Two movements have proven influential in applying algorithmic thinking to architectural design, albeit independently thus far. In parametric design, coined in 2008 by Patrik Schumacher, equations and variables are manipulated to produce designs with highly correlated and readily tuneable geometrical features.[1] Computational software tools to realize such goals, e.g. Dynamo through Revit and Grasshopper through Rhino, have advanced rapidly in recently years and achieved widespread adoption. Such parametric design tools can be efficiently integrated with and analyzed through the tools of building information modeling (BIM), allowing for the dynamic analysis of environmental influences such as daylight, humidity, and temperature on building energy efficiency and sustainability.

Roughly concurrently, additive manufacturing (AM), also known as 3D printing, invented in the 1980’s, has only now reached a threshold in material properties and scalability to move from a prototyping tool only to implementation in real-world designs, even reaching architectural scales.[2],[3] Such digital fabrication approaches, which translate directly from a computer-aided design (CAD) model to a geometrically-complex physical structure, offer the possibility of bringing the traditionally divorced processes of intellectual design and physical fabrication closer together, reuniting the architect with the act of making.

Here, we argue that while to date these two movements – one focused on digital design, the other digital fabrication – have almost entirely operated independently, recent progress in extending 3D printing to the temporal dimension, in so-called 4D printing, opens up the possibility for their radical combination. The benefits of such a union could, we argue, come in the form of adaptive structures that respond to environmental cues at the architectonic scale, predictably and in real-time, with profound implications for the sustainability of built structures.

While 3D printing has already expanded the ability of designers to realize intricate geometries unmakeable by traditional methods, such as complex lattice structures, 4D printing adds the temporal dimension. Pioneered by Skylar Tibbits, leading the Self Assembly Lab at the Massachusetts Institute of Technology (MIT), this new fabrication approach “describes the ability for a material system or object to change form and/or function after printing.”[4] In contrast to purely electro-mechanical or robotic approaches to actuating shape change in structures, as Tibbits has argued, the use of such “intelligent materials” offers a more scalable, as well as cost- and time-effective, route to responsive architectural-scale structures.

A vast array of different materials have been shown to allow printed objects to shape change, including commercially-available hydrophilic polymers, as developed by the Self-Assembly Lab and Stratasys Ltd.[5]; hydrogels with dramatic swelling ability[6]; light-activated materials[7]; and fiber-filled composites actuated by external heating.[8] In addition to printed materials that change shape, self-healing capabilities can also be embedded, as can materials with programmable opacities[9] and changing thermal properties through the integration of phase change materials.[10] Often times such shape changing objects are enabled by multimaterial 3D printing, through digital mixing of material properties in an approach Neri Oxman, while leading the MIT Mediated Matter group, termed “parametric chemistry.”[11] Altogether, such approaches point to a future where materials are embedded with advanced functionalities that can be digitally simulated, analyzed, and designed.

But what is the relevance for Architecture? In order to realize any real-world benefit from these intelligent materials to the built environment, it is essential to go beyond the level of isolated printed objects, and instead understand their interaction, at the building scale, with the environmental cues to which they are digitally programmed to respond. To this end, parametric design offers valuable tools. Unlike other simulation platforms, it can iteratively relate environmental factors to building material performance through, among others, daylight and solar analyses, enabling an analytical leap between parametric chemistry and real-world architectural design.

To date, however, such a connection has not been explored. Why BIM and additive manufacturing, each constituting a major trend in the usage of algorithms in contemporary design, have remained largely separate is unclear. Epistemologically speaking, profound differences in the tools used by practioners in the respective fields may be to blame. While BIM is largely taught in schools of architectural design and structural engineering, it is not learned by those materials and mechanical engineers developing the next generation of 3D printing methods. Conversely, the fundamental materials science and mechanics familiar to 3D printing inventors is not often taught in detail to architectural and structural designers. With respect to CAD softwares, mechanical engineers well-trained in tools for product scale design, e.g. SolidWorks and Autodesk Fusion 360, rarely encounter building scale softwares, e.g. Autodesk Revit, through which parametric design and BIM models are implemented.

Perhaps not surprisingly as a result, in academic reports describing new 4D printing approaches, of which there are numerous in recent years, the dynamic interaction of these printed objects with environmental cues relevant at the architectural scale is rarely, if ever, considered. This lack of analytical and simulation capabilities has undoubtedly hindered the application of materials and mechanical engineers’ otherwise promising 4D printing prototypes in the architectural realm. The other disciplinary camp has lost out, too: while the integration of insolation and daylighting analyses in architectural design is routine practice using software tools such as Autodesk Insight, these are run at a relatively gross scale, not reaching the level of detail required to truly understand and predict the performance of an adaptive skin design. Architecture thus remains static, leaving potentially massive gains in building sustainability entirely untapped.

Here we demonstrate the feasibility of an integrative algorithmic analysis tool that combines 4D printing and BIM, while pointing to the potential benefits for building sustainability that can result.

For a case study 4D printed component, we take as inspiration the report of an initially flat printed panel comprising an elastomeric polymer that, upon heating, rapidly folds into a cubic hyperparabaloid spline.[12] We then apply this 4D printed component to a prototypical architectural form often parametrically modeled, a curvilinear open-air tensile fabric structure.[13]

To encode shape change behavior, each 4D printed component is parameterized as a custom Revit family by eight total adaptive points: four define the heights of the two-way hyperbolic paraboloid in the z axis, and the remaining four the lateral boundary insets. These instance parameters can be adjusted to vary the surface area and orientation of the simulated component, thus affecting the quantity of light allowed through: higher lateral parabolic curvatures allow in more sunlight, whereas shallower lateral curvatures less. The overall parametrically-controlled shape change behavior is shown in Figure 1a.

While the 4D printed component parameters could be adjusted manually, this would be unfeasible at the architectural scale, and impossible to dynamically adapt as environmental stimuli inevitably change. To that end, a Dynamo script is instead written to compute a dot product, at incremental times during the day, between the panel orientation on a hosting surface in the tensile fabric structure design and the orientation of the sun, i.e. the panel directness to sun, whose position is readily extracted from the Revit BIM model via geography settings. The overall software architecture is described in Figure 1b.

Figure 1: Dynamo parametric logic for simulating shape change behavior of 4D printed adaptive panel skin components. In order to simulate the shape changing behavior of a 4D printed component, Dynamo is used to parametrically vary the position of eight adaptive points in an adaptive family model custom designed in Revit. Here (a-e), the component changes gradually from a semi-open, to a flat, to a fully-open conformation. In the Dynamo software architecture described below (f), green code blocks isolate environmental factors, orange code blocks perform dot product computations, and purple blocks adjust Revit geometry.

This sun directness metric is then used to parametrically adjust the corresponding eight degrees of freedom encoded into the adaptive component over the course of the day: higher dot product values, indicating higher sun directness, are counter-balanced by component configurations that lessen the amount of light infiltration. In practice, such a material logic could be embedded in the printed object by active means, for instance by directly heating the panel components’ surfaces or by external magnetic B fields. Passive means could alternatively be employed, by utilizing a shape memory polymer that, in response to sunlight or UV, adopts a rubbery mechanical response, precipitating a change in conformation under structural loads. Regardless of technical details, the algorithm simulates the resultant shape change behavior of the printed part.

The tensile fabric structure hosting these dynamic printed components, spanning in total 32’ by 48’, is itself parametrically modeled in Revit, with a barrel vault supported structurally by an array of vertical two-membered tree columns. While the size of an individually 4D printed panel decorating the tensile fabric surface may be small compared to the overall surface of this architectural form, well-established methods of mechanically linking unit-based components with sufficient resultant metastructural integrity could be implemented for such a scenario.[14],[15] Moreover, the geometrical versatility of additive manufacturing means the appropriate panel dimensions for a given panelized surface can be achieved, for a variety of different surfaces. Within the context of the Revit model designed here, the 4D printed components are attached at their corners to the supporting barrel vaults, which constrain the components’ behavior as boundary conditions. The ultimate design presented in this study comprises a 10 x 5 array of printed components, whose dimensions are variable according to the panel size at a given position in the parametric surface.

Figure 2: Tensile fabric open-air structure treated as a case study for panelized 4D printed components. On top are shown isometric (a), side (b), and front (c) views of the open-air tensile fabric structure designed to host the 4D printed shape changing components. On bottom are three parametrically-controlled configurations of the 4D printed components responding to different sun directness conditions quantified through dot product computations. For higher sun directness values (d), the components close to mitigate high light intensities; conversely, for low sun directness values (f), the components morph to an open conformation to allow more indirect sunlight light in.

We then analyze the aggregate effect of such an architectural skin panelized with 4D printed objects on the daylighting and insolation of the overall structure, making use of well-established BIM simulation tools. The results are shown in Figures 3-4. In this scheme, component parameters are optimized to regulate the sunlight hitting the floor surface underneath the tensile fabric structure. Near to mid-noon, when sunlight hitting the structure is at its zenith, the 4D printed components could be made to shape change to reflect more light, especially those positioned particularly direct with respect to the sun. Conversely, late in the afternoon, when the path of sunlight into the structure is more indirect, the components reverse shape change to allow more diffuse light in.