Homogenization methods for multi-phase elastic composites: Comparisons and benchmarks

Usually homogenization methods are investigated regarding the volume fraction of the inclusion. In this paper classical homogenization methods are recalled and compared on the basis of the contrast in the elastic properties of the constituents. This has a significant influence on the accuracy of the homogenization method. In addition two relatively new approaches, the ESCS and IDD method, are introduced and compared to more standard homogenization approaches. The analysis of these methods shows that the IDD method is an improvement due to its simple but universally applicable structure. A number of comparisons of these and other analytical approaches are carried out with the corresponding finite element results

Continuum Thermodynamic Modeling and Simulation of Electromagnetic Metal Forming

The purpose of this work is the formulation and application of a continuum field approach to the phenomenological modeling of a class of engineering materials which can be dynamically formed using strong magnetic fields. This is done in the framework of a thermodynamic, internal-variable-based formulation in which the deformation, temperature and magnetic fields are in general coupled. As is well-known, this coupling takes the form of the Lorentz force as an additional supply of momentum, and the electromotive power as an additional supply of energy, in the material. The constitutive formulation is based as usual on the exploitation of the dissipation principle, here for the case of generally anisotropic, elastoviscoplastic material behaviour. In particular, the general results so obtained are applied in particular to the case of small strain and large rotation. As shown here, in this special case, the electromagnetic field relations become independent of the deformation field. As such, they can be solved independently and used as input for the solution of the thermomechanical field relations. Application of this reduced formulation for small strain to the simulation of the electromagnetic forming of an aluminum tube shows the importance of accounting for inertial effects and rate-dependence in the modeling

Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dependence of the stiffness. In general, the relevant strain tensor is related to the left Cauchy-Green deformation tensor. In isotropic one- and two-dimensional situations the elastic energy can be expressed equivalently through the right deformation tensor. The predicted isotropic low temperature non-linear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative $K'=4$ for bcc. A two-dimensional generalization suggests $K'_{2D}=5$. These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical non-linearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformations the magnitudes of the amplitudes depend on their relative orientation to the applied strain.Comment: 16 page

Modified dipole-dipole interactions in the presence of a nanophotonic waveguide

When an emitter ensemble interacts with the electromagnetic field, dipole-dipole interactions are induced between the emitters. The magnitude and shape of these interactions are fully determined by the specific form of the electromagnetic field modes. If the emitters are placed in the vicinity of a nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional form of these modes makes the analytical evaluation of the dipole-dipole interaction cumbersome and numerically costly. In this work, we provide a full detailed description of how to successfully calculate these interactions, outlining a method that can be easily extended to other environments and boundary conditions. Such exact evaluation is of importance as, due to the collective character of the interactions and dissipation in this kind of systems, any small modification of the interactions may lead to dramatic changes in experimental observables, particularly as the number of emitters increases. We illustrate this by calculating the transmission signal of the light guided by a cylindrical nanofiber in the presence of a nearby chain of emitters.Comment: 14 pages, 5 figures, comments welcom

Modeling of internal tides in fjords

A previous model for the distribution of internal tides above irregular topography is generalized to include arbitrary stratification and a radiation condition at the open boundary. Thanks to a small amount of dissipation, this model remains valid in the presence of resonant internal tides, leading to intense wave-energy beams. An application to a Norwegian fjord correctly reproduces the observed energy pattern consisting of two beams both originating at the 60-meter deep entrance sill and extending in-fjord, one upward toward the surface, the other downward toward the bottom. After correction for the varying width of the fjord, the observed and modelled energy levels are in good agreement, especially in the upper levels where energy is the greatest. Furthermore, the substantial phase lag between these two energy beams revealed by the observations is correctly reproduced by the model. Finally, a third and very narrow energy spike is noted in the model at the level of a secondary bump inward of the sill. This beam is missed by the current meter data, because the current meters were placed only at a few selected depths. But an examination of the salinity profiles reveals a mixed layer at approximately the same depth. The explanation is that high-wave energy leads to wave breaking and vigorous mixing. The model\u27s greatest advantage is to provide the internal-tide energy distribution throughout the fjord. Discrepancies between observations and model are attributed to coarse vertical resolution in the vicinity of the sill and to unaccounted cross-fjord variations

Collaborative intimacies

Pigs and pig organs are frequently used prior to human trials in experimental transplant research into how to optimise human transplantation. But what exactly happens when transplant professionals perform experimental research on pigs? Similarly, what happens when a pig is on the surgical table? Based on ethnographic fieldwork in Danish transplant research laboratories, we investigate how pig experiments facilitate ‘collaborative intimacies’ among medical professionals. Collaborative intimacies are used here as an empirical and theoretical framework for conceptualising and re-imagining the social relationships between species and the medical disciplines that emerge in laboratory work. Collaborative intimacies in the lab provide medical training and facilitate moral reflection and social networking among transplant professionals. As such, we argue that research utilising animal models is not only about technological progress and ethical dilemmas; rather, collaborative intimacies make us understand how intimate relations among medical professionals in translational research unfold and how such relations matter for professional and technological futures

Differentiation of Palaeogene sand by glauconitic and geochemical fingerprinting, Siri Canyon, Danish North Sea

The submarine Siri Canyon is NE–SW-oriented and located in the Danish North Sea (Fig. 1). It contains a number of oil reservoirs with glauconite-rich sand. The reservoirs of interest in the Nini oil field are the Late Paleocene Tyr Member of the Lista Formation and the Kolga Member of the Sele Formation (Schiøler et al. 2007), presumably of Early Eocene age. These members have previously been known as the Ty and Hermod members (Hamberg et al. 2005; Poulsen et al. 2007). The sand shows signs of injection, both in cores and in seismic data. The aim of this work is to chemically characterise and fingerprint the sand in order to reveal the origin of the sand found in three horizontal wells, which could have been injected from one or both of the Tyr and Kolga members. Core samples were collected from two vertical wells of known stratigraphy to make a basis of comparison, whereas samples of the cuttings were collected from the three horizontal wells with ages primarily corresponding to the Kolga Member. The purpose was moreover to evaluate whether cuttings samples can be used for fingerprinting as an alternative to core samples

Meta-analysis of insulin aspart versus regular human insulin used in a basal-bolus regimen for the treatment of diabetes mellitus

Background: The objective of the current study was to compare the efficacy of two different insulin formulations, insulin aspart (IAsp) and regular human insulin (RHI), for prandial insulin coverage with neutral protamine Hagedorn (NPH) insulin as basal insulin using a meta-analysis approach. The primary endpoint was change in A1c over time. Secondary endpoints included incidence of hypoglycemia and postprandial glycemic control. Methods: Clinical trials (Type 1 and Type 2 diabetes) complying with Good Clinical Practice, and with individual patient data, were included in the meta-analysis. Trials were randomized, consisting of (at least) two treatment arms and had a minimum duration of 12 weeks. Estimates were calculated using fixed-effects and random-effects models. Heterogeneity was assessed for each analysis. The effect of baseline parameters on A1c was analyzed in extended simultaneous models. Results: The mean difference in A1c was 0.1% (95% confidence interval [CI] [−0.15; −0.04], P < 0.001) in favor of IAsp. Higher accumulated dose of IAsp, higher age and increased rates of hypoglycemia were associated with improved A1c outcome. Fasting plasma glucose was not significantly different between regimens. Postprandial glucose was significantly lower after treatment with IAsp compared with RHI, but the analysis did present a significant level of heterogeneity (P < 0.001). The overall rate of hypoglycemia was the same with both regimens, but nocturnal hypoglycemia was significantly lower with IAsp. Conclusions: A basal–bolus regimen with IAsp as bolus insulin provided minimal, but statistically significant, improvement in overall glycemic control with a lower rate of nocturnal hypoglycemic episodes, compared with a corresponding regimen with bolus RHI

Computational modeling of gradient hardening in polycrystals

A gradient hardening crystal plasticity model for polycrystals is introduced in Ekh et al. (2007). It is formulated in a thermodynamically consistent fashion and is capable of modeling a grain-size-dependent stress-strain response. In this contribution we extend that model to also include cross-hardening. A free energy is stated which includes contributions from the gradient of hardening along each slip direction. This leads to hardening stresses depending on the second derivative of the plastic slip. The governing equations for a nonlinear coupled system of equations is solved numerically with the help of a dual-mixed finite element method. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening: Moreover, cross-hardening further enhances the strengthening gradient effect

Numerical modeling of phase-separation in binary media based on the cahn-hilliard equation

In the article numerical procedure for solution of the Cahn-Hilliard equation which is based on the forward Euler method in time and mixed (due to 4th order nature of differential operator) linear finite element formulation in space is described. Numerical examples consist of idealized model with double well potential (in 2 and 3 spatial dimensions) and more physically relevant model with logarithmic potential (in 2D only).У статті описано процедуру наближеного рішення рівняння Кана-Хіллярда в частинних похідних 4-го порядку, котра базується на явному методі Ейлера в часі та змішаній постановці з білінійними скінченими елементами в просторі. Наведено чисельні рішення для ідеалізованої моделі з двуямним потенціалом (в 2-х та 3-х просторових вимірах) та більш фізично релевантної моделі з логарифмічним потенціалом (тільки в 2-х просторових вимірах)