Biomedical subjects

H J Herrmann

Publications and source records attributed to H J Herrmann.

At least 19 recordsLinked to original sources

PubMed2006

Critical role of gravity in filters.

The efficiency of filters depends crucially on the mass of the particles one wants to capture. Using analytical and numerical calculations we reveal a very rich scenario of scaling laws relating this efficiency to particle size and density and the velocity and viscosity of the carrying fluid. These are combined in the dimensionless, so-called Stokes number St. In the case of horizontal flow or neutrally buoyant particles, we find a critical number St{c} below which no particles are trapped; i.e., the filter does not work. Above St{c} the capture efficiency increases like the square root of (St-St{c}). Under the action of gravity, the threshold abruptly vanishes and capture occurs at any Stokes number increasing linearly in St. We discovered further scaling laws in the penetration profile and as function of the porosity of the filter.

Biophysics↗

PubMed2006

Effect of rolling on dissipation in fault gouges.

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

Journal Article↗

PubMed2006

Periodic neural activity induced by network complexity.

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with nonperiodic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.

Journal Article↗

PubMed2006

Scaling behavior of fragment shapes.

We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have shown that the fragments vary from completely isotropic to highly anisotropic elongated shapes, depending on the microscopic cracking mechanism of the shell. Anisotropic fragments proved to have a self-affine character described by a scaling exponent. The distribution of fragment shapes exhibits a power-law decay. The robustness of the scaling laws is illustrated by a stochastic hierarchical model of fragmentation. Our results provide a possible improvement of the representation of fragment shapes in models of space debris.

Journal Article↗

PubMed2005

Simple beam model for the shear failure of interfaces.

We propose a model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises-type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.

Journal Article↗

PubMed2005

Characterization of the material response in granular ratcheting.

The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading. In this state, the system accumulates a small permanent deformation after each cycle. The value of this permanent strain accumulation becomes independent of the number of cycles after a short transient regime. We show in this paper that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. The definition of these variables is such that they can be easily measured both in the experiments and in the simulations. A thorough investigation of the micro- and macromechanical factors affecting these variables has been carried out by means of molecular-dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with periodically varying load were implemented. The effect on the plastic response of the confining pressure, the deviatoric stress, and the number of cycles has been investigated. The stiffness of the contacts and friction has been shown to play an important role in the overall response of the system. Especially illustrative is the influence of the peculiar hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.

Journal Article↗

PubMed2005

Role of anisotropy in the elastoplastic response of a polygonal packing.

We study the effect of the anisotropy induced by loading on the elastoplastic response of a two dimensional discrete element model granular material. The anisotropy of the contact network leads to a breakdown of the linear isotropic elasticity. We report on a linear dependence of the Young moduli and Poisson ratios on the fabric coefficients, measuring the anisotropy of the contact network. The resulting nonassociated plastic flow rule and the linear relationship between dilatancy and stress ratio are discussed in terms of several existing models. We propose a paradigm for understanding soil plasticity, based on the correlation between the plastic flow rule and the induced anisotropy on the subnetwork of sliding contacts.

Journal Article↗

PubMed2005

A model of Barchan dunes including lateral shear stress.

Barchan dunes are found where sand availability is low and wind direction quite constant. The two dimensional shear stress of the wind field and the sand movement by saltation and avalanches over a barchan dune are simulated. The model with one dimensional shear stress is extended including surface diffusion and lateral shear stress. The resulting final shape is compared to the results of the model with a one dimensional shear stress and confirmed by comparison to measurements. We found agreement and improvements with respect to the model with one dimensional shear stress. Additionally, a characteristic edge at the center of the windward side is discovered which is also observed for big barchans. Diffusion effects reduce this effect for small dunes.

Computer Simulation↗

PubMed2005

Breakup of shells under explosion and impact.

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on eggshells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class, different from that of two- and three-dimensional bulk systems.

Journal Article↗

PubMed2004

Multiple invaded consolidating materials.

We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as a function of the generation number G , i.e., with the number of times the invasion process takes place. The averaged mass M of the invaded region decreases with a power law as a function of G , M approximately Gbeta , where the exponent beta approximately 0.6 . We also find that the fractal dimension of the invaded cluster changes from d(1) =1.887+/-0.002 to d(s) =1.217+/-0.005 . This result confirms that the multiple invasion process (for the case in which uninvaded regions are forbidden) follows a continuous transition from one universality class (nontrapping invasion percolation) to another (optimal path). In addition, we report extensive numerical simulations that indicate that the mass distribution of avalanches P (S,L) has a power-law behavior and we find that the exponent tau governing the power-law P (S,L) approximately S-tau changes continuously as a function of the parameter G . We propose a scaling law for the mass distribution of avalanches for different number of generations G .

Journal Article↗

PubMed2004

Fragmentation of shells.

We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.

Journal Article↗

PubMed2004

Ratcheting of granular materials.

We investigate the quasistatic mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasiperiodic ratchetlike behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows exploration of the role of friction in the permanent deformation of unbound granular materials subjected to cyclic loading.

Journal Article↗

PubMed2004

Space-filling bearings in three dimensions.

We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops of an even number of spheres can be constructed in a self-similar way and that it can act as a three-dimensional bearing in which spheres can rotate without slip and with negligible torsion friction.

Journal Article↗

PubMed2003

Comparing simulation and experiment of a 2D granular Couette shear device.

We present experiments along with molecular-dynamics (MD) simulations of a two-dimensional (2D) granular material in a Couette cell undergoing slow shearing. The grains are disks confined between an inner, rotating wheel and a fixed outer ring. The simulation results are compared to experimental studies and quantitative agreement is found. Tracking the positions and orientations of individual particles allows us to obtain density distributions, velocity and particle rotation rates for the system. The key issue of this paper is to show the extent to which quantitative agreement between an experiment and MD simulations is possible. Besides many differences in model details and the experiment, the qualitative features are nicely reproduced. We discuss the quantitative agreement/disagreement, give possible reasons, and outline further research perspectives.

Journal Article↗

PubMed2002

Calculation of the incremental stress-strain relation of a polygonal packing.

The constitutive relation of the quasistatic deformation on two-dimensional packed samples of polygons is calculated using molecular dynamics simulations. The stress values at which the system remains stable are bounded by a failure surface, which shows a power law dependence on the pressure. Below the failure surface, nonlinear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results show that the stiffness tensor can be directly related to the microcontact rearrangements. The plasticity obeys a nonassociated flow rule with a plastic limit surface that does not agree with the failure surface.

Journal Article↗

PubMed2002

Restructuring of force networks.

The compaction of granular packings or soils is a collective process which for higher densities becomes increasingly slower reaching glassy behaviour. We present a study of this problem from various points of view, in particular we will represent the evolving force network that percolates through the system by an inverse fiber rupture model.

Journal Article↗

PubMed2001

Bursts in a fiber bundle model with continuous damage.

We study the constitutive behavior, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive behaviors including macroscopic plasticity. Analytical results are obtained to characterize the damage process along the plastic plateau under strain controlled loading; furthermore, for stress controlled experiments we develop a simulation technique, and numerically explore the distribution of bursts of fiber breaks assuming an infinite range of interaction. Simulations revealed that under certain conditions power law distribution of bursts arises with an exponent significantly different from the mean field exponent 5/2. A phase diagram of the model characterizing the possible burst distributions is constructed.

Journal Article↗

PubMed2001

Continuum saltation model for sand dunes.

We derive a phenomenological continuum saltation model for aeolian sand transport that can serve as an efficient tool for geomorphological applications. The coupled differential equations for the average density and velocity of sand in the saltation layer reproduce both the known equilibrium relations for the sand flux and the time evolution of the sand flux as predicted by microscopic saltation models. The three phenomenological parameters of the model are a reference height for the grain-air interaction, an effective restitution coefficient for the grain-bed interaction, and a multiplication factor characterizing the chain reaction caused by the impacts leading to a typical time or length scale of the saturation transients. We determine the values of these parameters by comparing our model with wind tunnel measurements. Our main interest are out of equilibrium situations where saturation transients are important, for instance at phase boundaries (ground/sand) or under unsteady wind conditions. We point out that saturation transients are indispensable for a proper description of sand flux over structured terrain, by applying the model to the windward side of an isolated dune, thereby resolving recently reported discrepancies between field measurements and theoretical predictions.

Journal Article↗