Falk K. Wittel

Fragmentation processes in impact of spheres

We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.

Adhesive penetration in beech wood: experiments

A study with synchrotron radiation X-ray tomographic microscopy (SRXTM) of PUR, PVAc, and UF adhesive bond lines in beech wood, bonded under various growth ring angles, is presented. The bond line morphologies and the adhesive penetration into the wood structure were evaluated after determining the hardening characteristics of the adhesives. Distinct bond line imperfections were found for the different adhesive systems. To describe the adhesive distribution inside the bond line, the saturation of the pore space instead of the commonly used maximum penetration depth seems to be adequate.

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.

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension.

Progressive collapse mechanisms of brittle and ductile framed structures

In this paper, we study the progressive collapse of three-dimensional framed structures made of reinforced concrete after the sudden loss of a column. The structures are represented by elastoplastic Euler-Bernoulli beams with elongation-rotation failure threshold. We performed simulations using the discrete element method considering inelastic collisions between the structural elements. The results show what collapse initiation and impact-driven propagation mechanisms are activated in structures with different geometric and mechanical features. Namely, we investigate the influence of the cross sectional size and reinforcement α and of the plastic capacity β of the structural elements. We also study the final collapse extent and the fragment size distribution and their relation to α , β , and to the observed collapse mechanisms. Finally, we compare the damage response of structures with symmetric and asymmetric reinforcement in the beams.

Pore space analysis of beech wood: The vessel network

Abstract Water transport in wood is vital for the survival of trees. With synchrotron radiation X-ray tomographic microscopy (SRXTM), it has become possible to characterize and quantify the three-dimensional (3D) network formed by vessels that are responsible for longitudinal transport. In the present study, the spatial size dependence of vessels and the organization inside single growth rings in terms of vessel-induced porosity was studied by SRXTM. Network characteristics, such as connectivity, were deduced by digital image analysis from the processed tomographic data and related to known complex network topologies.

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.

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.

Particle–Fluid–Structure Interaction for Debris Flow Impact on Flexible Barriers

Flexible barriers are increasingly used for the protection from debris flow in mountainous terrain due to their low cost and environmental impact. How- ever, the development of a numerical tool for the ratio- nal design of such structures is still a challenge. In this work, a hybrid computational framework is presented, using a total Lagrangian formulation of the finite element method to represent aflexible barrier. The actions exerted on the structure by a debris flow are obtained from si- multaneous simulations of the flow of a fluid-grain mix- ture, using two conveniently coupled solvers: the discrete element method governs the motion of the grains, while the free-surface non-Newtonian fluid phase is solved us- ing the lattice Boltzmann method. Simulations on real- istic geometries show the dependence of the momentum transfer on the barrier on the composition of the debris flow, challenging typical assumptions made during the design process today. In particular, we demonstrate that both grains and fluid contribute in a nonnegligible way to the momentum transfer. Moreover, we show how the flexibility of the barrier reduces its vulnerability to struc- tural collapse, and how the stress is distributed on its fabric, highlighting potential weak points.

Morphological phases of crumpled wire.

We find that in two dimensions wires can crumple into different morphologies and present the associated morphological phase diagram. Our results are based on experiments with different metallic wires and confirmed by numerical simulations using a discrete element model. We show that during crumpling, the number of loops increases according to a power law with different exponents in each morphology. Furthermore, we observe a power law divergence of the structures bulk stiffness similar to what is observed in forced crumpling of membranes.