Comparing structural models of linear elastic responses to bending in inosculated joints

Abstract

Key message Mechanical models of inosculations benefit from moderate geometric detail and characterisation of the structurally optimised area of interwoven tension-resistant fibres between the branches. Abstract Living architecture is formed by shaping and merging trees, often in combination with non-living technical elements. These structures often employ the mechanical and physiological adaptations of living trees to support structural loads. Designed and vernacular buildings utilise inosculations to redistribute forces, redirect growth, and provide redundancy. Mechanical models of inosculations in living architecture must be built according to the adaptations available to the tree. Here, mass allocation and fibre orientation are examined. Under typical gravity loads, a zone at the top of the inosculation is subject to tension. This is of particular interest because a trade-off in fibre orientation between mechanical and physiological optimisation is necessary. In tree forks, this results in specifically adapted interwoven fibres. In this study, Finite Element Analysis (FEA) is used to develop different mechanical models to fit bending experiments of four Salix alba inosculations, comparing the models’ accuracy in replicating rotations in the joint. Nine models were developed. Three levels of detail of mass allocation are considered for global isotropic (3 models) and orthotropic (3 models) mechanical properties as well as a model including the interwoven tension zone, a model of local branch and trunk orthotropy, and a model combining these two localised features. Results show significant accuracy gains come from moderate geometric accuracy and consideration of the tension-zone optimisation. The construction of the tension zone in FEA is simple and applicable to natural and artificially induced inosculations.

Conjoining Trees for the Provision of Living Architecture in Future Cities: A Long-Term Inosculation Study

“…However, because of the complex geometry of inosculations and branch junctions, mechanical tests are difficult to analyze. Therefore, Middleton et al [ 47 ] used Finite Element Analysis to develop mechanical models of S. alba inosculations that are in good agreement with bending experiments performed in the elastic range. Moreover, the results might also contribute to a better understanding of the natural inosculations of roots [ 26 , 27 , 28 ].…”

Effect of Geometry Precision and Load Distribution on Branch Mechanical Response

“…Solid geometry opens the possibility of implementing wood anisotropy and heterogeneously distributed properties [28]. The precisely extracted scanned shapes used in the details (stem junction) showed more agreement with the static response in the experiment than the cylinder-created geometry [30]. In a modal analysis, the model accuracy varied according to the type of mode shape [32].…”

“…Furthermore, the bending moment is a useful and measurable parameter for static and dynamic analyses [22,25,26]. The emergence of tree structure (crown and stem) creation provides the option to apply, for example, (a) beam-shaped geometry based on directly measured and 3D scan-based parameters [20,27]; (b) solid geometry, which can be generated from a 3D scan by cylinders [28,29]; or (c) solid geometry, precisely extracted by Poisson surface reconstruction [30][31][32]. Solid geometry opens the possibility of implementing wood anisotropy and heterogeneously distributed properties [28].…”

Elasto-plastic material model of green beech wood

“…Vojackova et al [10] present an FEM simulation of tree response to static loading and the interaction between stem and root-plate stiffness, which they validate by comparison with field-measured data. Middleton et al [11] use different mechanical finiteelement (FE) models of tree forks to replicate rotations in the joints and validate them by bending mechanical testing of different Salix alba inosculations.…”