This thesis investigates minimal surfaces in design and researches their potential for constructability in concrete through the creation of physical prototypes with the design of two mold making processes, one being sacrificial and the other reusable. The study starts by acknowledging that minimal surfaces have been extensively explored in the field of differential geometry for decades. In spite of the availability of geometric definitions which provide the basic background for digital model generation (which in this text is assumed to be equal to design itself), minimal surfaces inspired very few people in their architectural design. This study attempts to look into the wider implications of minimal surfaces for architecture by taking up the challenge of designing and realizing various processes of mold making for the fabrication of such surfaces in concrete. Throughout this study, a gradient of complexity in the definition and digital modeling of minimal surfaces will be included as well as a variety of production methods in a research and fabrication based process, in order to investigate the correlation between what can be designed and what can be produced. I shall begin with a historical survey of the constructability of surfaces in thin shell concrete to provide background information for the reader. This chapter on the evolution of concrete structures presents a compilation of selected projects to illustrate the progress of thin shell construction throughout the history of architecture. It is here that I review what happened, why, and who made it possible. I draw heavily on published scholarly studies as most of the selected projects are cornerstones of the evolution of architecture and have been discussed by many others. Here, I simply attempt to remind the reader of the achievements of these projects in order to justify why investigation of the constructability of minimal surfaces may be the next step in the evolutionary process. After this section, the mathematics of surfaces in the complex plane is discussed based on information retrieved from many excellent resources. Here, the intention is to acquire information related to descriptions of various minimal surface types in differential geometry in order to be able to generate their representations in the digital environment. It would have been impossible to generate digital representations of minimal surfaces without the knowledge acquired through these descriptions. The last section provides a comparison of ruled surfaces and minimal surfaces meant to reveal the similarities and differences of such surfaces with regard to the principles of digital representation and fabrication. It provides insight into various fabrication techniques and materials to illuminate the design of a making process in which the goal is to know and control every parameter regarding both the design and fabrication of an object. The discussion of the design of a making process for a complexly shaped object provided in this part is followed by discussion of casting prototypes in concrete. In that section, the subject matter is the design and testing of various mold making techniques for the production of concrete prototypes of a selected minimal surface geometry. This section presents an increasing complexity of mold making from a sacrificial mold to a reusable mold.

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L’intégration du langage informatique dans l’architecture et l’ingénierie a commencé dès les années 1960, mais a connu un réel essor dans les années 1990. Les outils de modélisation ont alors progressivement fait émerger une nouvelle architecture. Tout d’abord baptisée « architecture blob », on lui a ensuite attribué le nom de « blobisme » et ses dérivés sont aujourd’hui appelés « architecture non standard ». Au cours de la dernière décennie, certains chercheurs comme Mario Carpo ou praticiens comme Patrick Schumacher ont introduit les termes de « paramétrisme », « customisation de masse », et « architecture non standard » pour définir ces nouvelles constructions complexes. Elles ne sont pas nécessairement savantes, mais ont été conçues grâce à des outils numériques et réalisées avec des méthodes de fabrication digitales. Cette thèse prend appui sur le postulat qu’une approche non standard dans un projet est loin de se résumer à une démarche purement plastique ou fonctionnelle : elle est destinée à produire des objets constructibles. Le domaine d’étude est celui des murs et enveloppes construites en bois et plus particulièrement les parois de type cellulaire. Ce travail inclut donc un outil paramétrique d’aide à la conception (ACPT, Aided-Conception Parametric Tool) et à la fabrication qui peut accompagner les concepteurs dans l’exploration de solutions non-standards pour des problèmes architecturaux spécifiques Cet outil paramétrique et intégré s’appuie sur une modélisation géométrique et technique des parois murales et des différents dispositifs cellulaires qui les composent. L’approche paramétrique autorise le développement de nombreuses variantes morphologiques. Sa dimension intégrée permet la production et l’optimisation des données tant topologiques que constructives. La production grandeur nature d’une paroi réalisée par un robot de coupe a servi de cadre expérimental pour démontrer les potentialités de notre approche mais aussi en identifier les difficultés. Les améliorations effectuées ont conduit à produire une série de clusters (groupes de fonctions) pour Rhinoceros-Grasshopper (RGH) qui ont permis de mettre en oeuvre la première version opérationnelle de cet outil, baptisée Fab-Cell / The integration of computing language into architecture and engineering has been present since the 1960s but it only proved practical by the 1990s when modeling tools started to participate in an architectural shift that has conceptually mutated through the years. By then, the trend was called “blob architecture” and thirteen years ago, trends succeeding “blobism” were named as non-standard architecture. In the last ten years, academicians like Mario Carpo and practitioners such as Patrick Schumacher nested the terms parametricism, mass customization, and nonstandard architecture to define those complex –not necessarily complicated architectures created by using of digital tools and aided-manufacturing methods. This thesis is underpinned on the fact that using the non-standard approach in any architectural project needs more than just a plastic or functional intention but the means to translate that intention into actual buildable objects. The aims of this study are therefore oriented towards architectural elements using cellular-like patterns as morphologic resource. This work brings up an Aided-Conception Parametric Tool (ACPT) that actually helps designers to explore non-standard solutions to specific architectural problems regarding timber-built walls and envelopes. This ACPT is meant then to succeed architectural intentions in which geometric patterns –as morphologic modifiers- are used to provide walls and envelopes with a particular language (a cellular structure) that might require morphologic form searching (Carpo, 2015a) and topologic optimization by means of parametric generative modeling. The previously mentioned aims were validated by means of a full-scale prototyping exercise in which the first version of the ACPT is tested. Furthermore A series of modeling improvements regarding pattern generation, jointing calculation and fabrication simulation, helped fixing the difficulties found during the first validation stage in order to produce a set of Rhinoceros-Grasshopper (RGH) functional clusters that embody the early operational state of this ACPT called Fab-Cell