Fracture toughness investigations on UHPC by spalling tests

Ultra High Performance Concrete (UHPC) is defined as a new generation of concrete which shows improved performance and higher strength than traditional concrete. This allows to realize slender and much more durable structures and in this way significantly reduces the required resources. Despite its huge potential in construction, technical information about this new type of material is still limited. This contribution presents investigations on the dynamic mechanical behavior and properties of UHPC specimens by spalling experiments. Two different recipes were used to compare the properties. Due to the special specimen geometry (slender cylindrical) a flowable consistency was required to enable a sufficient degassing of the mixtures. For the test, a Split Hopkinson Pressure Bar (SHPB) has been modified and used. A high speed photograph system was focused on the fragmentation process during the test. On the basis of these experiments the dynamic E-moduli as well as the dynamic tensile strength of the UHPC specimens were determined. By observation of the specific crack patterns on each tested specimen and corresponding times, the dynamic fracture energy is calculated. Numerical simulations also were performed and compared to the experimental result. It is concluded that the dynamic tensile strength of the UHPC increases at higher strain rates. The results of the current study provide technical information about fracture and dynamic behavior of UHPC and the obtained values could be used for future computational models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulations for a variable order fractional cable equation

In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the RiemannLiouville and the Gr¨unwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.     

Numerical properties of high order discrete velocity solutions to the BGK kinetic equation

A high order numerical method for the solution of model kinetic equations is proposed. The new method employs discontinuous Galerkin (DG) discretizations in the spatial and velocity variables and Runge-Kutta discretizations in the temporal variable. The method is implemented for the one-dimensional Bhatnagar-Gross-Krook equation. Convergence of the numerical solution and accuracy of the evaluation of macroparameters are studied for different orders of velocity discretization. Synthetic model problems are proposed and implemented to test accuracy of discretizations in the free molecular regime. The method is applied to the solution of the normal shock wave problem and the one-dimensional heat transfer problem.     

Multiscale simulations of concrete mechanical tests

In civil engineering, computational modeling is widely used in the design process at the structural level. In contrast to that, an automated support for the selection or design of construction materials is currently not available. Specification of material properties and model parameters has a strong influence on the results. Therefore, an uncoupled two-step approach is employed to provide relatively quick and reliable simulations of concrete (mortar) tests. First, the Mori–Tanaka method is utilized to include the majority of small aggregates and air voids. The strain incremental form of MT approach serves for the prediction of material properties subsequently used in the finite element simulations of mechanical tests.     

Numerical approach to differential equations of fractional order

In this paper, the variational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper presents a numerical comparison between the two methods for solving systems of fractional differential equations. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.     

Numerical simulations of acoustic emissions due to offshore-pile installation

The use of renewable energy is growing due to economic reasons and a spreading sense of ecology. One possible source for renewable energy is wind energy. It is predicted that the number of offshore wind parks will be increasing within the next ten years. The foundation piles of offshore wind power plants are normally installed by impact driving. This leads to an emission of acoustic noise which possibly influences or even damages the sense of hearing of marine mammals like seals and whales. In this contribution the propagation of acoustic waves in air and water due to pile driving is investigated using the finite element method (FEM) with an explicit time integration scheme. In the analyses a mass representing the pile hammer falls on an elastically modeled offshore monopile. The surrounding media is varied between air and water in order to investigate the acoustic emissions due to the pile driving process with respect to the medium. The numerical results are compared to measurements which can be found in literature to verify the numerical models. Furthermore, as a practical example the numerical model can be used in order to simulate noise reduction techniques such as the bubble curtain. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular static simulations of ferroelectric material hysteresis behaviour

The present contribution deals with molecular static modelling and the simulation of ferroelectric material hysteresis behaviour. Therefore the core-shell model is implemented in a molecular static algorithm. Moreover the algorithm is implemented as a finite element method for nonlinear trusses. Thereby the computational costs are reduced significantly compared to molecular dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulations of the improved Boussinesq equation

In this study, numerical simulations of the improved Boussinesq equation are obtained using two finite difference schemes and two finite element methods, based on the second‐and third‐order time discretization. The methods are tested on the problems of propagation of a soliton and interaction of two solitons. After the L_∞ error norm is used to measure differences between the exact and numerical solutions, the results obtained by the proposed methods are compared with recently published results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Using data compressors to construct order tests for homogeneity and component independence

Nonparametric order tests for homogeneity and component independence are proposed, which are based on data compressors. For homogeneity testing the idea is to compress the word obtained by ordering the combined samples and writing the number of the sample in the place of each element. H₀ should be rejected if the string is compressed to a certain degree and accepted otherwise. We show that such a test obtained from an ideal data compressor is valid against all alternatives. Component independence is reduced to homogeneity testing.     

Numerical simulations of measurements of capillary contact angles

In a recent paper, Fischer and Finn have proposed a procedureto improve the accuracy in the measurement of capillary contactangles, based on the use of vessels with canonical cross-sections.We simulate numerically the behaviour of such shapes for a numberof cross-sections and fluid contact angles. Our approximationconsists of the minimization of a suitable convex functionaldiscretized by finite elements. e-mail: bellettini{at}sns.it e-mail: paolini{at}isa.mat.unimi.it     

Work-roll surface degradation due to spalling of oxide layer

Surface damage of work-rolls in hot strip rolling mills is often associated with the local removal of the oxide layer developing in service. A simple thermomechanical stress analysis in combination with an estimated buckling stress shows that the size of oxide free spots on the roll surface is roughly the same as the lateral distance between the cracks in the observed crack pattern. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Third order efficiency of conditional tests for exponential families

Let P_η, η = (θ, γ) ∈ Θ × Γ ? $\text{R}$ × $\text{R}$^k, be a (k + 1)-dimensional exponential family. Let $\text{?}{}_{\mathrm{n}}{}^1$, n ∈ $\text{N}$, be an optimal similar test for the hypothesis {P_(θ,γ)ⁿ: γ ∈ Γ} (θ ∈ Θ fixed) against alternatives P_(θ1,γ1)ⁿ, θ₁ > θ, γ₁ ∈ Γ. It is shown that (?_n¹)_{n∈$\text{N}$} is third order efficient in the class of all test-sequences that are asymptotically similar of level α + o(n^?1) (locally uniformly in the nuisance parameter γ).     

Limiting properties of order statistics

We consider the relationship between the convergence of the distribution functions of sums of independent random variables and the asymptotic distribution of order statistics.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 128–144, 1986.     

Bearing of geometric and material properties to bone strength in bending

Osteoporosis is characterized by decreasing of bone mass and bone strength with advanced age. For characterization of material properties of bone the volumetric bone mineral density is one of the most important contributing factors to bone strength. Often bending tests of whole bone are used to get information about the state of osteoporosis. From an uniaxial test of a bone specimen it is assumed that an elastic region exists up to initial yield stress and a following hardening region. In bending tests beside material properties geometric properties like shape and cortical thickness appropriate the non-linear moment-curvature curve. The aim of this contribution is to show how an elastic-plastic material law including tensile damage influences the global bending behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulations of flows in an elastic cylinder with two chambers

We present a mathematical model of valveless pumping in a tube with two elastic chambers, which are motivated by the Liebau's two-tank model. The tube consists of partially soft and partially (almost) rigid. We employ a two-dimensional model using the immersed boundary method. In this new model, we have showed the important features of valveless pumping as the previous experiments and mathematical models have been discovered. For instance, we have observed that the direction and the amount of a net flow are sensitively dependent on the pumping frequency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)