Topological interlocking assemblies (TIA) are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are prevented by the neighbouring blocks and the frame. In the literature, several blocks are introduced that can be arranged into interlocking assemblies, however only few of them can be arranged in non-unique ways. This study investigates a particularly versatile interlocking block called the Versatile Block: this block can be arranged in three different doubly periodic ways given by wallpaper symmetries. We investigate the hypothesis that the arrangement of copies of the same block influences the mechanical response of a TIA. We examine the interlocking mechanism and the correlation between arrangement and overall structural performance in planar TIA consisting of the Versatile Block. Furthermore, we analyse load transfer mechanisms within the assemblies and from the assemblies onto the frame. For fast apriori evaluation of the load transfer onto the frame we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection under a given load, thereby confirming our hypothesis. We also evaluate the accuracy of the proposed Interlocking Flow model by a comparison with the finite element simulations.

Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the literature several blocks are introduced that can be arranged into different interlocking assemblies. In this study we investigate the influence of arrangement on the overall structural behaviour of the resulting interlocking assemblies. This is performed using the Versatile Block, as it can be arranged in three different doubly periodic ways given by wallpaper symmetries. Our focus lies on the load transfer mechanisms from the assembly onto the frame. For fast a priori evaluation of the assemblies we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection. The results of the finite element analysis are in very good agreement with the predictions of the Interlocking Flow model. Our source code, data and examples are available under https://doi.org/10.5281/zenodo.10246034.

Pflanzen zeigen eine Vielzahl unterschiedlicher Blattformen. Die mechanischen Eigenschaften der Blätter werden durch die innere Zusammensetzung der verschiedenen Gewebe bestimmt. Die biomechanischen Eigenschaften von peltaten Blättern wurden bisher nur wenig erforscht. Die komplexe Faserorganisation in dieser Art von Blättern kann als Inspiration für neuartige Carbonbeton-Strukturen dienen. Aufgrund der komplexen morphologischen Anatomie von Blättern können nicht alle Informationen über das mechanische Verhalten aus Experimenten gewonnen werden. Daher untersuchen wir in diesem Beitrag das mechanische Verhalten von peltaten Blättern von Stephania japonica mithilfe der numerischen Simulation. Für die Finite-Elemente-Simulationen wird ein kontinuumsmechanisches Materialmodell verwendet. Zunächst werden die numerischen Ergebnisse mit den realen Versuchen verglichen. Dann wird das Modell eingesetzt, um das Verhalten des Pflanzengewebes unter verschiedenen Belastungsbedingungen zu simulieren. Darüber hinaus werden auf der Grundlage der CT-Daten des Blattgewebes einige mögliche Carbonbeton-Strukturen vorgeschlagen.

Plant leaves are exposed to a variety of stresses and must resist these stresses without being damaged. The mechanical properties of leaves are defined by the internal composition and organization of different tissues. Fibers, as tissues stronger in tension, are combined with tissues stronger in compression. Thus, plant leaves can be described as fiber-reinforced structures. Not many research efforts have been devoted to investigate biomechanical properties of the peltate leaf shape, which is characterized by the attachment of the leaf stalk to the underside of the leaf blade. In other words, a peltate leaf can be defined as a beam supporting a flying roof. The organization and arrangement of the fibers stabilizing the structure as a whole and the connection between beam and roof can serve as an inspiration for novel carbon reinforced concrete structures. Due to the complex morphology and anatomy of leaves, not all information about the mechanical behavior can be obtained from experiments. Therefore, in this contribution, we investigate the mechanical behavior of a peltate-leaved species by means of the numerical simulation. For the finite element simulations a continuum mechanical transversely isotropic viscoelastic material model is used. First, the numerical results are compared with the results obtained in the real experiments to show the validity of the model. Then, the model is used to simulate the behavior of the leaf elements under various loading conditions. Furthermore, based on the numerical results and CT-data of leaf elements some possible carbon reinforced concrete structures are proposed.

This work is concerned with an adaptive reduced order model of modular structures assembled from parameter-dependent substructures. The substructures are reduced by proper orthogonal decomposition (POD) and connected by means of a tied contact formulation. We present a method to adapt the matrices of the substructures to parameter changes. We employ interpolation on Grassmann manifolds for the parametric adaption of the projection matrices. For the adaptation of the stiffness matrices, we use the direct empirical interpolation method (DEIM). Manifold interpolation of the reduced stiffness matrices, cannot be applied here since it would require semi-positive definiteness, which is here not fulfilled because of necessary rigid body motion modes. The novelty of this work is the application of these interpolation methods to the special problem class of POD-based tied contact model order reduction. Furthermore, we show a methodology to compute significant snapshots on the substructure level to compute a POD basis that can be used in different global structures.

Carbonbeton bietet gegenüber der klassischen Stahlbetonbauweise neue Konstruktionsansätze. Um diese auszuschöpfen, werden Entwurfsstrategien entwickelt, welche auf eine materialminimierte Bauweise und auf maschinengestützte Fertigungsmethoden abzielen. Die Inspiration für innovative Strukturen, deren Bewertung sowie der Gewinn eines tiefergehenden Verständnisses für Material-, Bruch- und Verbundverhalten des Werkstoffs können durch Simulationen unterstützt werden. Dieser Beitrag bietet einen Überblick über verschiedene numerische Methoden, die den Prozess von der Ideenfindung, über den Übertrag auf den Werkstoff Carbonbeton und dessen Untersuchung und Bewertung unterstützen sollen. Das umfasst zum einen Methoden, die Inspiration für Geometrie- und Bewehrungsentwürfe aus der Mathematik und der Botanik ableiten sowie Modellreduktionsstrategien, um unterschiedlichste Geometrien effizient zusammenzusetzen und numerisch zu testen. Zum anderen werden verschiedene Mehrskalenmethoden und Material- und Schädigungsmodelle präsentiert, die dazu dienen, das Materialverhalten zuverlässig voraussagen zu können. Weiterhin wird eine Methode zur automatischen Rissdetektion vorgestellt.

In this contribution, we present a continuum mechanical transversely isotropic viscoelastic material model at finite deformations to model the mechanical behavior of the plant tissues of peltate leaves of Stephania japonica . Not many research efforts have been devoted to investigate the mechanical properties of this type of leaf shape. The model is obtained by postulating a particular Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on the structural tensors to account for the transversely isotropic material behavior. The evolution equations are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The numerical example reveals that the proposed model is capable of predicting the mechanical response of the real plant tissues at different loading rates.

Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work.

AbstractA model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.