A gradient-enhanced continuum damage model for fibre-reinforced materials at finite strains

The assumption of purely local continuum damage formulations may imply a loss of well-posedness of the underlying boundary value problem. With regard to numerical methods such as the finite element method, this may lead to mesh-dependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, i.e. to regularise the problem, we, in this contribution, apply a non-local gradient-based damage formulation within a geometrically non-linear setting allowing for large deformations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty and Sensitivity Analysis of Different Models of Brake Squeal

In this contribution, the brake-squeal phenomenon is investigated using the pin-on-disc setup. The setup is analyzed numerically using the finite element method. The finite element model is evaluated in the time domain, and the vibration mechanism leading to squeal as well as the limit cycles of the vibration are analyzed. Against the background of the high computational costs, it is evaluated to what extent the Hoffmann-Gaul minimal model can reproduce the results of the finite element model. Moreover, as brake squeal is very sensitive with respect to parametric uncertainties, the influence of several parametric uncertainties on the limit cycles is analyzed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Control of Large Deformation Elasticity by Fiber Tension

Object of our interest is an elastic body Ω ⊂ ℝ³ which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of numerical homogenization techniques in BT-CFO multiferroic particle composites

This work is restricted to linear material behavior, i.e. the structure is considered to be in a perfectly poled state. Different numerical homogenization methods are investigated and used to calculate effective properties of a 0-2 composite modelled in reprensentative volume elements. Bariumtitanate (BT) and cobaltferrite (CFO) are employed in the Finite Element model, where the roles of matrix and inclusion are mutable in principle. Mixed magnetoelectromechanical boundary conditions based on different homogenization theories are applied to the model. The calculated macroscopic behaviors described by the different approaches are compared and presented in the paper. The special focus is on the prediction of coefficients of magnetoelectric coupling with respect to an optimization of the structural arrangement of the composite. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Surfactant Concentration in a Coupled Bulk Surface Problem

Surface active agents (surfactants) are on high interest for physical and chemical industries. Their presence lowers the surface tension of fluids. This is used to achieve special flow properties. These mechanisms are not only influenced by the overall amount of surfactant. They highly depend on the local surfactant distribution. The surfactant concentration is modeled by two convection diffusion equations, one in the bulk and the other on its surface. Adsorption- and desorption processes are included and lead to a (non linear) coupling of both equations. We present a numerical scheme for solving the coupled problem. Additionally, first analytical results will be given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Existence of Bifurcating Invariant Tori in a Spatially Extended Reaction-Diffusion-Convection System with Spatially Localized Amplification

We consider a spatially extended reaction-diffusion-convection system with a marginally stable ground state and a spatially localized amplification. We are interested in solutions bifurcating from the spatially homogeneous ground state in the case when pairs of imaginary eigenvalues simultaneously cross the imaginary axis. For this system we prove the bifurcation of a family of invariant tori which may contain quasiperiodic solutions. There is a serious difficulty in obtaining this result, because the linearization at the ground state possesses an essential spectrum up to the imaginary axis for all values of the bifurcation parameter. To construct the invariant tori, we use their invariance under the flow which manifests in a condition in PDE form. The nonlinear terms of this resulting PDE exhibit a loss of regularity. Since the linear part of this PDE is not smoothing, an adaption of the hard implicit function theorem (or Nash-Moser scheme) and energy estimates will be used to prove our result.     

K-Theory of Surfaces at the Prime 2

We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence.     

On the planarity of Hanoi graphs

Hanoi graphs are the state graphs for Tower of Hanoi problems with three or more pegs. We prove hamiltonicity and present a complete analysis of planarity of these graphs.     

Hydride-assisted growth of GaN nanowires on Au/Si(0 0 1) via the reaction of Ga with NH3 and H2

High quality, straight GaN nanowires (NWs) with diameters of 50 nm and lengths up to 3 μm have been grown on Si(0 0 1) using Au as a catalyst and the direct reaction of Ga with NH₃ and N₂:H₂ at 900 °C. These exhibited intense, near band edge photoluminescence at 3.42 eV in comparison to GaN NWs with non-uniform diameters obtained under a flow of Ar:NH₃, which showed much weaker band edge emission due to strong non-radiative recombination. A significantly higher yield of β-Ga₂O₃ NWs with diameters of ≤50 nm and lengths up to 10 μm were obtained, however, via the reaction of Ga with residual O₂ under a flow of Ar alone. The growth of GaN NWs depends critically on the temperature, pressure and flows in decreasing order of importance but also the availability of reactive species of Ga and N. A growth mechanism is proposed whereby H₂ dissociates on the Au nanoparticles and reacts with Ga giving Ga_xH_y thereby promoting one-dimensional (1D) growth via its reaction with dissociated NH₃ near or at the top of the GaN NWs while suppressing at the same time the formation of an underlying amorphous layer. The higher yield and longer β-Ga₂O₃ NWs grow by the vapor liquid solid mechanism that occurs much more efficiently than nitridation.     

Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered. A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces. Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover, compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics.