arXiv subjects

Falk K. Wittel

Publications and source records attributed to Falk K. Wittel.

48 records · Page 3Linked to original sources

arXiv2014

Fragmentation processes in two-phase materials

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential stress field is tensile. Cracks initiated in this region grow to form meridional planes. If the collision energy exceeds a critical value which depends on the material's internal structure, cracks reach the sample surface resulting in fragmentation. We show that this primary fragmentation mechanism is very robust with respect to the internal structure of the material. For all configurations, a sharp transition from the damage to the fragmentation regime is observed, with smaller critical collision energies for crystalline samples. The mass distribution of the fragments follows a power law for small fragments with an exponent that is characteristic for the branching merging process of unstable cracks. Moreover this exponent depends only on the dimensionally of the system and not on the micro structure.

cond-mat.mtrl-sci↗

arXiv2014

Rheological Model for Wood

Wood as the most important natural and renewable building material plays an important role in the construction sector. Nevertheless, its hygroscopic character basically affects all related mechanical properties leading to degradation of material stiffness and strength over the service life. Accordingly, to attain reliable design of the timber structures, the influence of moisture evolution and the role of time- and moisture-dependent behaviors have to be taken into account. For this purpose, in the current study a 3D orthotropic elasto-plastic, visco-elastic, mechano-sorptive constitutive model for wood, with all material constants being defined as a function of moisture content, is presented. The corresponding numerical integration approach, with additive decomposition of the total strain is developed and implemented within the framework of the finite element method (FEM). Moreover to preserve a quadratic rate of asymptotic convergence the consistent tangent operator for the whole model is derived. Functionality and capability of the presented material model are evaluated by performing several numerical verification simulations of wood components under different combinations of mechanical loading and moisture variation. Additionally, the flexibility and universality of the introduced model to predict the mechanical behavior of different species are demonstrated by the analysis of a hybrid wood element. Furthermore, the proposed numerical approach is validated by comparisons of computational evaluations with experimental results.

cond-mat.soft↗

arXiv2014

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. However, a numerical tool for rational design of such structures is still missing. In this work, a hybrid computational framework is presented, using a total Lagrangian formulation of the Finite Element Method (FEM) to represent a flexible barrier. The actions exerted on the structure by a debris flow are obtained from simultaneous simulations of the flow of a fluid-grain mixture, using two conveniently coupled solvers: the Discrete Element Method (DEM) governs the motion of the grains, while the free-surface non-Newtonian fluid phase is solved using the Lattice-Boltzmann Method (LBM). Simulations on realistic 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 non-negligible way to the momentum transfer. Moreover, we show how the flexibility of the barrier reduces its vulnerability to structural collapse, and how the stress is distributed on its fabric, highlighting potential weak points.

cond-mat.soft↗

arXiv2014

Multi-scale approach to invasion percolation of rock fracture networks

A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizations of ACNs are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties. Typical situations in fracture networks are parameterized by fracture inclination, flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures. Using these scaling relations obtained from the finer scales, we simulate the invasion process of immiscible fluids into saturated discrete fracture networks, which were studied in previous works.

physics.geo-ph↗

arXiv2014

Morphogenesis of filaments growing in flexible confinements

Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of deformable vesicles or soft tissue like cell walls, chorions, and buds. Surprisingly little is known about morphogenesis due to growth in flexible confinements - perhaps owing to the daunting complexity lying in the nonlinear feedback between packed material and expandable cavity. Here we show by experiments and simulations how geometric and material properties lead to a plethora of morphologies when elastic filaments are growing far beyond the equilibrium size of a flexible thin sheet they are confined in. Depending on friction, sheet flexibility and thickness, we identify four distinct morphological phases emerging from bifurcation and present the corresponding phase diagram. Four order parameters quantifying the transitions between these phases are proposed.

cond-mat.soft↗

arXiv2013

Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.

math.NA↗

arXiv2012

Finite Element Simulation of Dense Wire Packings

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.

cond-mat.soft↗

arXiv2011

From invasion percolation to flow in rock fracture networks

The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distribution function or are conditioned on measured data from deep geological investigations. We introduce several modifications to the invasion percolation (MIP) to incorporate fracture inclinations, intersection lines, as well as the hydraulic path length inside the fractures. Additionally a trapping algorithm is implemented that forbids any advance of the invading fluid into a region, where the defending fluid is completely encircled by the invader and has no escape route. We study invasion, saturation, and flow through artificial fracture networks, with varying anisotropy and size and finally compare our findings to well studied, conditioned fracture networks.

cond-mat.stat-mech↗

arXiv2010

Self-contact and instabilities in the anisotropic growth of elastic membranes

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e-cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric \textit{e}-cone solution is energetically minimal any more. Instead, we obtain skewed e-cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.

physics.bio-ph↗

arXiv2004

Modeling of Damage Evolution in Soft-Wood Perpendicular to Grain by means of a Discrete Element Approach

The anisotropy of wood within the radial-tangential (RT) growth plane has a major influence on the cracking behavior perpendicular to grain. Within the scope of this work, a two-dimensional discrete element model is developed, consisting of beam elements for the representation of the micro structure of wood. Molecular dynamics simulation is used to follow the time evolution of the model system during the damage evolution in the RT plane under various loading conditions. It is shown that the results are in good agreement with experiments on spruce wood, and that the presented discrete element approach is applicable for detailed studies of the dependence of the micro structure on mesoscopic damage mechanism and dynamics of crack propagation in micro structured and cellular materials like wood.

cond-mat.mtrl-sci↗

arXiv2004

Combined Numerical and Experimental Investigation of Progressive Failure of Composites

The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix boundary. Investigations were made using model specimens containing up to five parallel glass fibres loaded at angles from 0 to 15 degrees. The material properties of the geometrically equivalent FE models are calibrated using the experimental photoelastic outputs. In contrast to the experimental results, FE simulations provide full 3D stress fields. For verification purposes, the 3D stress fields are reduced to two-dimensional synthetic photoelastic phase images, showing good agreement. Furthermore, detailed studies on the components of the stress tensor, particularly statements concerning the shear transmitted by fibre-matrix boundary, progressive fibre failure and the effect of load angle variation are presented.

cond-mat.mtrl-sci↗

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↗