Macroscopic mechanical properties of metal foam in dependence on the inhomogenities of the mesoscale

In this contribution, a way of simulating the influence of the mesoscopic irregular structure of metal foams on the macroscale is shown. To this end, mesoscopic periodic volume elements of a foam are derived in order to compute the mechanical properties including the effects of inhomogenities like imperfections, irregular structure and varying cell wall thicknesses. With the help of these volume elements, which are analysed via the finite element method, and their varying mechanical properties, a local varying stiffness can be computed and inserted into the macromechanical model. In this way the propagation of uncertainities from the mesoscale to the macroscale can be assessed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of crystalline bubble structure in wet metal foams

Small monodispersed bubbles form regular patterns when they agglomerate. Many experimental investigations revealed a preference of f.c.c. packing against h.c.p. packing in these structures, that could not yet be explained. In the present work this feature is reproduced numerically and analyzed. It is shown that drainage from layers above causes the preference. By investigating the transient crystal growth and packing rearrangement a mechanism is found that reduces the stability of h.c.p. packing and explains the phenomenom. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of large strain behavior of polymeric crushable foams

This paper describes a constitutive law modeling isotropic polymeric foam materials. Focus has been placed on modeling the relative density dependency effect on polymeric foams subjected to large deformations using uniaxial and hydrostatic compressive hardening laws. The constitutive model is written in terms of the rotated Kirchhoff stress and of its conjugate logarithmic, or Hencky, strain measure. A numerical scheme for solving the constitutive model is described and implemented using both the finite element and the element-free Galerkin methods, in a Total Lagrangian finite strain framework. The imposition of the unilateral contact with friction and the essential boundary conditions are obtained by applying the Augmented Lagrangian method. Numerical examples are presented in order to attest the performance of the proposed constitutive model.     

A contribution to the Zarankiewicz problem

Given positive integers let z(m,n,s,t) be the maximum number of ones in a (0,1) matrix of size m×n that does not contain an all ones submatrix of size s×t. We show that if s?2 and t?2, then for every k=0,…,s-2,

z(m,n,s,t)?(s-k-1)^1/tnm^1-1/t+kn+(t-1)m^1+k/t.     

A contribution to the theory of condition

Summary In this paper the use of the condition number of a problem, as defined by Rice in 1966, is discussed. For the eigenvalue, eigenvector, and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived.     

Experimental and numerical investigation of metal foams undergoing large deformations

Open cell aluminum metal foams are a new kind of material that are used in composite structures to reduce their weight, to increase their sound or energy absorption capability or to decrease their thermal conductivity. The design and analysis of such structures requires a macroscopic constitutive model of the foam that has to be determined by various experiments under different loading conditions. We support this procedure by analyzing the microstructure of the metal foam numerically under large deformations. To this end, we employ the finite cell method that can deal with large deformations and allows for an automatic and efficient discretization of the CT-image of the foam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A contribution to the closed geodesic problem

The closed geodesic problem has been solved by many authors under additional hypothesis. In this paper we develop a new way to solve this problem, by defining finitely many obstruction classes. This permits to enlarge significantly the family of manifolds for which this problem is solved. Our method which relies on the concept of A_∞-section of a homomorphism of differential graded algebras, shows explicitly how the natural structure of shc-algebra on the singular cochains of a space comes into play.     

A contribution to Segal algebras

Let A and B be Banach algebras. If B is an abstract Segal algebra in A, we have a bijective correspondence between the strictly irreducible representations of A and those of B. This gives a bijective correspondence for maximal modular left ideals. If A and B have approximate right units, we obtain a bijective correspondence for right resp. Two-sided ideals. For two-sided ideals this correspondence preserves the property of an ideal having approximate right units. This generalizes a Theorem by H. Reiter.It would be sufficient to require B to be a Banachspace.     

Numerical analysis of Ni/Al hybrid metal foams using the finite cell method

Aluminium metal foams are a new type of material that can be used in many lightweight applications. One method to improve their mechanical properties is to coat them with a thin layer of nickel by electrodeposition. A voxel representation of this hybrid foam can be obtained in a straightforward way using a CT scanner. The voxel-based geometry can then be processed and modified with respect to the thickness of the nickel layer in order to investigate its influence on the effective properties. By employing the finite cell method (FCM) we are able to automatically convert the voxel-based geometry into a finite cell grid and to directly perform a homogenization procedure. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A contribution to the plastic behavior of cellular bone

In a first approximation the inelastic behavior of cellular bone is modelled by an isotropic elastic-plastic material. Plastic strains can deduced using a yield-criterion and a plastic potential which depends on invariants of the stress tensor. Irreversible (plastic) volumetric strains occur. The plastic material functions can be determined in an uniaxial experiment with a Laser Extensometer. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A contribution to the statistical theory of linear graduation

Moving (weighted) average techniques provide a flexible tool for the graduation (smoothing) of vital rates. As is shown in the present paper, one may construct linear graduation methods which are superior with respect to some formal evaluation criteria, but such ‘improved’ methods lack an important robustness property which the moving average graduation techniques possess and which is a main motivation for their use.A linear graduation technique is an estimation method, and an important consideration in the evaluation of its properties is the class for which it is unbiased, i.e., the class of functions which it reproduces unchanged. A classical test usually said to be a chi-square test of the goodness-of-fit of a graduation is revealed to be a test of the hypothesis that the graduation method is indeed unbiased for the set of theoretical rates actually estimated, and its properties are investigated along with those of alternative chi-square tests.     

A contribution to quadratic assignment problems

We discuss special eases of the quadratic assignment problem (QAP) being polynomially solvable. In particular we give an algebraic condition for the cost; Matrices of a QAP which guarantees that it is equivalent with a linear assignment problem. Based on these results we develop an approximation algorithm for QAPs with non-negative symmetric cost matrices.