140 research outputs found
Different mechanics of snap-trapping in the two closely related carnivorous plants Dionaea muscipula and Aldrovanda vesiculosa
The carnivorous aquatic Waterwheel Plant (Aldrovanda vesiculosa L.) and the
closely related terrestrial Venus Flytrap (Dionaea muscipula SOL. EX J. ELLIS)
both feature elaborate snap-traps, which shut after reception of an external
mechanical stimulus by prey animals. Traditionally, Aldrovanda is considered as
a miniature, aquatic Dionaea, an assumption which was already established by
Charles Darwin. However, videos of snapping traps from both species suggest
completely different closure mechanisms. Indeed, the well-described snapping
mechanism in Dionaea comprises abrupt curvature inversion of the two trap
lobes, while the closing movement in Aldrovanda involves deformation of the
trap midrib but not of the lobes, which do not change curvature. In this paper,
we present the first detailed mechanical models for these plants, which are
based on the theory of thin solid membranes and explain this difference by
showing that the fast snapping of Aldrovanda is due to kinematic amplification
of the bending deformation of the midrib, while that of Dionaea unambiguously
relies on the buckling instability that affects the two lobes.Comment: accepted in Physical Review
Rolling at small scales
The rolling process is widely used in the metal forming industry and has been so for many years. However, the process has attracted renewed interest as it recently has been adapted to very small scales where conventional plasticity theory cannot accurately predict the material response. It is well-established that gradient effects play a role at the micron scale, and the objective of this study is to demonstrate how strain gradient hardening affects the rolling process. Specifically, the paper addresses how the applied roll torque, roll forces, and the contact conditions are modified by strain gradient plasticity. Metals are known to be stronger when large strain gradients appear over a few microns; hence, the forces involved in the rolling process are expected to increase relatively at these smaller scales. In the present numerical analysis, a steady-state modeling technique that enables convergence without dealing with the transient response period is employed. This allows for a comprehensive parameter study. Coulomb friction, including a stick–slip condition, is used as a first approximation. It is found that length scale effects increase both the forces applied to the roll, the roll torque, and thus the power input to the process. The contact traction is also affected, particularly for sheet thicknesses on the order of 10 μm and below. The influences of the length parameter and the friction coefficient are emphasized, and the results are presented for multiple sheet reductions and roll sizes.</jats:p
Soft modes near the buckling transition of icosahedral shells
Icosahedral shells undergo a buckling transition as the ratio of Young's
modulus to bending stiffness increases. Strong bending stiffness favors smooth,
nearly spherical shapes, while weak bending stiffness leads to a sharply
faceted icosahedral shape. Based on the phonon spectrum of a simplified
mass-and-spring model of the shell, we interpret the transition from smooth to
faceted as a soft-mode transition. In contrast to the case of a disclinated
planar network where the transition is sharply defined, the mean curvature of
the sphere smooths the transitition. We define elastic susceptibilities as the
response to forces applied at vertices, edges and faces of an icosahedron. At
the soft-mode transition the vertex susceptibility is the largest, but as the
shell becomes more faceted the edge and face susceptibilities greatly exceed
the vertex susceptibility. Limiting behaviors of the susceptibilities are
analyzed and related to the ridge-scaling behavior of elastic sheets. Our
results apply to virus capsids, liposomes with crystalline order and other
shell-like structures with icosahedral symmetry.Comment: 28 pages, 6 figure
Accelerated high-cycle phase field fatigue predictions
Phase field fracture models have seen widespread application in the last
decade. Among these applications, its use to model the evolution of fatigue
cracks has attracted particular interest, as fatigue damage behaviour can be
predicted for arbitrary loading histories, dimensions and complexity of the
cracking phenomena at play. However, while cycle-by-cycle calculations are
remarkably flexible, they are also computationally expensive, hindering the
applicability of phase field fatigue models for technologically-relevant
problems. In this work, a computational framework for accelerating phase field
fatigue calculations is presented. Two novel acceleration strategies are
proposed, which can be used in tandem and together with other existing
acceleration schemes from the literature. The computational performance of the
proposed methods is documented through a series of 2D and 3D boundary value
problems, highlighting the robustness and efficiency of the framework even in
complex fatigue problems. The observed reduction in computation time using both
of the proposed methods in tandem is shown to reach a speed-up factor of 32,
with a scaling trend enabling even greater reductions in problems with more
load cycles
A micro-mechanics based extension of the GTN continuum model accounting for random void distributions
Randomness in the void distribution within a ductile metal complicates
quantitative modeling of damage following the void growth to coalescence
failure process. Though the sequence of micro-mechanisms leading to ductile
failure is known from unit cell models, often based on assumptions of a regular
distribution of voids, the effect of randomness remains a challenge. In the
present work, mesoscale unit cell models, each containing an ensemble of four
voids of equal size that are randomly distributed, are used to find statistical
effects on the yield surface of the homogenized material. A yield locus is
found based on a mean yield surface and a standard deviation of yield points
obtained from 15 realizations of the four-void unit cells. It is found that the
classical GTN model very closely agrees with the mean of the yield points
extracted from the unit cell calculations with random void distributions, while
the standard deviation varies with the imposed stress state. It is
shown that the standard deviation is nearly zero for stress triaxialities
, while it rapidly increases for triaxialities above ,
reaching maximum values of about at . At even higher triaxialities it decreases slightly. The results indicate
that the dependence of the standard deviation on the stress state follows from
variations in the deformation mechanism since a well-correlated variation is
found for the volume fraction of the unit cell that deforms plastically at
yield. Thus, the random void distribution activates different complex
localization mechanisms at high stress triaxialities that differ from the
ligament thinning mechanism forming the basis for the classical GTN model. A
method for introducing the effect of randomness into the GTN continuum model is
presented, and an excellent comparison to the unit cell yield locus is
achieved
Steady-state fracture toughness of elastic-plastic solids: Isotropic versus kinematic hardening
The fracture toughness for a mode I/II crack propagating in a ductile material has been subject to numerous investigations. However, the influence of the material hardening law has received very limited attention, with isotropic hardening being the default choice if cyclic loads are absent. The present work extends the existing studies of monotonic mode I/II steady-state crack propagation with the goal to compare the predictions from an isotropic hardening model with that of a kinematic hardening model. The work is conducted through a purpose-built steady-state framework that directly delivers the steady-state solution. In order to provide a fracture criterion, a cohesive zone model is adopted and embedded at the crack tip in the steady-state framework, while a control algorithm for the far-field, that significantly reduces the number of equilibrium iterations is employed to couple the far-field loading to the correct crack tip opening. Results show that the steady-state fracture toughness (shielding ratio) obtained for a kinematic hardening material is larger than for the corresponding isotropic hardening case. The difference between the isotropic and kinematic model is tied to the nonproportional loading conditions and reverse plasticity. This also explains the vanishing difference in the shielding ratio when considering mode II crack propagation as the non-proportional loading is less pronounced and the reverse plasticity is absent
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