Mechanical and Thermal Stability of Adhesive Membranes with Nonzero Bending Rigidity

Membranes at a microscopic scale are affected by thermal fluctuations and self-adhesion due to van der Waals forces. Methods to prepare membranes of even molecular scale, e.g., graphene, have recently been developed, and the question of their mechanical and thermal stability is of crucial importance. To this end we modeled microscopic membranes with an attractive interaction and applied Langevin dynamics. Their behavior was also analyzed under external loading. Even though these membranes folded during isotropic compression as a result of energy minimization, the process at high confinement was similar to crumpling of macroscopic nonadhesive sheets. The main difference appeared when the com…

Crack dynamics and crack surfaces in elastic beam lattices

The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as t1/7. At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a “mirror-mist-mirror” crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the “mirror-mist-hackle”–type interface typical in many experimental situations. Peer reviewed

Scaling Behavior in Non-Hookean Compression of Thin-Walled Structures

The mechanics and stability of thin-walled structures is a challenging and important branch in structural mechanics. Under vertical compression the deformation of a thin-walled box differs from that of, e.g., a cylindrical shell. It is demonstrated here that compression of a box can be described by a set of generic scaling laws representing three successive regimes: a linear, wrinkled, and collapsed regime. The linear Hookean regime represents the normal behavior before any instability sets in, while the following wrinkled regime is shown to be analogous to compression of thin-film blisters. The compression force reaches its maximum at the onset of the final collapsed regime that has all th…

Universality in Fragmentation

Fragmentation of a two-dimensional brittle solid by impact and ``explosion,'' and a fluid by ``explosion'' are all shown to become critical. The critical points appear at a nonzero impact velocity, and at infinite explosion duration, respectively. Within the critical regimes, the fragment-size distributions satisfy a scaling form qualitatively similar to that of the cluster-size distribution of percolation, but they belong to another universality class. Energy balance arguments give a correlation length exponent that is exactly one-half of its percolation value. A single crack dominates fragmentation in the slow-fracture limit, as expected.

Fracture Processes Observed with A Cryogenic Detector

In the early stages of running of the CRESST dark matter search using sapphire detectors at very low temperature, an unexpectedly high rate of signal pulses appeared. Their origin was finally traced to fracture events in the sapphire due to the very tight clamping of the detectors. During extensive runs the energy and time of each event was recorded, providing large data sets for such phenomena. We believe this is the first time the energy release in fracture has been directly and accurately measured on a microscopic event-by-event basis. The energy threshold corresponds to the breaking of only a few hundred covalent bonds, a sensitivity some orders of magnitude greater than that of previou…

Deterministic folding in stiff elastic membranes.

Crumpled membranes have been found to be characterized by complex patterns of spatially seemingly random facets separated by narrow ridges of high elastic energy. We demonstrate by numerical simulations that compression of stiff elastic membranes with small randomness in their initial configurations leads to either random ridge configurations (high entropy) or nearly deterministic folds (low elastic energy). For folding with symmetric ridge configurations to appear in part of the crumpling processes, the crumpling rate must be slow enough. Folding stops when the thickness of the folded structure becomes important, and crumpling continues thereafter as a random process.

Friction of Shear-Fracture Zones

A shear fracture of brittle solids under compression undergoes a substantial evolution from the initial microcracking to a fully formed powder-filled shear zone. Experiments covering the entire process are relatively easy to conduct, but they are very difficult to investigate in detail. Numerically, the large strain limit has remained a challenge. An efficient simulation model and a custom-made experimental device are employed to test to what extent a shear fracture alone is sufficient to drive material to spontaneous selflubrication. A “weak shear zone” is an important concept in geology, and a large number of explanations, specific for tectonic conditions, have been proposed. We demonstra…

Solution for the fragment-size distribution in a crack-branching model of fragmentation

It is well established that rapidly propagating cracks in brittle material are unstable such that they generate side branches. It is also known that cracks are attracted by free surfaces, which means that they attract each other. This information is used here to formulate a generic model of fragmentation in which the small-size part of the fragment-size distribution results from merged crack branches in the damage zones along the paths of the propagating cracks. This model is solved under rather general assumptions for the fragment-size distribution. The model leads to a generic distribution S(-gamma) exp(-S/S(0)) for fragment sizes S, where gamma = 2d-1/d with d the Euclidean dimension, an…

Termini of calving glaciers as self-organized critical systems

Calving margins are highly sensitive to changes in climate and glacier terminus geometry. Numerical modelling suggests that calving glacier termini are self-organized critical systems that are fluctuating between states of advance and retreat. Over the next century, one of the largest contributions to sea level rise will come from ice sheets and glaciers calving ice into the ocean1. Factors controlling the rapid and nonlinear variations in calving fluxes are poorly understood, and therefore difficult to include in prognostic climate-forced land-ice models. Here we analyse globally distributed calving data sets from Svalbard, Alaska (USA), Greenland and Antarctica in combination with simulat…

Comment on “Scaling behavior in explosive fragmentation”

We discuss the data analysis and the conclusions based upon the analysis given in the paper by Diehl et al. Following the suggestion in the Comment on our previous work by Astrom, Linna, and Timonen [Phys. Rev. E 65,048101 (2002)], we performed extensive molecular-dynamics simulations to confirm that our numerical results for the mass distribution of fragments after the "explosion" of thermalized samples are consistent with the scaling form n(m)∼m - ( α + 1 ) f(m/M 0 ), where ∫(m/M 0 ) is a cutoff function, M 0 is a cutoff parameter, and the exponent a is close to zero.

Exponential and power-law mass distributions in brittle fragmentation

Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size $s…

A discrete-element model for viscoelastic deformation and fracture of glacial ice

a b s t r a c t A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

Crumpling of a stiff tethered membrane.

first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The ratio of the amplitude and wave length of the wrinkles, and the scaling exponent of the stiffness divergence, are consistent with both theory and experiment. We observe that close to the stiffness divergence there appears a crossover beyond which the elastic behavior of a tethered membrane becomes similar to that of dry granular media. This suggests that ridge formation in membranes and force-chain network formation in granular packings are different manife…

Unconstrained periodic boundary conditions for solid state elasticity

We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.

The effect of plasticity in crumpling of thin sheets

Bridging the gap between theoretical and experimental work to understand the effect of plasticity on the crumpling of thin sheets into a small volume has proved difficult. A realistic numerical model now makes a distinction between elastic and elasto-plastic behaviour. Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges1,2. Scaling properties of a single elastic vertex3,4,5 or ridge have been analysed theoretically6,7,8, and crumpling of a sheet by numerical simulations1,9,10. Real materials are however elasto-plastic11,12,13,14,15 and large local strains induce irreversible plastic deformations. Hence, a …

Universal Dynamic Fragmentation inDDimensions

A generic model is introduced for brittle fragmentation in $D$ dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for $D=2$. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for $D=3$. In the experiments the nonzero grain size of rock causes deviation from th…

Granular packings and fault zones

The failure of a two-dimensional packing of elastic grains is analyzed using a numerical model. The packing fails through formation of shear bands or faults. During failure there is a separation of the system into two grain-packing states. In a shear band, local ``rotating bearings'' are spontaneously formed. The bearing state is favored in a shear band because it has a low stiffness against shearing. The ``seismic activity'' distribution in the packing has the same characteristics as that of the earthquake distribution in tectonic faults. The directions of the principal stresses in a bearing are reminiscent of those found at the San Andreas Fault.

Crack bifurcations in a strained lattice

Dynamic crack propagation in a strained, granular, and brittle material is investigated by modeling the material as a lattice network of elastic beams. By tuning the strain and the ratio of axial to bending stiffness of the beams, a crack propagates either straight, or it branches, or it bifurcates. The crack tip velocity is calculated approximately for cracks that propagate straight. In a bifurcated crack the number of broken beams follows a scaling law. The shape of the branches is found to be the same as in recent experiments.

The role of connectivity in the properties of sedimented materials

Effective-medium theories for both random packings of elastic discs and mats of randomly sedimented elastic fibers can be constructed such that the effective material stiffness depends on the stiffness and geometry of the constituents of the material, and the number density of contacts. It is demonstrated that the number density of contacts together with the geometry of the constituents also determine the porosity of these materials. The simplicity and similar structure of the effective-medium estimates for the properties of these two qualitatively different materials indicate that the number density of contacts may play a similar role in an appropriate effective-medium description of a lar…

Elastic waves in random-fibre networks

The propagation of the first displacement maximum of a semi-infinite wavetrain in a two-dimensional random-fibre network is analysed. Model calculations and numerical simulations are used for demonstrating that two qualitatively different wavefront velocities appear in the network. A transient wave, which travels fast and whose amplitude decreases exponentially, dominates the short-time behaviour when the bending stiffness of the fibres is small and the driving frequency is high. This mode can be described by a one-dimensional model. The transient-wave mode propagates even if the bending stiffness of the fibres vanishes, in which case the normal sound velocity is zero. The usual, and slower…

Fracture processes studied in CRESST

In the early stages of running of the CRESST dark matter search with sapphire crystals as detectors, an unexpectedly high rate of signal pulses appeared. Their origin was finally traced to fracture events in the sapphire due to the very tight clamping of the detectors. During extensive runs the energy and time of each event was recorded, providing large data sets for such phenomena. We believe this is the first time that the energy release in fracture has been accurately measured on a microscopic event-by-event basis. The energy distributions appear to follow a power law, dN/dE proportional to E-beta, similar to the Gutenberg-Richter power law for earthquake magnitudes, and after appropriat…

Elasticity of Poissonian fiber networks

An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks. These networks are commonly used as basic models of heterogeneous fibrous structures such as paper. Using the exact Poissonian statistics to describe the microscopic geometry of the network, the tensile modulus can be expressed by a single-parameter function. This parameter depends on the network density and fiber dimensions, which relate the macroscopic modulus to the relative importance of axial and bending deformations of the fibers. The model agrees well with simulation results and experimental findings. We also discuss the possible generalizations of the model. Peer reviewed

Fragmentation dynamics within shear bands--a model for aging tectonic faults?

A numerical model for packing of fragmenting blocks in a shear band is introduced, and its dynamics is compared with that of a tectonic fault. The shear band undergoes a slow aging process in which the blocks are being grinded by the shear motion and the compression. The dynamics of the model have the same statistical characteristics as the seismic activity in faults. The characteristic magnitude distribution of earthquakes appears to result from frictional slips at small and medium magnitudes, and from fragmentation of blocks at the largest magnitudes. Aftershocks to large-magnitude earthquakes are local recombinations of the fragments before they reach a new quasi-static equilibrium. The …

Dynamic rigidity transition.

An inflated closed loop (or membrane) is used to demonstrate a dynamic rigidity transition that occurs when impact energy is added to the loop in static equilibrium at zero temperature. The only relevant parameter in this transition is the ratio of the energy needed to collapse the loop and the impact energy. When this ratio is below a threshold value close to unity, the loop collapses into a high-entropy floppy state, and it does not return to the rigid state unless the impact energy can escape. The internal oscillations are in the floppy state dominated by 1/f(2) noise. When the ratio is above the threshold, the loop does not collapse, and the internal oscillations resulting from the impa…

Discrete element simulations of crumpling of thin sheets

Forced crumpling of stiff self-avoiding sheets is studied by discrete element simulations. Simulations display stress condensation and scaling of ridge energy in agreement with theoretical expectations for elastic and frictionless sheets, and extends such behavior to elasto-plastic sheets. Crumpling of ideally elastic and frictionless sheets is compared to that of elasto-plastic sheets and sheets with friction.

A particle based simulation model for glacier dynamics

This publication is contribution number 22 of the Nordic Centre of Excellence SVALI, “Stability and Variations of Arctic Land Ice”, funded by the Nordic Top-level Research Initiative (TRI). The work has been supported by the SVALI project through the University of Lapland, Arctic Centre, and through the University Centre in Svalbard. Funding was also provided by the Conoco-Phillips and Lunding High North Research Program (CRIOS: Calving Rates and Impact on Society). A particle-based computer simulation model was developed for investigating the dynamics of glaciers. In the model, large ice bodies are made of discrete elastic particles which are bound together by massless elastic beams. These…

Fouling dynamics in suspension flows

A particle suspension flowing in a channel in which fouling layers are allowed to form on the channel walls is investigated by numerical simulation. A two-dimensional phase diagram with at least four different behaviors is constructed. The fouling is modeled by attachment during collision with the deposits and by detachment caused by large enough hydrodynamic drag. For fixed total number of particles and small Reynolds numbers, the relevant parameters governing the fouling dynamics are the solid volume fraction of the suspension and the detachment drag force threshold. Below a critical curve in this 2D phase space only transient fouling takes place when the suspension is accelerated from re…

Fracture of a Brittle Membrane

Fracture mechanics of snow avalanches.

Dense snow avalanches are analyzed by modeling the snow slab as an elastic and brittle plate, attached by static friction to the underlying ground. The grade of heterogeneity in the local fracture (slip) thresholds, and the ratio of the average substrate slip threshold to the average slab fracture threshold, are the decisive parameters for avalanche dynamics. For a strong pack of snow there appears a stable precursor of local slips when the frictional contacts are weakened (equivalent to rising temperature), which eventually trigger a catastrophic crack growth that suddenly releases the entire slab. In the opposite limit of very high slip thresholds, the slab simply melts when the temperatu…

Clustering and viscosity in a shear flow of a particulate suspension

A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the char…

Roughening of a propagating planar crack front

A numerical model of the front of a planar crack propagating between two connected elastic plates is investigated. The plates are modeled as square lattices of elastic beams. The plates are connected by similar but breakable beams with a randomly varying stiffness. The crack is driven by pulling both plates at one end in Mode I at a constant rate. We find $\ensuremath{\zeta}=1/3, z=4/3,$ and $\ensuremath{\beta}=1/4$ for the roughness, dynamical, and growth exponents, respectively, that describe the front behavior. This is similar to continuum limit analyses based on a perturbative stress-intensity treatment of the front [H. Gao and J. R. Rice, J. Appl. Mech. 56, 828 (1989)]. We discuss the …

Rigidity and Dynamics of Random Spring Networks

The static and dynamic elastic properties of two-dimensional random networks composed of Hookean springs are analyzed. These networks are proved to be nonrigid with respect to small deformations, and the floppy mode ratio is calculated exactly. The vibrational spectrum is shown to consist only of zero-frequency and localized modes. The exponential decay of the amplitude and velocity of the transient wave front are shown to be exactly described by a quasi-one-dimensional model of noninteracting paths of propagation.

Dimensional effects in dynamic fragmentation of brittle materials.

It has been shown previously that dynamic fragmentation of brittle $D$-dimensional objects in a $D$-dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent $2\ensuremath{-}1∕D$. We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of $\ensuremath{\sim}1.17$.