arXiv subjects

Hans J. Herrmann

Publications and source records attributed to Hans J. Herrmann.

At least 199 records · Page 11Linked to original sources

arXiv2003

Simulation of the Sedimentation of a Falling Oblate

We present a numerical investigation of the dynamics of one falling oblate ellipsoid particle in a viscous fluid, in three dimensions, using a constrained-force technique \cite{Kai}, \cite{Kaih} and \cite{Esa}. We study the dynamical behavior of the oblate for a typical downward motion and obtain the trajectory, velocity, and orientation of the particle. We analyze the dynamics of the oblate generated when the height of the container, the aspect-ratio, and the dynamical viscosity are changed. Three types of falling motions are established: steady-falling, periodic oscillations and chaotic oscillations. In the periodic regime we find a behavior similar to the case of falling flat strips reported in ref. \cite{Belmonte}. In the chaotic regime the trajectory of the oblate is characterized by a high sensitivity to tiny variations in the initial orientation. The Lyapunov exponent is $λ= 0.052 \pm 0.005$. A phase space comparing to the results of ref \cite{Nori}, is shown.

cond-mat↗

arXiv2002

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 rate for the system. The key issue of this paper is to show the extent to which {\em 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.

cond-mat.stat-mech↗

arXiv2002

Time evolution of damage under variable ranges of load transfer

We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a crossover from mean field to short range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.

cond-mat.stat-mech↗

arXiv2002

Scaling laws of creep rupture of fiber bundles

We study the creep rupture of fiber composites in the framework of fiber bundle models. Two novel fiber bundle models are introduced based on different microscopic mechanisms responsible for the macroscopic creep behavior. Analytical and numerical calculations show that above a critical load the deformation of the creeping system monotonically increases in time resulting in global failure at a finite time $t_f$, while below the critical load the system suffers only partial failure and the deformation tends to a constant value giving rise to an infinite lifetime. It is found that approaching the critical load from below and above the creeping system is characterized by universal power laws when the fibers have long range interaction. The lifetime of the composite above the critical point has a universal dependence on the system size.

cond-mat.stat-mech↗

arXiv2002

Evolution of percolating force chains in compressed granular media

The evolution of effective force chains percolating through a compressed granular system is investigated. We performed experiments by compressing an ensemble of spherical particles in a cylindrical container monitoring the macroscopic constitutive behavior and the acoustic signals emitted by microscopic rearrangements of particles. As a novel approach, we applied the continuous damage model of fiber bundles to describe the evolution of the array of force chains during the loading process. The model provides a nonlinear constitutive behavior in good quantitative agreement with the experimental results. For a system of hard particles the model predicts a universal power law divergence of stress when approaching a critical deformation. The amplitude distribution of acoustic signals was found experimentally to follow a power law with exponent $δ= 1.15 \pm 0.05$ which is in a good agreement with the analytic solution of the model.

cond-mat↗

arXiv2002

Size segregation and convection

The size segregation of granular materials in a vibrating container is investigated using Molecular Dynamics. We find that the rising of larger particles is accompanied by the existence of convection cells even in the case of the lowest possible frequencies. The convection can, however, also be triggered by the larger particle itself. The possibility of rising through this mechanism strongly depends on the depth of the larger particle.

cond-mat.mtrl-sci↗

arXiv2002

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.

cond-mat.soft↗

arXiv2002

Minimal Model for Sand Dunes

We propose a minimal model for aeolian sand dunes. It combines an analytical description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The model provides a qualitative understanding of important features of real dunes, such as their longitudinal shape and aspect ratio, the formation of a slip face, the breaking of scale invariance, and the existence of a minimum dune size.

cond-mat.soft↗

arXiv2002

Fracture model with variable range of interaction

We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing schemes. By varying the range of interaction several features of the model are numerically studied and a crossover from mean field to short range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.

cond-mat.stat-mech↗

arXiv2001

A study of transverse ply cracking using a discrete element method

We study the transverse cracking of the 90 degree ply in [0/90] cross-ply laminates by means of a discrete element method. To model the 90 degree ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice model fibers, and springs with random breaking thresholds represent the disordered matrix material in between. The spring-lattice is coupled by interface springs to two rigid bars which represent the two 0 degree plies in the model, which could be sublaminate as well. Molecular dynamics simulation is used to follow the time evolution of the model system. It was found that under gradual loading of the specimen, after some distributed cracking, segmentation cracks occur in the 90 degree ply which then develop into a saturated state where the ply cannot support additional load. The stress distribution between two neighboring segmentation cracks was determined, furthermore, the dependence of the microstructure of damage on the ply's thickness was also studied. To give a quantitative characterization of stiffness degradation, the Young modulus of the system is monitored as a function of the density of segmentation cracks. The results of the simulations are in satisfactory agreement with experimental findings and with the results of analytic calculations.

cond-mat.mtrl-sci↗

arXiv2000

Damage in Fiber Bundle Models

We introduce a continuous damage fiber bundle model that gives rise to macroscopic plasticity and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors are found in this model depending on the value of the damage parameter and on the form of the disorder distribution. In addition, we compare the behavior of global load transfer models with local load transfer models and study in detail the damage evolution before failure. We emphasize the analogies between our results and spinodal nucleation in first-order phase transitions.

cond-mat.stat-mech↗

arXiv2000

Planar cracks in the fuse model

We simulate the propagation of a planar crack in a quasi-two dimensional fuse model, confining the crack between two horizontal plates. We investigate the effect on the roughness of microcrack nucleation ahead of the main crack and study the structure of the damage zone. The two dimensional geometry introduces a characteristic length in the problem, limiting the crack roughness. The damage ahead of the crack does not appear to change the scaling properties of the model, which are well described by gradient percolation.

cond-mat.stat-mech↗

arXiv2000

Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell

One of the essential questions in the area of granular matter is, how to obtain macroscopic tensorial quantities like stress and strain from ``microscopic'' quantities like the contact forces in a granular assembly. Different averaging strategies are introduced, tested, and used to obtain volume fractions, coordination numbers, and fabric properties. We derive anew the non-trivial relation for the stress tensor that allows a straightforward calculation of the mean stress from discrete element simulations and comment on the applicability. Furthermore, we derive the ``elastic'' (reversible) mean displacement gradient, based on a best-fit hypothesis. Finally, different combinations of the tensorial quantities are used to compute some material properties. The bulk modulus, i.e. the stiffness of the granulate, is a linear function of the trace of the fabric tensor which itself is proportional to the density and the coordination number. The fabric, the stress and the strain tensors are {\em not} co-linear so that a more refined analysis than a classical elasticity theory is required.

cond-mat.stat-mech↗

arXiv1999

Effect of impact energy on the shape of granular heaps

We study experimentally the shape of a granular heap formed pouring a granular material into a vertical Hele-Shaw cell and analyze the effect of the grain impact energy. We propose a continuous model for the steady profile of the heap that explicitly considers energy dissipation of flowing grains through inelastic collisions. We solve the model analytically and analyze the resulting height profile as a function of several parameters, such as the restitution coefficient of the grains and their impact energies. We find good agreement between theory and experiments.

cond-mat.soft↗

arXiv1998

Transition from damage to fragmentation in collision of solids

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged and a fragmented state with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.

cond-mat.stat-mech↗

arXiv1998

Extending the Broad Histogram Method for Continuous Systems

We propose a way of extending the Broad Histogram Monte Carlo method (BHMC) to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model. Our method gives results in excellent agreement with Metropolis and Histogram Monte Carlo simulations and calculates for the whole temperature range 1.2<T<4.7 using only 2 times more computer effort than the Histogram method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.

cond-mat.stat-mech↗

arXiv1998

Broad Histogram Method for Continuous Systems: the XY-Model

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.

cond-mat.stat-mech↗

arXiv1998

Microscopic Model for Granular Stratification and Segregation

We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured in two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the dissipation of energy in collisions between rolling and static grains and an energy barrier describing the geometrical asperities of the grains. We study the phase diagram of the different morphologies predicted by the model as a function of the two parameters. We find regions of segregation and stratification, in agreement with experimental finding, as well as a region of total mixing.

cond-mat.stat-mech↗