From surface to volume

Since geometric models of architectural components are typically surface‐based, mapping heterogeneous properties onto 2D surfaces is sufficient to communicate differences between geometrically identical components. However, certain applications can make full use of the volumetric distribution of heterogeneous material properties, such asfinite element analysis(FEA) of material behaviour and structural engineering.

A volumetric representation and mapping of properties also opens up the potential to model glue‐laminated timber elements that have a varying internal organization which might be invisible from the outside.

This requires corresponding methods of discretizing 3D models into elements. This development therefore extends the initial 2D triangulation methods with a 3D tetrahedralization and follows a similar approach for mapping properties. To implement this, the TetGen library by Si (2015) was integrated into a plug‐in for the RhinoCommon API. TetGen is written in C++, which meant that several steps were required: exposing the functionality of TetGen as a shared library in C++, writing a wrapper in C# to expose the functionality of this shared library in the .NET framework, and writing a plug‐in for both Rhino and Grasshopper in C# using the RhinoCommon API.

The results are much the same as the previous discussion with the 2D discretization and mapping of heterogeneity, except in a volumetric sense (Fig. 4.13). The benefit of both 2D and 3D methods is that they yield simplex

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(a)A physical prototype of a diverging glue‐laminated component.

(b)A cutaway of the laminated element, revealing the different regions inside, each with its own fibre direction.

Fig. 4.13:The model discretization in 3D, with wood fibre direction encoded as colour.

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elements ‐ triangles and tetrahedra ‐ which can be interfaced with FEA models in domains of material science or engineering. The simulation of wood in FEA software such as Abaqus relies on the generation of individual elements and a designation of their material properties, as explained by Mirianon, Fortino, and Toratti (2008), building on the work of Ormarsson (1999). Engineering values are available for a large variety of wood types and species (Obara 2018), meaning that a design interface to these domains can begin to extend the realm of the architectural designer towards the specification and control of properties and performance at a material level, through digital simulation.

Finally,Probe 1: Modelling wood propertiesprioritizes the longitudinal material axis in its explorations, since this aligns with the fibre direction of the timber. This privileges the strongest material axis and serves to illustrate the focus of the probe, especially in two dimensions. Detailed behaviour simulations of timber and more in‐depth models no doubt would require the full orthotropic frame, which includes the radial and tangential vectors.

The encoding of direction vectors as colour remains valid, however, because the rest of the frame can be derived from the addition of just one of these vectors. This means that the fibre direction map must be supplanted by an additionradial maportangent map. The precedent for this again comes from the computer graphics field: a technique called ”frame mapping” is presented by Kajiya (1985) for the representation of anisotropic lighting models in computer graphics. This uses both a normal map and a tangent map to derive the orthonormal local coordinate system, used to modulate lighting effects and simulate anisotropic surfaces. The derivation of a full orthonormal frame can therefore be borrowed for the encoding of the orthonormal material frame of timber in the same way.

This has a particular consequence for the representation of a glulam beam.

As an assembly of lumber that is generally pointing in the same direction, a fibre orientation map would not show much deviation. However, depending on where each lamella is cut from in relation to the tree trunk, the radial and tangential directions could greatly vary. Using a tangent or radial map as described above, the amount of variation or crowning in the glulam cross‐section could be thus communicated (Fig. 4.15).

Probe 1: Modelling wood propertiesconcludes with the question of how these lower‐level material distributions and associated datasets can be integrated into models of glulam components and structures at meso and macro scales, respectively. Further, generating and controlling fibre orientation data through higher‐level models would allow the presented methods ofrepresentingtimber properties andinterfacingwith other domains of simulation to be deployed at a wider architectural scale (Fig. 4.14). A significant component of that is how local properties ‐ such as

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Fig. 4.14:Representing fibre direction (top) as colour and deviation (bottom) as a green‐to‐red heat map on an architecturally scaled component ‐ RB_4_0

‐ fromDemonstrator: MBridge.

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Fig. 4.15:Using the fibre direction mapping to visualize differences in the radial material direction on a timber cross‐section. The concentric circles show growth rings. The top two cross‐sections show less colour variation due to being cut further away from the centre of the log. The bottom two cross‐sections show much variation due to being cut around the centre of the log.

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(a)The orthonormal wood axes vary between lamellae and within each lamella cross‐section. The longitudinal direction (blue) represents the fibre growth direction, along which the wood is strongest. Radial (green) and tangential (red) directions vary strongly depend on their distance to the centre of the tree and the orientation of the lamella in the cross‐section.

(b)The main axes in a glulam beam section become the averaged longitudinal fibre direction (blue) and the width (red) and height (green) directions.

Fig. 4.16:Moving from a material scale to a component scale requires the abstracting of properties.

the longitudinal material direction or fibre orientation ‐ can be abstracted into a larger‐scale, simplified property more suitable for assemblies with more numerous components (Fig. 4.16).

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