Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.

     

Communities of shared interests and cognitive bridges: the case of the anti-vaccination movement on Twitter

Scientometrics - This paper presents an analysis of the anti-vaccination movement’s referencing of research articles on the topic of vaccination in the social media network Twitter. Drawing...     

A GENERALIZED BLOCK BOOTSTRAP FOR SEASONAL TIME SERIES

When time‐series data contain a periodic/seasonal component, the usual block bootstrap procedures are not directly applicable. We propose a modification of the block bootstrap – the generalized seasonal block bootstrap (GSBB) – and show its asymptotic consistency without undue restrictions on the relative size of the period and block size. Notably, it is exactly such restrictions that limit the applicability of other proposals of block bootstrap methods for time series with periodicities. The finite‐sample performance of the GSBB is also illustrated by means of a small simulation experiment.     

Temperature characterization of flip-chip packaged piezoresistive barometric pressure sensors

In order to miniaturize piezoresistive barometric pressure sensors, a new flip-chip packaging technology has been developed. The thermal expansions of chip and package are different. So in a standard flip-chip package the strong mechanical coupling by the solder bumps would lead to stress in the sensor chip, which is unacceptable for piezoresistive pressure sensors. To solve this problem, in the new packaging technology the chip is flip-chip bonded on compliant springs to decouple chip and package. As the first step of the packaging process an under bump metallization (UBM) is patterned on the sensor wafer. Then solder bumps are printed. After wafer-dicing the chips are flip-chip bonded on copper springs within a ceramic cavity housing. Due to the compliance of the springs, packaging stress is induced into the sensor chip. As sources of residual stress the UBM and the solder bumps on the sensor chip were identified. Different coefficients of thermal expansion of the silicon chip, the UBM and the solder lead to plastic straining of the aluminum metallization between UBM and chip. As a consequence the measurement accuracy is limited by a temperature hysteresis. The influence of the chip geometry, e.g., the thickness of the chip or the depth of the cavity, on the hysteresis was investigated by simulation and measurements. As a result of this investigation a sensor chip was designed with very low residual stress and a temperature hysteresis which is only slightly larger than the noise of the sensor.     

Effect of Rare-Earth (La,Ce, and Y) Additions on the Microstructure and Mechanical Behavior of Sn-3.9Ag-0.7Cu Solder Alloy

In this article, we report on the microstructure and mechanical properties of Ce- and Y-containing Sn-3.9Ag-0.7Cu solders. The microstructures of both as-processed solder and solder joints containing rare-earth (RE) elements (up to 0.5 wt pct) are more refined compared to conventional Sn-3.9Ag-0.7Cu, with decreases in secondary Sn dendrite size and spacing and a thinner Cu₆Sn₅ intermetallic layer at the Cu/solder interface. These results agree well with similar observations seen in La-containing solders reported previously. The monotonic shear behavior of reflowed Sn-3.9Ag-0.7Cu-X(Ce, Y)/Cu lap shear joints was studied as well as the creep behavior at 368 K (95 °C). The data were compared with results obtained for Sn-3.9Ag-0.7Cu and Sn-3.9Ag-0.7Cu-XLa alloys. All RE-containing alloys exhibited creep behavior similar to Sn-3.9Ag-0.7Cu. Alloys with Ce additions exhibited a small decrease in ultimate shear strength but higher elongations compared with Sn-Ag-Cu. Similar observations were seen in La-containing solders. The influence of the RE-containing intermetallics (CeSn₃ and YSn₃) that form in these alloys on the microstructural refinement, solidification behavior, and mechanical performance of these novel materials is discussed.     

Interval-valued fuzzy graphs

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self-complementary and self-weak complementary interval-valued fuzzy complete graphs.     

Structural analysis of W7-X: From design to assembly and operation

The Wendelstein 7-X (W7-X) modular stellarator is in the assembly phase at the Max-Planck-Institut für Plasmaphysik in Greifswald, Germany. The design of the “basic machine”, i.e. without in-vessel components, diagnostics and periphery, is largely completed, structural parameters such as bolt preload, initial conditions for contact elements, etc. are defined, and most of the components are manufactured and partly assembled. Therefore, the focus of structural analysis was shifted towards fast analyses of non-conformities, changes in the assembly procedure, and exploration of operational limits. Assembly-related work is expected to continue until commissioning of the machine, however, with decreasing intensity. In parallel the analysis requirements for in-vessel components, diagnostics and periphery will increase.This paper focuses on the most remarkable results, on special problems which had to be solved, on strategic issues like parameterization, complex finite element model structuring and benchmarking with alternative models in different codes, on assumptions of reasonable safety margins and expected tolerances, and on confirmation of analysis results by tests. Finally it highlights some lessons learned so far, which might be relevant also for other large fusion machines, and gives an outlook on future work.     

Evaluation of the mechanical behavior of W7-X central support connections by means of semi-automated FE analysis

The stellarator Wendelstein 7-X is under construction at the Max-Planck-Institut für Plasmaphysik in Greifswald. Its superconducting coil system is fixed by a massive structure. During machine operation the coils exert high forces and moments against each other and the central support structure (CSS). Therefore, the detailed analysis of the coil to CSS connections, the so-called central support elements (CSE), is a critical item. The major details of the design have been frozen; nevertheless, there is still need for detailed analysis of the CSEs due to assembly issues, and later on for exploring operational limits of the machine. These analyses have to be performed quickly, reliably, and shall provide results in a standardized form to enable timely responses to the assembly team. Special numerical tools – finite element (FE) parametric models of CSEs – have been developed for the purpose of such analyses. In the models, the geometry, material properties, contact conditions, loads as well as results presentation are defined in a parametric way. The use of the developed models for the definition of the final weld parameters, bolt preloads, assessment of acceptable tolerances, and optimal positions of the CSE-wedges before welding is also discussed.     

Simulation based analysis of secondary effects on solder fatigue

Secondary effects on thermal fatigue of solder joints, which frequently have been neglected, were studied by means of the finite element method (FEM). Based on a semi-empirical approach to predict fatigue life by evaluating the cyclic accumulated equivalent creep strain or energy density, effects of organic boards intrinsic properties on solder joint fatigue were investigated. Aspects of more realistic FR-4 board modelling were studied, in particular concerning its in-plane anisotropy and intrinsic warpage behaviour. Intrinsic board warpage was measured on test board level as well as for boards from series production. High intrinsic warpage was in particular found for several test boards. The effects for the worst case scenario observed so far were analysed for both first level and second level interconnects. The change in predicted fatigue life varied between 30% and 500%, the latter most critical effects were found at large QFN components. Another secondary effect studied was to include the frequently neglected interfacial intermetallics into FEM. It turned out that for components with relatively large standoff like LFBGAs the effects were actually negligible, but for the highly miniaturized components like chip resistors CR0201 they are the decisive factor.