02 Fakultät Bau- und Umweltingenieurwissenschaften
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3
Browse
13 results
Search Results
Item Open Access Smooth or with a snap! Biomechanics of trap reopening in the Venus flytrap (Dionaea muscipula)(2022) Durak, Grażyna M.; Thierer, Rebecca; Sachse, Renate; Bischoff, Manfred; Speck, Thomas; Poppinga, SimonFast snapping in the carnivorous Venus flytrap (Dionaea muscipula) involves trap lobe bending and abrupt curvature inversion (snap‐buckling), but how do these traps reopen? Here, the trap reopening mechanics in two different D. muscipula clones, producing normal‐sized (N traps, max. ≈3 cm in length) and large traps (L traps, max. ≈4.5 cm in length) are investigated. Time‐lapse experiments reveal that both N and L traps can reopen by smooth and continuous outward lobe bending, but only L traps can undergo smooth bending followed by a much faster snap‐through of the lobes. Additionally, L traps can reopen asynchronously, with one of the lobes moving before the other. This study challenges the current consensus on trap reopening, which describes it as a slow, smooth process driven by hydraulics and cell growth and/or expansion. Based on the results gained via three‐dimensional digital image correlation (3D‐DIC), morphological and mechanical investigations, the differences in trap reopening are proposed to stem from a combination of size and slenderness of individual traps. This study elucidates trap reopening processes in the (in)famous Dionaea snap traps - unique shape‐shifting structures of great interest for plant biomechanics, functional morphology, and applications in biomimetics, i.e., soft robotics.Item Open Access Transverse shear parametrization in hierarchic large rotation shell formulations(2024) Thierer, Rebecca; Oesterle, Bastian; Ramm, Ekkehard; Bischoff, ManfredConsistent treatment of large rotations in common Reissner-Mindlin formulations is a complicated task. Reissner-Mindlin formulations that use a hierarchic parametrization provide an elegant way to facilitate large rotation shell analyses. This can be achieved by the assumption of linearized transverse shear strains, resulting in an additive split of strain components, which technically simplifies implementation of corresponding shell finite elements. The present study aims at validating this assumption by systematically comparing numerical solutions with those of a newly implemented hierarchic and fully nonlinear Reissner-Mindlin shell element.Item Open Access The structural and mechanical basis for passive‐hydraulic pine cone actuation(2022) Eger, Carmen J.; Horstmann, Martin; Poppinga, Simon; Sachse, Renate; Thierer, Rebecca; Nestle, Nikolaus; Bruchmann, Bernd; Speck, Thomas; Bischoff, Manfred; Rühe, JürgenThe opening and closing of pine cones is based on the hygroscopic behavior of the individual seed scales around the cone axis, which bend passively in response to changes in environmental humidity. Although prior studies suggest a bilayer architecture consisting of lower actuating (swellable) sclereid and upper restrictive (non‐ or lesser swellable) sclerenchymatous fiber tissue layers to be the structural basis of this behavior, the exact mechanism of how humidity changes are translated into global movement are still unclear. Here, the mechanical and hydraulic properties of each structural component of the scale are investigated to get a holistic picture of their functional interplay. Measurements of the wetting behavior, water uptake, and mechanical measurements are used to analyze the influence of hydration on the different tissues of the cone scales. Furthermore, their dimensional changes during actuation are measured by comparative micro‐computed tomography (µ‐CT) investigations of dry and wet scales, which are corroborated and extended by 3D‐digital image correlation‐based displacement and strain analyses, biomechanical testing of actuation force, and finite element simulations. Altogether, a model allowing a detailed mechanistic understanding of pine cone actuation is developed, which is a prime concept generator for the development of biomimetic hygromorphic systems.Item Open Access A consistent finite element formulation of the geometrically non-linear Reissner-Mindlin shell model(2022) Müller, Alexander; Bischoff, ManfredWe present an objective, singularity-free, path independent, numerically robust and efficient geometrically non-linear Reissner-Mindlin shell finite element formulation. The formulation is especially suitable for higher order ansatz spaces. The formulation utilizes geometric finite elements presented by Sander [ 47 ] and Grohs [ 34 ] for the interpolation on non-linear manifolds. The proposed method is objective and free from artificial singularities and spurious path dependence. Due to the fact that the director field lives on the unit sphere, a special linearization procedure is required to obtain the stiffness matrix. Here, we use the simple constructions of Absil et al. [ 2 , 3 ], which yields an easy way to obtain the correct tangent operator of the potential energy. Additionally, we compare three different interpolation schemes for the shell director that can be found in the literature, where one of them is applied for the first time for the Reissner-Mindlin shell model. Furthermore, we compare the exponential map to the radial return normalization as procedure to update the nodal directors and conclude the superiority of the latter, in terms of fewer load steps. We also investigate the construction of a consistent tangent base update scheme. Path independence, efficiency and objectivity of the formulation are verified via a set of numerical examples.Item Open Access Constrained motion design with distinct actuators and motion stabilization(2021) Sachse, Renate; Geiger, Florian; Bischoff, ManfredThe design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure's energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.Item Open Access Analytical and numerical case studies on tailoring stiffness for the design of structures with displacement control(2023) Trautwein, Axel; Prokosch, Tamara; Senatore, Gennaro; Blandini, Lucio; Bischoff, ManfredThis paper discusses the role that structural stiffness plays in the context of designing adaptive structures. The focus is on load-bearing structures with adaptive displacement control. A design methodology is implemented to minimize the control effort by making the structure as stiff as possible against external loads and as flexible as possible against the effect of actuation. This rationale is tested using simple analytical and numerical case studies.Item Open Access Reciprocal mass matrices and a feasible time step estimator for finite elements with Allman's rotations(2020) Tkachuk, AntonFinite elements with Allman's rotations provide good computational efficiency for explicit codes exhibiting less locking than linear elements and lower computational cost than quadratic finite elements. One way to further raise their efficiency is to increase the feasible time step or increase the accuracy of the lowest eigenfrequencies via reciprocal mass matrices. This article presents a formulation for variationally scaled reciprocal mass matrices and an efficient estimator for the feasible time step for finite elements with Allman's rotations. These developments take special care of two core features of such elements: existence of spurious zero‐energy rotation modes implying the incompleteness of the ansatz spaces, and the presence of mixed‐dimensional degrees of freedom. The former feature excludes construction of dual bases used in the standard variational derivation of reciprocal mass matrices. The latter feature destroys the efficiency of the existing nodal‐based time step estimators stemming from the Gershgorin's eigenvalue bound. Finally, the developments are tested for standard benchmarks and triangular, quadrilateral, and tetrahedral finite elements with Allman's rotations.Item Open Access Artificial instabilities of finite elements for nonlinear elasticity : analysis and remedies(2023) Bieber, Simon; Auricchio, Ferdinando; Reali, Alessandro; Bischoff, ManfredWithin the framework of plane strain nonlinear elasticity, we present a discussion on the stability properties of various Enhanced Assumed Strain (EAS) finite element formulations with respect to physical and artificial (hourglassing) instabilities. By means of a linearized buckling analysis we analyze the influence of element formulations on the geometric stiffness and provide new mechanical insights into the hourglassing phenomenon. Based on these findings, a simple strategy to avoid hourglassing for compression problems is proposed. It is based on a modification of the discrete Green-Lagrange strain, simple to implement and generally applicable. The stabilization concept is tested for various popular element formulations (namely EAS elements and the assumed stress element by Pian and Sumihara). A further aspect of the present contribution is a discussion on proper benchmarking of finite elements in the context of hourglassing. We propose a simple bifurcation problem for which analytical solutions are readily available in the literature. It is tailored for an in-depth stability analysis of finite elements and allows a reliable assessment of its stability properties.Item Open Access Investigation and elimination of nonlinear Poisson stiffening in 3d and solid shell finite elements(2022) Willmann, Tobias; Bieber, Simon; Bischoff, ManfredWe show that most geometrically nonlinear three‐dimensional shell elements and solid shell elements suffer from a previously unknown artificial stiffening effect that only appears in geometrically nonlinear problems, in particular in the presence of large bending deformations. It can be interpreted as a nonlinear variant of the well‐known Poisson thickness locking effect. We explain why and under which circumstances this phenomenon appears and propose concepts to avoid it.Item Open Access Development of a material design space for 4D-printed bio-inspired hygroscopically actuated bilayer structures with unequal effective layer widths(2021) Krüger, Friederike; Thierer, Rebecca; Tahouni, Yasaman; Sachse, Renate; Wood, Dylan; Menges, Achim; Bischoff, Manfred; Rühe, Jürgen(1) Significance of geometry for bio-inspired hygroscopically actuated bilayer structures is well studied and can be used to fine-tune curvatures in many existent material systems. We developed a material design space to find new material combinations that takes into account unequal effective widths of the layers, as commonly used in fused filament fabrication, and deflections under self-weight. (2) For this purpose, we adapted Timoshenko’s model for the curvature of bilayer strips and used an established hygromorphic 4D-printed bilayer system to validate its ability to predict curvatures in various experiments. (3) The combination of curvature evaluation with simple, linear beam deflection calculations leads to an analytical solution space to study influences of Young’s moduli, swelling strains and densities on deflection under self-weight and curvature under hygroscopic swelling. It shows that the choice of the ratio of Young’s moduli can be crucial for achieving a solution that is stable against production errors. (4) Under the assumption of linear material behavior, the presented development of a material design space allows selection or design of a suited material combination for application-specific, bio-inspired bilayer systems with unequal layer widths.