Application and modification of the POD method and the POD-DEIM for model reduction in porous-media simulations

Researchers with a continuum-mechanical background typically use a multi-phasic and multi-component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuum-mechanical manner and solved using the finite-element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model-reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of proper-orthogonal decomposition (POD) for linear problems and the discrete-empirical-interpolation method (DEIM) in combination with the POD method (POD-DEIM) for nonlinear problems are investigated. Using the POD method, a given data set is approximated with a low-dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre-computation in the full (unreduced) system in each time-step (so-called “snapshots” of the system). Dealing with porous-media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non-negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel solution of volume-coupled multi-field problems using an Abaqus-PANDAS software interface

Numerical simulations have proven to be a powerful tool in several engineering disciplines, such as mechanical, civil and biomechanical engineering, and are thus widely used. However, the reliability of the simulations strongly relies on the governing material model. These models are usually developed in academic or industrial research projects and are implemented into dedicated software packages to proof their concepts. A transfer of these models from the research into a production-related environment is often time consuming and prone to failures, and therefore a costly task. The present work introduces a general interface between the research code PANDAS, which is a dedicated multi-field finite-element solver based on a monolithic solution strategy, and the commercial finite-element package Abaqus. The coupling is based on the user-defined element subroutine (UEL) of Abaqus. This procedure, on the one hand, allows for a straight-forward embedding of the PANDAS material models into Abaqus. On the other hand, it provides, in comparison to the native UEL subroutine of Abaqus, a user-friendly programming environment for user-defined material models with an extended number of degrees of freedom. Furthermore, the coupling also supports the parallel-analysis capabilities for large-scale problems on high-performance computing clusters. The Abaqus-PANDAS linkage can be applied to various coupled multi-field problems. However, the present contribution addresses, in particular, volume-coupled multi-field problems as they arise when proceeding from the Theory of Porous Media (TPM) as a modelling framework. For instance, it can be used to model partially or fully saturated soils, or chemically or electro-chemically driven swelling phenomena as they appear, for example, within hydrogels. Additionally, discontinuities, such as cracks, can be described for instance via phase-field models or by the extended finite-element method (XFEM). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molybdenum(VI) Bis(imido) Complexes: From Frustrated Lewis Pairs to Weakly Coordinating Cations

Molybdenum(VI) bis(imido) complexes [Mo(NtBu)₂(L^R)₂] (R=H 1 a ; R=CF₃ 1 b ) combined with B(C₆F₅)₃ ( 1 a /B(C₆F₅)₃, 1 b /B(C₆F₅)₃) exhibit a frustrated Lewis pair (FLP) character that can heterolytically split H−H, Si−H and O−H bonds. Cleavage of H₂ and Et₃SiH affords ion pairs [Mo(NtBu)(NHtBu)(L^R)₂][HB(C₆F₅)₃] (R=H 2 a ; R=CF₃ 2 b ) composed of a Mo(VI) amido imido cation and a hydridoborate anion, while reaction with H₂O leads to [Mo(NtBu)(NHtBu)(L^R)₂][(HO)B(C₆F₅)₃] (R=H 3 a ; R=CF₃ 3 b ). Ion pairs 2 a and 2 b are catalysts for the hydrosilylation of aldehydes with triethylsilane, with 2 b being more active than 2 a . Mechanistic elucidation revealed insertion of the aldehyde into the B−H bond of [HB(C₆F₅)₃]⁻. We were able to isolate and fully characterize, including by single-crystal X-ray diffraction analysis, the inserted products Mo(NtBu)(NHtBu)(L^R)₂][{PhCH₂O}B(C₆F₅)₃] (R=H 4 a ; R=CF₃ 4 b ). Catalysis occurs at [HB(C₆F₅)₃]⁻ while [Mo(NtBu)(NHtBu)(L^R)₂]⁺ (R=H or CF₃) act as the cationic counterions. However, the striking difference in reactivity gives ample evidence that molybdenum cations behave as weakly coordinating cations (WCC).     

Effects of hydrophobic polyhedral oligomeric silsesquioxane coating on water vapour barrier and water resistance properties of paperboard

The substitution of fossil based packaging materials with materials from renewable sources is a topic of current interest. Polyhedral oligomeric silsesquioxanes with fatty acid moieties can have a renewable content of more than 90 % and are therefore called bio-POSS. In this study the bio-POSS octa-(ethyl erucamide) silsesquioxane was coated on a paperboard substrate as a liquid coating. The water resistance and the water vapour barrier properties of the paperboard were improved. Samples on which the bio-POSS coating layer was dried at 80 °C had a slightly higher water resistance and water vapour barrier than samples dried at room temperature. UV treatment of the coating layer had little effect. Solid state ¹H-NMR of UV treated coatings showed no reaction of double bonds of bio-POSS in the coating layer. Multiple coating considerably enhanced the water resistance and water vapour barrier properties of the paperboard, due to an increase in the coating thickness and a reduction in number of pores on top coated surfaces.     

Cobalt‐Catalyzed Cross‐Coupling of Functionalized Alkylzinc Reagents with (Hetero)Aryl Halides

A combination of 10 % CoCl₂ and 20 % 2,2′‐bipyridine ligands enables cross‐coupling of functionalized primary and secondary alkylzinc reagents with various (hetero)aryl halides. Couplings with 1,3‐ and 1,4‐substituted cycloalkylzinc reagents proceeded diastereoselectively leading to functionalized heterocycles with high diastereoselectivities of up to 98:2. Furthermore, alkynyl bromides react with primary and secondary alkylzinc reagents providing the alkylated alkynes.     

Regiospecific Intramolecular Aldol Condensation Induced by Conjugate Addition of lithium dimethylcuprate to ζ-Oxo-α, β-enones preliminary communication [1]

ζ-Oxo-α, β-enones react with lithium dimethylcuprate to give cyclic aldols such as hydroxydecalone 1 and hydroxyspiro[4.5]decanone 2 in a regio- and stereospecific manner. This new reaction, a combination of conjugate methyl addition to α, β-enones with directed intramolecular aldolisation, is suggested to proceed via either enoate anions, such as 8 and 11 , or radical anions, such as 9 → 10 and 12 → 13 , as intermediates.