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)     

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.     

The idle period of the finite G/M/1 queue with an interpretation in risk theory

We consider a G/M/1 queue with restricted accessibility in the sense that the maximal workload is bounded by 1. If the current workload V _t of the queue plus the service time of an arriving customer exceeds 1, only 1−V _t of the service requirement is accepted. We are interested in the distribution of the idle period, which can be interpreted as the deficit at ruin for a risk reserve process R _t in the compound Poisson risk model. For this risk process a special dividend strategy applies, where the insurance company pays out all the income whenever R _t reaches level 1. In the queueing context we further introduce a set-up time a∈[0,1]. At the end of every idle period, an arriving customer has to wait for a time units until the server is ready to serve it.     

On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.