A geometric interpretation of frictional contact mechanics

The work-conjugacy of pressures and tangential tractions with so-called “gap”and “stick” constraints is deduced in order to delineate a rigid-plastic model of a frictional interface. This is accomplished by pursuing a differential-geometric view of the two surfaces that comprise the frictional interface. Given that contact is described in the current configuration, Lie derivatives are shown to be the natural means of establishing the work-conjugacy between tractions and constraints.     

Linking macroscopic deformation processes to microstructure evolution using an FE-FFT-based micro-macro transition and non-conserved phase-fields

The purpose of this work is the multiscale FE-FFT-based prediction of macroscopic material behavior, micromechanical fields and bulk microstructure evolution in polycrystalline materials subjected to macroscopic mechanical loading. The macroscopic boundary value problem (BVP) is solved using implicit finite element (FE) methods. In each macroscopic integration point, the microscopic BVP is embedded, the solution of which is found employing fast Fourier transform (FFT), fixed-point and Green's function methods. The mean material response is determined by the stress-strain relation at the micro scale or rather the volume average of the micromechanical fields. The evolution of the microstructure is modeled by means of non-conserved phase-fields. As an example, the proposed methodology is applied to the modeling of stress-induced martensitic phase transformations in metal alloys. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Anisotropic Damage Theories based on 2nd Order Damage Tensors

Isotropic and anisotropic damage theories are shortly reviewed concerning different aspects like thermodynamical consistency, effective undamaged configurations, crack-closure effects and the interpretation of the damage variable. A recently proposed damage growth criterion for second order damage tensors is discussed in integral as well as incremental form. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro-macro modelling of fiber reinforced composites exhibiting elastoplastic deformation

Fiber reinforced plastics such as carbon fiber-reinforced composites are typically characterized by their high siffness to weight ratio making them particularly attractive in lightweight construction. In addition, the architecture of these materials means that the correct modelling of their orthotropy is very important. In this work, volume averaged stress-strain responses are generated from a micro representative volume element (RVE). A nonlinear macro constitutive material model accounting for anisotropic plasticity is proposed. The model is fitted and compared to the micro stress-strain response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Morse Novikov theory and cohomology with forward supports

We present a new approach to Morse and Novikov theories, based on the deRham Federer theory of currents, using the finite volume flow technique of Harvey and Lawson [HL]. In the Morse case, we construct a noncompact analogue of the Morse complex, relating a Morse function to the cohomology with compact forward supports of the manifold. This complex is then used in Novikov theory, to obtain a geometric realization of the Novikov Complex as a complex of currents and a new characterization of Novikov Homology as cohomology with compact forward supports. Two natural ``backward-forward' dualities are also established: a Lambda duality over the Novikov Ring and a Topological Vector Space duality over the reals.     

Finite element modelling of orthotropic material behaviour in pneumatic membranes

In this paper, we develop a model to describe the hyperelastic material behaviour of pneumatic membranes reinforced with roven–woven fibres. A generalized stored energy function is developed via a series of loading tests on a representative sample of this composite material. The exponents in the effective law are chosen so as to fulfil basic restrictions, discussed in the body of the paper, as well as to match certain experimental values. Numerical examples demonstrate the application of the approach to inflated rubber matrix materials, as well as laminated shells.     

Evidence for dark energy from the cosmic microwave background alone using the Atacama Cosmology Telescope lensing measurements

For the first time, measurements of the cosmic microwave background radiation (CMB) alone favor cosmologies with w = -1 dark energy over models without dark energy at a 3.2-sigma level. We demonstrate this by combining the CMB lensing deflection power spectrum from the Atacama Cosmology Telescope with temperature and polarization power spectra from the Wilkinson Microwave Anisotropy Probe. The lensing data break the geometric degeneracy of different cosmological models with similar CMB temperature power spectra. Our CMB-only measurement of the dark energy density Ω(Λ) confirms other measurements from supernovae, galaxy clusters, and baryon acoustic oscillations, and demonstrates the power of CMB lensing as a new cosmological tool.     

Submicron focusing of XUV radiation from a laser plasma source using a multilayer Laue lens

The focusing properties of a one-dimensional multilayer Laue lens (MLL) were investigated using monochromatic soft X-ray radiation from a table-top, laser-produced plasma source. The MLL was fabricated by a focused ion beam (FIB) structuring of pulsed laser deposited ZrO₂/Ti multilayers. This novel method offers the potential to overcome limitations encountered in electron lithographic processes. Utilizing this multilayer Laue lens, a line focus of XUV radiation from a laser-induced plasma in a nitrogen gas puff target could be generated. The evaluated focal length is close to the designed value of 220 μm for the measurement wavelength of 2.88 nm. Divergence angle and beam waist diameter are measured by a moving knife edge and a far-field experiment, determining all relevant second-order moments based beam parameters. The waist diameter has been found to be approximately 370 nm (FWHM).