Graver basis and proximity techniques for block-structured separable convex integer minimization problems

We consider $N$ -fold $4$ -block decomposable integer programs, which simultaneously generalize $N$ -fold integer programs and two-stage stochastic integer programs with $N$ scenarios. In previous work (Hemmecke et al. in Integer programming and combinatorial optimization. Springer, Berlin, 2010), it was proved that for fixed blocks but variable  $N$ , these integer programs are polynomial-time solvable for any linear objective. We extend this result to the minimization of separable convex objective functions. Our algorithm combines Graver basis techniques with a proximity result (Hochbaum and Shanthikumar in J. ACM 37:843–862,1990), which allows us to use convex continuous optimization as a subroutine.     

Numerical Simulation of a Turbulent FSI Benchmark Case

In an effort to expand the capabilities of a validated simulation environment for fluid-structure interaction to turbulent flows, we present the simulation of a turbulent FSI benchmark case with large displacements in a simplified two-dimensional unsteady RANS setup. We find a fair agreement to experimental data that encourages further refinement of our approach and future three-dimensional simulations with eddy-resolving schemes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deep drawing of a layered composite: material characterization and finite-element simulation

Composite materials are widely used in different industrial fields, because of their good formability and their high strength to weight ratio. In the present work a triple-layered sandwich composite is investigated. Experimental tests at room temperature are carried out for the materials constituting the composite. A finite element model of a deep-drawing process of the composite is performed, where a finite strain constitutive model for the metal part, with material parameters calibrated to uniaxial tensile tests, has been implemented. Experimental results are compared to the numerical simulations in view of validation purposes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An accelerated simulation method of medium density wood fiber boards

An accelerated micro-scale simulation method for the prediction of the stiffness of medium density fiber boards is proposed with the aim to increase the speed of the coupled micro-macro simulation and to study the influence of fiber orientation on material properties. The stiffness is interpolated between loads in a n-dimensional simplex figure, which is constructed in a macroscopic strain, temperature, moisture, time and other load. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase field modeling of complex crack patterns in multi-physics problems

Recently developed continuum phase field models for brittle fracture show excellent modeling capability in situations with complex crack topologies including branching in the small and large strain applications. This work presents a generalization towards fully coupled multi-physics problems at large strains. A modular concept is outlined for the linking of the diffusive crack modeling with complex multi field material response, where the focus is put on the model problem of finite thermo-elasticity. This concerns a generalization of crack driving forces from the energetic definitions towards stress-based criteria, the constitutive modeling of degradation of non-mechanical fluxes on generated crack faces. Particular assumptions are made on the generation of convective heat exchanges approximating surface load integrals of the sharp crack approach by distinct volume integrals. The coupling effect is also shown in generation of cracks due to thermally induced stress states. We finally demonstrate the performance of the phase field formulation of fracture at large strains by means of representative numerical examples. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical Modeling and Flatness Based Control of a Belt Drive System

Belt driven systems are part of many industrial applications, like computerized numerical control (CNC) machines in particular cutting machines and 3D-printers. In this paper the dynamical modeling and a flatness based controller design for belt driven systems are proposed. Due to the special kinematics, the stiffness of the belt is nonlinear, leading to nonlinear equations of motion. By neglecting some minor dynamical effects, the resulting system simplifies to a differentially flat one. This allows to calculate nominal feed-forward control torques by using the flat output of the system. To stabilize the error dynamics, an additional PD control law is introduced. The proposed method is compared with a controller, where elastic deflections for the feed forward part are neglected and elastic deformations are compensated by modifying the desired trajectories in a model-based manner. The tracking performance of both methods is evaluated in certain simulations and experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About an analytical approach to a quasicontinuum method via Γ-convergence

We report on an analytical study of a quasicontinuum method in the context of fracture mechanics in a one-dimensional setting. To this end, we compare the asymptotic behaviour of a discrete model with nearest and next-to-nearest neighbour interactions of Lennard-Jones type and its quasicontinuum approximation via Γ-convergence. In case of fracture it turns out that one has to coarse grain in the continuum region and at the atomistic/continuum interface in order to capture the same behavior as the atomistic model, while this is not needed if the boundary conditions are such that the system behaves elastically. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)