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A parametric method for building design optimization based on Life Cycle Assessment - Appendix
(2016)
The building sector is responsible for a large share of human environmental impacts, over which architects and planners have a major influence. The main objective of this thesis is to develop a method for environmental building design optimization based on Life Cycle Assessment (LCA) that is applicable as part of the design process. The research approach includes a thorough analysis of LCA for buildings in relation to the architectural design stages and the establishment of a requirement catalogue. The key concept of the novel method called Parametric Life Cycle Assessment(PLCA) is to combine LCA with parametric design. The application of this method to three examples shows that building designs can be optimized time-efficiently and holistically from the beginning of the most influential early design stages, an achievement which has not been possible until now.
In this study, the behavior of a widely graded soil prone to suffusion and necessity of homogeneity quantifi cation for such a soil in internal stability considerations are discussed. With the help of suffusion tests, the dependency of the particle washout to homogeneity of sample is shown. The validity of the great infl uence of homogeneity on suffusion processes by the presentation of arguments and evidences are established. It is emphasized that the internal stability of a widely graded soil cannot be directly correlated to the common geotechnical parameters such as dry density or permeability. The initiation and propagation of the suffusion processes are clearly a particle scale phenomenon, so the homogeneity of particle assemblies (micro-scale) has a decisive effect on particle rearrangement and washout processes. It is addressed that the guidelines for assessing internal stability lack a fundamental, scientifi c basis for quantifi cation of homogeneity. The observation of the segregation processes within the sample in an ascending layered order (for downwards fl ow) inspired the author to propose a new packing model for granular materials which are prone to internally instability.
It is shown that the particle arrangement, especially the arrangement of soil skeleton particles or the so-called primary fabric has the main role in suffusiv processes. Therefore, an experimental approach for identifi cation of the skeleton in the soil matrix is proposed. 3D models of Sequential Fill Tests using Discrete Element Method (DEM) and 3D models of granular packings for relative, stochastically and ideal homogeneous particle assemblies were generated, and simulations have been carried out.
Based on the numerical investigations and in dependency on the soil skeleton behavior, an approach for measurement of relevant scale, the so-called Representative Elementary Volume (REV) for homogeneity investigation is proposed. The development of a new testing method for quantifi cation of homogeneity is introduced (in-situ). An approach for quantifi cation of homogeneity in numerically or experimentally generated packings (samples) based on image processing method of MATLAB has been introduced. A generalized experimental method for assessment of internal stability for widely graded soils with dominant coarse matrix is developed, and a new suffusion criterion based on ideal homogeneous internally stable granular packing is designed.
My research emphasizes that in a widely graded soils with dominant coarse matrix, the soil fractions with diameters bigger than D60 build essentially the soil skeleton. The mass and spatial distribution of these fractions governs the internal stability, and the mass and distribution of the fi ll fractions are a secondary matter. For such a soil, the homogeneity of the skeleton must be cautiously measured and verified.
Augmented Urban Model: Ein Tangible User Interface zur Unterstützung von Stadtplanungsprozessen
(2011)
Im architektonischen und städtebaulichen Kontext erfüllen physische und digitale Modelle aufgrund ihrer weitgehend komplementären Eigenschaften und Qualitäten unterschiedliche, nicht verknüpfte Aufgaben und Funktionen im Entwurfs- und Planungsprozess. Während physische Modelle vor allem als Darstellungs- und Kommunikationsmittel aber auch als Arbeitswerkzeug genutzt werden, unterstützen digitale Modelle darüber hinaus die Evaluation eines Entwurfs durch computergestützte Analyse- und Simulationstechniken.
Analysiert wurden im Rahmen der in diesem Arbeitspapier vorgestellten Arbeit neben dem Einsatz des Modells als analogem und digitalem Werkzeug im Entwurf die Bedeutung des Modells für den Arbeitsprozess sowie Vorbilder aus dem Bereich der Tangible User Interfaces mit Bezug zu Architek¬tur und Städtebau. Aus diesen Betrachtungen heraus wurde ein Prototyp entwickelt, das Augmented Urban Model, das unter anderem auf den frühen Projekten und Forschungsansätzen aus dem Gebiet der Tangible User Interfaces aufsetzt, wie dem metaDESK von Ullmer und Ishii und dem Urban Planning Tool Urp von Underkoffler und Ishii.
Das Augmented Urban Model zielt darauf ab, die im aktuellen Entwurfs- und Planungsprozess fehlende Brücke zwischen realen und digitalen Modellwelten zu schlagen und gleichzeitig eine neue tangible Benutzerschnittstelle zu schaffen, welche die Manipulation von und die Interaktion mit digitalen Daten im realen Raum ermöglicht.
Dieses Arbeitspapier beschreibt, wie ausgehend von einem vorhandenen Straßennetzwerk Bebauungsareale mithilfe von Unterteilungsalgorithmen automatisch umgelegt, d.h. in Grundstücke unterteilt, und anschließend auf Basis verschiedener städtebaulicher Typen bebaut werden können. Die Unterteilung von Bebauungsarealen und die Generierung von Bebauungsstrukturen unterliegen dabei bestimmten stadtplanerischen Einschränkungen, Vorgaben und Parametern. Ziel ist es aus den dargestellten Untersuchungen heraus ein Vorschlagssystem für stadtplanerische Entwürfe zu entwickeln, das anhand der Umsetzung eines ersten Softwareprototyps zur Generierung von Stadtstrukturen weiter diskutiert wird.
Aktionsräume in Dresden
(2012)
In vorliegender Studie werden die Aktionsräume von Befragten in Dresden über eine standardisierte Befragung (n=360) untersucht. Die den Aktionsräumen zugrundeliegenden Aktivitäten werden unterschieden in Einkaufen für den täglichen Bedarf, Ausgehen (z.B. in Café, Kneipe, Gaststätte), Erholung im Freien (z.B. spazieren gehen, Nutzung von Grünanlagen) und private Geselligkeit (z.B. Feiern, Besuch von Verwandten/Freunden). Der Aktionsradius wird unterschieden in Wohnviertel, Nachbarviertel und sonstiges weiteres Stadtgebiet. Um aus den vier betrachteten Aktivitäten einen umfassenden Kennwert für den durchschnittlichen Aktionsradius eines Befragten zu bilden, wird ein Modell für den Kennwert eines Aktionsradius entwickelt. Die Studie kommt zu dem Ergebnis, dass das Alter der Befragten einen signifikanten – wenn auch geringen – Einfluss auf den Aktionsradius hat. Das Haushaltsnettoeinkommen hat einen mit Einschränkung signifikanten, ebenfalls geringen Einfluss auf alltägliche Aktivitäten der Befragten.
In vorliegender Studie werden die Wohnstandortpräferenzen der Sinus-Milieugruppen in Dresden über eine standardisierte Befragung (n=318) untersucht. Es wird unterschieden zwischen handlungsleitenden Wohnstandortpräferenzen, die durch Anhaltspunkte auf der Handlungsebene stärker in Betracht gezogen werden sollten, und Wohnstandortpräferenzen, welche eher orientierenden Charakter haben. Die Wohnstandortpräferenzen werden untersucht anhand der Kategorien Ausstattung/Zustand der Wohnung/des näheren Wohnumfeldes, Versorgungsstruktur, soziales Umfeld, Baustrukturtyp, Ortsgebundenheit sowie des Aspektes des Images eines Stadtviertels. Um die Befragten den Sinus-Milieugruppen zuordnen zu können, wird ein Lebensweltsegment-Modell entwickelt, welches den Anspruch hat, die Sinus-Milieugruppen in der Tendenz abzubilden. Die Studie kommt zu dem Ergebnis, dass die Angehörigen der verschiedenen Lebensweltsegmente in jeder Kategorie - wenn auch z.T. auf geringerem Niveau - signifikante Unterschiede in der Bewertung einzelner Wohnstandortpräferenzen aufweisen.
Wissen wer wo wohnt
(2012)
In cities people live together in neighbourhoods. Here they can find the infrastructure they need, starting with shops for the daily purpose to the life-cycle based infrastructures like kindergartens or nursing homes. But not all neighbourhoods are identical. The infrastructure mixture varies from neighbourhood to neighbourhood, but different people have different needs which can change e.g. based on the life cycle situation or their affiliation to a specific milieu. We can assume that a person or family tries to settle in a specific neighbourhood that satisfies their needs. So, if the residents are happy with a neighbourhood, we can further assume that this neighbourhood satisfies their needs. The socio-oeconomic panel (SOEP) of the German Institute for Economy (DIW) is a survey that investigates the economic structure of the German population. Every four years one part of this survey includes questions about what infrastructures can be found in the respondents neighbourhood and the satisfaction of the respondent with their neighbourhood. Further, it is possible to add a milieu estimation for each respondent or household. This gives us the possibility to analyse the typical neighbourhoods in German cities as well as the infrastructure profiles of the different milieus. Therefore, we take the environment variables from the dataset and recode them into a binary variable – whether an infrastructure is available or not. According to Faust (2005), these sets can also be understood, as a network of actors in a neighbourhood, which share two, three or more infrastructures. Like these networks, this neighbourhood network can also be visualized as a bipartite affiliation network and therefore analysed using correspondence analysis. We will show how a neighbourhood analysis will benefit from an upstream correspondence analysis and how this could be done. We will also present and discuss the results of such an analysis.
K-dimensionale Bäume, im Englischen verkürzt auch K-d Trees genannt, sind binäre Such- und Partitionierungsbäume, die eine Menge von n Punkten in einem multidimensionalen Raum repräsentieren. Ihren Einsatz finden K-d Tree Datenstrukturen vor allem bei der Suche nach den nächsten Nachbarn, der Nearest Neighbor Query, und in weiteren Suchalgorithmen für beispielsweise Datenbankapplikationen. Im Rahmen des Forschungsprojekts Kremlas wurde die Raumpartitionierung durch K-d Trees als eine Teillösung zur Generierung von Layouts bei der Entwicklung einer kreativen evolutionären Entwurfsmethode für Layoutprobleme in Architektur und Städtebau entwickelt. Der Entwurf und die Entwicklung von Layouts, d.h. die Anordnung von Räumen, Baukörpern und Gebäudekomplexen im architektonischen und städtischen Kontext stellt eine zentrale Aufgabe in Architektur und Stadtplanung dar. Sie erfordert von Architekten und Planern funktionale sowie kreative Problemlösungen. Das Forschungsprojekt beschäftigt sich folglich nicht nur mit der Optimierung von Grundrissen sondern bindet auch gestalterische Aspekte mit ein. In der entwickelten Teillösung dient der K-d Tree Algorithmus zunächst zur Unterteilung einer vorgegebenen Fläche, wobei die Schnittlinien möglichen Raumgrenzen entsprechen. Durch die Kombination des K-d Tree Algorithmus mit genetischen Algorithmen und evolutionären Strategien werden Layouts hinsichtlich der Kriterien Raumgröße und Nachbarschaften optimiert. Durch die Interaktion des Nutzers können die Lösungen dynamisch angepasst und zur Laufzeit nach gestalterischen Kriterien verändert werden. Das Ergebnis ist ein generativer Mechanismus, der bei der kreativen algorithmischen Lösung von Layoutaufgaben in Architektur und Städtebau eine vielversprechende Variante zu bereits bekannten Algorithmen darstellt.
The key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME)
shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes
near the crack such as blending or shifting.
As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.
In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected
pipes.
Previous models for the explanation of settlement processes pay little attention to the interactions between settlement spreading and road networks. On the basis of a dielectric breakdown model in combination with cellular automata, we present a method to steer precisely the generation of settlement structures with regard to their global and local density as well as the size and number of forming clusters. The resulting structures depend on the logic of how the dependence of the settlements and the road network is implemented to the simulation model. After analysing the state of the art we begin with a discussion of the mutual dependence of roads and land development. Next, we elaborate a model that permits the precise control of permeability in the developing structure as well as the settlement density, using the fewest necessary control parameters. On the basis of different characteristic values, possible settlement structures are analysed and compared with each other. Finally, we reflect on the theoretical contribution of the model with regard to the context of urban dynamics.
How does it come to particular structure formations in the cities and which strengths play a role in this process? On which elements can the phenomena be reduced to find the respective combination rules? How do general principles have to be formulated to be able to describe the urban processes so that different structural qualities can be produced? With the aid of mathematic methods, models based on four basic levels are generated in the computer, through which the connections between the elements and the rules of their interaction can be examined. Conclusions on the function of developing processes and the further urban origin can be derived.
PLANUNGSUNTERSTÜTZUNG DURCH DIE ANALYSE RÄUMLICHER PROZESSE MITTELS COMPUTERSIMULATIONEN. Erst wenn man – zumindest im Prinzip – versteht, wie eine Stadt mit ihren komplexen, verwobenen Vorgängen im Wesentlichen funktioniert, ist eine sinnvolle Stadtplanung möglich. Denn jede Planung bedeutet einen Eingriff in den komplexen Organismus einer Stadt. Findet dieser Eingriff ohne Wissen über die Funktionsweise des Organismus statt, können auch die Auswirkungen nicht abgeschätzt werden. Dieser Beitrag stellt dar, wie urbane Prozesse mittels Computersimulationen unter Zuhilfenahme so genannter Multi-Agenten-Systeme und Zellulärer Automaten verstanden werden können. von
At the end of the 1960s, architects at various universities world- wide began to explore the potential of computer technology for their profession. With the decline in prices for PCs in the 1990s and the development of various computer-aided architectural design systems (CAAD), the use of such systems in architectural and planning offices grew continuously. Because today no ar- chitectural office manages without a costly CAAD system and because intensive soſtware training has become an integral part of a university education, the question arises about what influence the various computer systems have had on the design process forming the core of architectural practice. The text at hand devel- ops ten theses about why there has been no success to this day in introducing computers such that new qualitative possibilities for design result. RESTRICTEDNESS
The structure and development of cities can be seen and evaluated from different points of view. By replicating the growth or shrinkage of a city using historical maps depicting different time states, we can obtain momentary snapshots of the dynamic mechanisms of the city. An examination of how these snapshots change over the course of time and a comparison of the different static time states reveals the various interdependencies of population density, technical infrastructure and the availability of public transport facilities. Urban infrastructure and facilities are not distributed evenly across the city – rather they are subject to different patterns and speeds of spread over the course of time and follow different spatial and temporal regularities. The reasons and underlying processes that cause the transition from one state to another result from the same recurring but varyingly pronounced hidden forces and their complex interactions. Such forces encompass a variety of economic, social, cultural and ecological conditions whose respective weighting defines the development of a city in general. Urban development is, however, not solely a product of the different spatial distribution of economic, legal or social indicators but also of the distribution of infrastructure. But to what extent is the development of a city affected by the changing provision of infrastructure? As
In the Space Syntax community, the standard tool for computing all kinds of spatial graph network measures is depthmapX (Turner, 2004; Varoudis, 2012). The process of evaluating many design variants of networks is relatively complicated, since they need to be drawn in a separated CAD system, exported and imported in depthmapX via dxf file format. This procedure disables a continuous integration into a design process. Furthermore, the standalone character of depthmapX makes it impossible to use its network centrality calculation for optimization processes. To overcome this limitations, we present in this paper the first steps of experimenting with a Grasshopper component (reference omitted until final version) that can access the functions of depthmapX and integrate them into Grasshopper/Rhino3D. Here the component is implemented in a way that it can be used directly for an evolutionary algorithm (EA) implemented in a Python scripting component in Grasshopper
The described study aims to find correlations between urban spatial configurations and human emotions. To this end, the authors measured people’s emotions while they walk along a path in an urban area using an instrument that measures skin conductance and skin temperature. The corresponding locations of the test persons were measured recorded by using a GPS-tracker (n=13). The results are interpreted and categorized as measures for positive and negative emotional arousal. To evaluate the technical and methodological process. The test results offer initial evidence that certain spaces or spatial sequences do cause positive or negative emotional arousal while others are relatively neutral. To achieve the goal of the study, the outcome was used as a basis for the study of testing correlations between people’s emotional responses and urban spatial configurations represented by Isovist properties of the urban form. By using their model the authors can explain negative emotional arousal for certain places, but they couldn’t find a model to predict emotional responses for individual spatial configurations.
Urban planning involves many aspects and various disciplines, demanding an asynchronous planning approach. The level of complexity rises with each aspect to be considered and makes it difficult to find universally satisfactory solutions. To improve this situation we propose a new approach, which complement traditional design methods with a computational urban plan- ning method that can fulfil formalizable design requirements automatically. Based on this approach we present a design space exploration framework for complex urban planning projects. For a better understanding of the idea of design space exploration, we introduce the concept of a digital scout which guides planners through the design space and assists them in their creative explorations. The scout can support planners during manual design by informing them about potential im- pacts or by suggesting different solutions that fulfill predefined quality requirements. The planner can change flexibly between a manually controlled and a completely automated design process. The developed system is presented using an exemplary urban planning scenario on two levels from the street layout to the placement of building volumes. Based on Self-Organizing Maps we implemented a method which makes it possible to visualize the multi-dimensional solution space in an easily analysable and comprehensible form.
It's not uncommon that analysis and simulation methods are used mainly to evaluate finished designs and to proof their quality. Whereas the potential of such methods is to lead or control a design process from the beginning on. Therefore, we introduce a design method that move away from a “what-if” forecasting philosophy and increase the focus on backcasting approaches. We use the power of computation by combining sophisticated methods to generate design with analysis methods to close the gap between analysis and synthesis of designs. For the development of a future-oriented computational design support we need to be aware of the human designer’s role. A productive combination of the excellence of human cognition with the power of modern computing technology is needed. We call this approach “cognitive design computing”. The computational part aim to mimic the way a designer’s brain works by combining state-of-the-art optimization and machine learning approaches with available simulation methods. The cognition part respects the complex nature of design problems by the provision of models for human-computation interaction. This means that a design problem is distributed between computer and designer. In the context of the conference slogan “back to command”, we ask how we may imagine the command over a cognitive design computing system. We expect that designers will need to let go control of some parts of the design process to machines, but in exchange they will get a new powerful command on complex computing processes. This means that designers have to explore the potentials of their role as commanders of partially automated design processes. In this contribution we describe an approach for the development of a future cognitive design computing system with the focus on urban design issues. The aim of this system is to enable an urban planner to treat a planning problem as a backcasting problem by defining what performance a design solution should achieve and to automatically query or generate a set of best possible solutions. This kind of computational planning process offers proof that the designer meets the original explicitly defined design requirements. A key way in which digital tools can support designers is by generating design proposals. Evolutionary multi-criteria optimization methods allow us to explore a multi-dimensional design space and provide a basis for the designer to evaluate contradicting requirements: a task urban planners are faced with frequently. We also reflect why designers will give more and more control to machines. Therefore, we investigate first approaches learn how designers use computational design support systems in combination with manual design strategies to deal with urban design problems by employing machine learning methods. By observing how designers work, it is possible to derive more complex artificial solution strategies that can help computers make better suggestions in the future.
In this paper we introduce LUCI, a Lightweight Urban Calculation Interchange system, designed to bring the advantages of a calculation and content co-ordination system to small planning and design groups by the means of an open source middle-ware. The middle-ware focuses on problems typical to urban planning and therefore features a geo-data repository as well as a job runtime administration, to coordinate simulation models and its multiple views. The described system architecture is accompanied by two exemplary use cases that have been used to test and further develop our concepts and implementations.
Nanostructured materials are extensively applied in many fields of material science for new industrial applications, particularly in the automotive, aerospace industry due to their exceptional physical and mechanical properties. Experimental testing of nanomaterials is expensive, timeconsuming,challenging and sometimes unfeasible. Therefore,computational simulations have been employed as alternative method to predict macroscopic material properties. The behavior of polymeric nanocomposites (PNCs) are highly complex.
The origins of macroscopic material properties reside in the properties and interactions taking place on finer scales. It is therefore essential to use multiscale modeling strategy to properly account for all large length and time scales associated with these material systems, which across many orders of magnitude. Numerous multiscale models of PNCs have been established, however, most of them connect only two scales. There are a few multiscale models for PNCs bridging four length scales (nano-, micro-, meso- and macro-scales). In addition, nanomaterials are stochastic in nature and the prediction of macroscopic mechanical properties are influenced by many factors such as fine-scale features. The predicted mechanical properties obtained by traditional approaches significantly deviate from the measured values in experiments due to neglecting uncertainty of material features. This discrepancy is indicated that the effective macroscopic properties of materials are highly sensitive to various sources of uncertainty, such as loading and boundary conditions and material characteristics, etc., while very few stochastic multiscale models for PNCs have been developed. Therefore, it is essential to construct PNC models within the framework of stochastic modeling and quantify the stochastic effect of the input parameters on the macroscopic mechanical properties of those materials.
This study aims to develop computational models at four length scales (nano-, micro-, meso- and macro-scales) and hierarchical upscaling approaches bridging length scales from nano- to macro-scales. A framework for uncertainty quantification (UQ) applied to predict the mechanical properties
of the PNCs in dependence of material features at different scales is studied. Sensitivity and uncertainty analysis are of great helps in quantifying the effect of input parameters, considering both main and interaction effects, on the mechanical properties of the PNCs. To achieve this major
goal, the following tasks are carried out:
At nano-scale, molecular dynamics (MD) were used to investigate deformation mechanism of glassy amorphous polyethylene (PE) in dependence of temperature and strain rate. Steered molecular dynamics (SMD)were also employed to investigate interfacial characteristic of the PNCs.
At mico-scale, we developed an atomistic-based continuum model represented by a representative volume element (RVE) in which the SWNT’s properties and the SWNT/polymer interphase are modeled at nano-scale, the surrounding polymer matrix is modeled by solid elements. Then, a two-parameter model was employed at meso-scale. A hierarchical multiscale approach has been developed to obtain the structure-property relations at one length scale and transfer the effect to the higher length
scales. In particular, we homogenized the RVE into an equivalent fiber.
The equivalent fiber was then employed in a micromechanical analysis (i.e. Mori-Tanaka model) to predict the effective macroscopic properties of the PNC. Furthermore, an averaging homogenization process was also used to obtain the effective stiffness of the PCN at meso-scale.
Stochastic modeling and uncertainty quantification consist of the following ingredients:
- Simple random sampling, Latin hypercube sampling, Sobol’ quasirandom sequences, Iman and Conover’s method (inducing correlation in Latin hypercube sampling) are employed to generate independent and dependent sample data, respectively.
- Surrogate models, such as polynomial regression, moving least squares (MLS), hybrid method combining polynomial regression and MLS, Kriging regression, and penalized spline regression, are employed as an approximation of a mechanical model. The advantage of the surrogate models is the high computational efficiency and robust as they can be constructed from a limited amount of available data.
- Global sensitivity analysis (SA) methods, such as variance-based methods for models with independent and dependent input parameters, Fourier-based techniques for performing variance-based methods and partial derivatives, elementary effects in the context of local SA, are used to quantify the effects of input parameters and their interactions on the mechanical properties of the PNCs. A bootstrap technique is used to assess the robustness of the global SA methods with respect to their performance.
In addition, the probability distribution of mechanical properties are determined by using the probability plot method. The upper and lower bounds of the predicted Young’s modulus according to 95 % prediction intervals were provided.
The above-mentioned methods study on the behaviour of intact materials. Novel numerical methods such as a node-based smoothed extended finite element method (NS-XFEM) and an edge-based smoothed phantom node method (ES-Phantom node) were developed for fracture problems. These methods can be used to account for crack at macro-scale for future works. The predicted mechanical properties were validated and verified. They show good agreement with previous experimental and simulations results.