contact problems. To take this concept further, a simultaneous topology and shape optimization method is proposed, which allows parts of the structural boundaries to be modeled exactly up to numerical precision. This approach is proven to be especially useful in the design of pressure-driven soft robots

A Metastable Modular Structure Approach for Shape Morphing, Property Tuning and Wave Propagation Tailoring

The emerging concept of reconfigurable mechanical metamaterials has received increasing attention for realizing future advanced multifunctional adaptive structural systems partially due to their advantages over conventional bulk materials that are beneficial and desirable in many engineering applications. However, some of the critical challenges remain unaddressed before the concept can effectively and efficiently achieve real-world impacts. For instance, in the state-of-art, modules of mechanical metamaterials only reconfigure collectively to achieve global topology adaptation. As a result, the structure merely exhibits limited number of configurations that are discretely different from each other, which greatly undermines the benefits and impact of the reconfiguration effect. Additionally, most of the metamaterials investigations are focusing on the “materials” characteristics assuming infinite domain without considering the “structure” aspect of the systems. The effects of having finite domains and boundary conditions will generate new research issues and phenomena that are critical to real-world systems. To address the challenges and fundamentally advance the state of the art of multifunctional adaptive structures, this dissertation seeks to create a paradigm shift by exploiting and harnessing metastable modular mechanics and dynamics. Through developing new analysis and synthesis methodologies and conducting rigorous analytical, numerical, and experimental investigations, this research creates a new class of reconfigurable metastructure that can achieve mechanical property and topology adaptation as well as adaptive non-reciprocal vibration/wave transmission. The intellectual merit of this dissertation lies in introducing metastable modules that can be synergistically assembled and individually tuned to realize near continuous topology and mechanical property adaptation and elucidating the intricate nonlinear dynamics afforded by the metastructure. This research reveals different kinds of nonlinear instabilities that are able to facilitate the onset of supratransmission, a bandgap transmission phenomenon pertained to nonlinear periodic metastructure. In addition, utilizing this novel phenomenon, supratransmission, together with inherent spatial asymmetry of strategically configured constituents, the proposed metastructure is shown to be able to facilitate unprecedented broadband non-reciprocal vibration and wave transmission and on-demand adaptation. Since the proposed approach depends primarily on scale-independent principles, the broader impact of this dissertation is that the proposed metastructure could foster a new generation of reconfigurable structural and material systems with unprecedented adaptation and unconventional vibration control and wave transmission characteristics that are applicable to vastly different length scales for a wide spectrum of applications.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147525/1/wuzhen_1.pd

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