A single touch can provide sufficient mechanical stimulation to trigger Venus flytrap closure.

The carnivorous Venus flytrap catches prey by an ingenious snapping mechanism. Based on work over nearly 200 years, it has become generally accepted that two touches of the trap's sensory hairs within 30 s, each one generating an action potential, are required to trigger closure of the trap. We developed an electromechanical model, which, however, suggests that under certain circumstances one touch is sufficient to generate two action potentials. Using a force-sensing microrobotic system, we precisely quantified the sensory-hair deflection parameters necessary to trigger trap closure and correlated them with the elicited action potentials in vivo. Our results confirm the model's predictions, suggesting that the Venus flytrap may be adapted to a wider range of prey movements than previously assumed.

Inversion of force lines in fiber-reinforced jammed granular material.

Freestanding columns, built out of nothing but loose gravel and continuous strings can be stable even at several meters in height and withstand vertical loads high enough to severely fragment grains of the column core. We explain this counter-intuitive behavior through dynamic simulations with polyhedral rigid particles and elastic wire chains. We evaluate the fine structure of the particle contact networks, as well as confining forces and reveal fundamental intrinsic differences to the well-studied case of confining silos.

Kinematics Governing Mechanotransduction in the Sensory Hair of the Venus flytrap.

Insects fall prey to the Venus flytrap (Dionaea muscipula) when they touch the sensory hairs located on the flytrap lobes, causing sudden trap closure. The mechanical stimulus imparted by the touch produces an electrical response in the sensory cells of the trigger hair. These cells are found in a constriction near the hair base, where a notch appears around the hair's periphery. There are mechanosensitive ion channels (MSCs) in the sensory cells that open due to a change in membrane tension; however, the kinematics behind this process is unclear. In this study, we investigate how the stimulus acts on the sensory cells by building a multi-scale hair model, using morphometric data obtained from µ-CT scans. We simulated a single-touch stimulus and evaluated the resulting cell wall stretch. Interestingly, the model showed that high stretch values are diverted away from the notch periphery and, instead, localized in the interior regions of the cell wall. We repeated our simulations for different cell shape variants to elucidate how the morphology influences the location of these high-stretch regions. Our results suggest that there is likely a higher mechanotransduction activity in these 'hotspots', which may provide new insights into the arrangement and functioning of MSCs in the flytrap.

Collapse of Orthotropic Spherical Shells.

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy.

Unifying model for the rheological behavior of hygroresponsive materials.

Hygroresponsive materials exhibit a complex structure-to-property relationship. The interactions of water within these materials under varying hygric and mechanical loads play a crucial role in their macroscopic deformation and final application. While multiple models are available in literature, many lack a comprehensive physical understanding of these phenomena. In this paper, we introduce a stick-slip fiber bundle model that captures the fundamental behaviors of hygroresponsive materials. We incorporate moisture-dependent elements and rules governing the initiation and relaxation of slip strains as well as failure to the statistical approach offered by fiber bundle models. The additional features are based on well-founded interpretations of the structure-to-property relationship in cellulosic materials. Slip strains are triggered by changes in load and moisture, as well as by creep deformations. When subjected to moisture cycles, the model accumulates slip strains, resulting in mechanosorptive behavior. When the load is removed, slip strains are partially relaxed, and subsequent moisture cycles trigger further relaxation, as expected from observations with mechanosorptive material. Importantly, these slip strains are not considered plastic strains; instead, they are unified, nonlinear frozen strains, activated by various stimuli. Failure of fibers is defined by a critical number of slip events allowing for an integrated simulation from intact, via damaged, failed states. We investigate the transition between these regimes upon changes in the hygric and mechanical loading history for relevant parameter ranges. Our enhanced stick-slip fiber bundle model increases the understanding of the intricate behavior of hygroresponsive materials and contributes to a more robust framework for analyzing and interpreting their properties.

Wood Derived Cellulose Scaffolds-Processing and Mechanics.

Wood-derived cellulose materials obtained by structure-retaining delignification are attracting increasing attention due to their excellent mechanical properties and great potential to serve as renewable and CO2 storing cellulose scaffolds for advanced hybrid materials with embedded functionality. Various delignification protocols and a multitude of further processing steps including polymer impregnation and densification are applied resulting in a large range of properties. However, treatment optimization requires a more comprehensive characterization of the developed materials in terms of structure, chemical composition, and mechanical properties for faster progress in the field. Herein, the current protocols for structure-retaining delignification are reviewed and the emphasis is placed on the mechanical characterization at different hierarchical levels of the cellulose scaffolds by experiments and modeling to reveal the underlying structure-property relationships.

Mechanical factors contributing to the Venus flytrap's rate-dependent response to stimuli.

The sensory hairs of the Venus flytrap (Dionaea muscipula Ellis) detect mechanical stimuli imparted by their prey and fire bursts of electrical signals called action potentials (APs). APs are elicited when the hairs are sufficiently stimulated and two consecutive APs can trigger closure of the trap. Earlier experiments have identified thresholds for the relevant stimulus parameters, namely the angular displacement [Formula: see text] and angular velocity [Formula: see text]. However, these experiments could not trace the deformation of the trigger hair's sensory cells, which are known to transduce the mechanical stimulus. To understand the kinematics at the cellular level, we investigate the role of two relevant mechanical phenomena: viscoelasticity and intercellular fluid transport using a multi-scale numerical model of the sensory hair. We hypothesize that the combined influence of these two phenomena and [Formula: see text] contribute to the flytrap's rate-dependent response to stimuli. In this study, we firstly perform sustained deflection tests on the hair to estimate the viscoelastic material properties of the tissue. Thereafter, through simulations of hair deflection tests at different loading rates, we were able to establish a multi-scale kinematic link between [Formula: see text] and the cell wall stretch [Formula: see text]. Furthermore, we find that the rate at which [Formula: see text] evolves during a stimulus is also proportional to [Formula: see text]. This suggests that mechanosensitive ion channels, expected to be stretch-activated and localized in the plasma membrane of the sensory cells, could be additionally sensitive to the rate at which stretch is applied.

Self-contact and instabilities in the anisotropic growth of elastic membranes.

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e cone solution is energetically minimal any more. Instead, we obtain skewed e cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.

Computational analysis of hygromorphic self-shaping wood gridshell structures.

Bi-layered composites capable of self-shaping are of increasing relevance to science and engineering. They can be made out of anisotropic materials that are responsive to changes in a state variable, e.g. wood, which swells and shrinks by changes in moisture. When extensive bending is desired, such bilayers are usually designed as cross-ply structures. However, the nature of cross-ply laminates tends to prevent changes of the Gaussian curvature so that a plate-like geometry of the composite will be partly restricted from shaping. Therefore, an effective approach for maximizing bending is to keep the composite in a narrow strip configuration so that Gaussian curvature can remain constant during shaping. This represents a fundamental limitation for many applications where self-shaped double-curved structures could be beneficial, e.g. in timber architecture. In this study, we propose to achieve double-curvature by gridshell configurations of narrow self-shaping wood bilayer strips. Using numerical mechanical simulations, we investigate a parametric phase-space of shaping. Our results show that double curvature can be achieved and that the change in Gaussian curvature is dependent on the system's geometry. Furthermore, we discuss a novel architectural application potential in the form of self-erecting timber gridshells.

Evolution of fragment size distributions from the crushing of granular materials.

We study fragment size distributions after crushing single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single-particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many-grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives information about the origin of the power-law distributions for the granular assembly under uniaxial compression.

Analysis of hygroscopic self-shaping wood at large scale for curved mass timber structures.

The growing timber manufacturing industry faces challenges due to increasing geometric complexity of architectural designs. Complex and structurally efficient curved geometries are nowadays easily designed but still involve intensive manufacturing and excessive machining. We propose an efficient form-giving mechanism for large-scale curved mass timber by using bilayered wood structures capable of self-shaping by moisture content changes. The challenge lies in the requirement of profound material knowledge for analysis and prediction of the deformation in function of setup and boundary conditions. Using time- and moisture-dependent mechanical simulations, we demonstrate the contributions of different wood-specific deformation mechanisms on the self-shaping of large-scale elements. Our results outline how to address problems such as shape prediction, sharp moisture gradients, and natural variability in material parameters in light of an efficient industrial manufacturing.

Modeling and design of thin bending wooden bilayers.

In recent architectural research, thin wooden bilayer laminates capable of self-actuation in response to humidity changes have been proposed as sustainable, programmed, and fully autonomous elements for facades or roofs for shading and climate regulation. Switches, humidistats, or motor elements represent further promising applications. Proper wood-adapted prediction models for actuation, however, are still missing. Here, a simple model that can predict bending deformation as a function of moisture content change, wood material parameters, and geometry is presented. We consider material anisotropy and moisture-dependency of elastic mechanical parameters. The model is validated using experimental data collected on bilayers made out of European beech wood. Furthermore, we present essential design aspects in view of facilitated industrial applications. Layer thickness, thickness-ratio, and growth ring angle of the wood in single layers are assessed by their effect on curvature, stored elastic energy, and generated axial stress. A sensitivity analysis is conducted to identify primary curvature-impacting model input parameters.

Characterization of size-dependent mechanical properties of tip-growing cells using a lab-on-chip device.

Quantification of mechanical properties of tissues, living cells, and cellular components is crucial for the modeling of plant developmental processes such as mechanotransduction. Pollen tubes are tip-growing cells that provide an ideal system to study the mechanical properties at the single cell level. In this article, a lab-on-a-chip (LOC) device is developed to quantitatively measure the biomechanical properties of lily (Lilium longiflorum) pollen tubes. A single pollen tube is fixed inside the microfluidic chip at a specific orientation and subjected to compression by a soft membrane. By comparing the deformation of the pollen tube at a given external load (compressibility) and the effect of turgor pressure on the tube diameter (stretch ratio) with finite element modeling, its mechanical properties are determined. The turgor pressure and wall stiffness of the pollen tubes are found to decrease considerably with increasing initial diameter of the pollen tubes. This observation supports the hypothesis that tip-growth is regulated by a delicate balance between turgor pressure and wall stiffness. The LOC device is modular and adaptable to a variety of cells that exhibit tip-growth, allowing for the straightforward measurement of mechanical properties.

Granular-front formation in free-surface flow of concentrated suspensions.

A granular front emerges whenever the free-surface flow of a concentrated suspension spontaneously alters its internal structure, exhibiting a higher concentration of particles close to its front. This is a common and yet unexplained phenomenon, which is usually believed to be the result of fluid convection in combination with particle size segregation. However, suspensions composed of uniformly sized particles also develop a granular front. Within a large rotating drum, a stationary recirculating avalanche is generated. The flowing material is a mixture of a viscoplastic fluid obtained from a kaolin-water dispersion with spherical ceramic particles denser than the fluid. The goal is to mimic the composition of many common granular-fluid materials, such as fresh concrete or debris flow. In these materials, granular and fluid phases have the natural tendency to separate due to particle settling. However, through the shearing caused by the rotation of the drum, a reorganization of the phases is induced, leading to the formation of a granular front. By tuning the particle concentration and the drum velocity, it is possible to control this phenomenon. The setting is reproduced in a numerical environment, where the fluid is solved by a lattice-Boltzmann method, and the particles are explicitly represented using the discrete element method. The simulations confirm the findings of the experiments, and provide insight into the internal mechanisms. Comparing the time scale of particle settling with the one of particle recirculation, a nondimensional number is defined, and is found to be effective in predicting the formation of a granular front.

Grain-scale modeling of arbitrary fluid saturation in random packings.

We propose a model for increasing liquid saturation in a granular packing, which can account for liquid redistribution at saturation levels beyond the well-studied capillary bridge regime. The model is capable of resolving and combining capillary bridges, menisci, and fully saturated pores to form local liquid clusters of any shape. They can exchange volume due to the local Laplace pressure gradient via a liquid film on the surfaces of grains. Local instabilities such as Haines jumps trigger the discontinuous evolution of the liquid front. The applicability of the model is demonstrated and compared to benchmark experiments on the level of individual liquid structures as well as on larger systems.