Dynamic finite deformation viscoelasticity and energy-consistent time integration

In the present work we deal with the conserving integration of viscoelastic bodies undergoing finite deformations. Isotropic viscoelastic materials can be described by using a symmetric viscous internal variable for measuring the inelastic strains, and the right Cauchy-Green tensor as measure of the total strain (see Reese & Govindjee [1]). Then, by using the unsymmetric product tensor , the purely elastic strains enter the isotropic free energy function. Alternatively, the i application of the symmetric right stretch tensor as internal variable allows to define a symmetric elastic strain tensor which enters the free energy (see also Miehe [2]). These two different approaches lead to different evolution equations for the viscous internal variable. In this lecture, both evolution equations are discretised by an ordinary midpoint rule at each Gauss point of a standard nonlinear displacement-based finite element in space. For discretising the semidiscrete Hamilton's equations of motion in time, we use numerical time integrators which preserve the fundamental conservation laws of the underlying system. In particular, we make use of a modified midpoint rule according to the discrete gradient method, proposed in Gonzalez [3]. Numerical examples demonstrate the difference between both formulations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

Material models in principal stretches for elastodynamics

In the present work we deal with the conserving integration of elastic bodies undergoing finite deformations. In particular, we make use of constitutive laws formulated in terms of principal stretches. Most material models for hyperelastic isotropic materials are described in terms of principal stretches (Simo and Taylor [1]), like the Neo–Hooke material which is a special case of the Ogden material, or in invariants. The main advantage of principal stretches is the fact that they can be measured directly, which means that the numerical results can be compared easily with experimental ones, see for example, Ogden [2]. Moreover, it is advantageous to describe viscoelastic material behaviour (e.g. rubberlike materials) in terms of principal stretches. Concerning the discretization in space we apply the enhanced assumed strain (EAS) method, see Simo and Armero [3]. For the discretization in time we aim at numerical integrators which inherit fundamental conservation laws from the underlying continuous system. In particular, we propose an energy and momentum conserving time–stepping scheme which relies on the notion of a discrete gradient (or derivative) in the sense of Gonzalez [4]. The proposed approach starts from our previous developments in [5]. Numerical examples demonstrate the advantageous properties of the present formulation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lowering Energy Barriers in Surface Reactions through Concerted Reaction Mechanisms

Any technologically important chemical reaction typically involves a number of different elementary reaction steps consisting of bond‐breaking and bond‐making processes. Usually, one assumes that such complex chemical reactions occur in a step‐wise fashion where one single bond is made or broken at a time. Using first‐principles calculations based on density functional theory we show that the barriers of rate‐limiting steps for technologically relevant surface reactions are significantly reduced if concerted reaction mechanisms are taken into account.     

On quasigroups with few associative triples

There are numerous application of quasigroups in cryptology. It turns out that quasigroups with the relatively small number of associative triples can be utilized in designs of hash functions. In this paper we provide both a new lower bound and a new upper bound on the minimum number of associative triples over quasigroups of a given order.     

Parallel synthesis of 2-substituted 6-(5-oxo-1-phenylpyrrolidin-3-yl)pyrimidine-5-carboxamides

A library of 24 6-(5-oxo-1-phenylpyrrolidin-3-yl)pyrimidine-5-carboxamides 10{1,2; 1-12} was prepared by a parallel solution-phase approach. The synthesis comprises a five-step transformation of itaconic acid (11) into 1-methyl and 1-phenyl substituted 6-(5-oxo-1-phenylpyrrolidin-3-yl)pyrimidine-5-carboxylic acids 17{1,2} followed by parallel amidation of 17{1,2} with a series of 12 aliphatic amines 18{1-12} to afford the corresponding carboxamides 10 in good overall yields and in 80-100% purity.     

Galerkin methods in time for semi-discrete viscoelastodynamics

In semi-discrete nonlinear elastodynamics, higher order energy and momentum conserving time stepping schemes turned out to be well suited for computing long time motions [1]. In comparison to standard ODE integrators, conserving schemes exhibit superior stability properties which are of utmost importance in a nonlinear .nite element framework. We show that conserving schemes are particularly well suited as starting point for the development of energy consistent schemes for dissipative dynamical systems. In particular, viscoelastic material behaviour is considered. A key advantage of energy consistent schemes lies in the fact that the equilibrium state of viscoelastic systems can be de.nitely reached, independent of the material parameters. In the paper, we compare two Galerkin methods for the temporal discretisation of semi-discrete nonlinear viscoelastodynamics: the standard continuous Galerkin (cG) method and an enhanced continuous Galerkin (eG) method which ful.ls the total energy balance exactly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)