8. 1. 2020, 10:00, posluchĂˇrna B
First-principles calculations of elastic constants for complex systems
Ing. Martin ZelenĂ˝, Ph.D., fakulta strojnĂ VUT v BrnÄ›
First principles or ab initio means to perform the calculations of the properties of a system from fundamental quantum mechanics with no parametrization or knowledge of experimental data. The Density Functional Theory (DFT) forms the basis for most of current first-principles methods and it is able to provide the exact information about the electronic structure of the system under study and subsequently about its internal energy. Nowadays, employing DFT for calculations of elastic properties is routine task for system with ideal crystal lattices. On the other hand, estimation of elastic properties is still challenging for systems with chemical disorder or with defect in crystal lattice despite large computational resources available to the scientific community. The recently introduced stress-strain method together with the DFT package VASP is able to provide the full matrix of elastic constants with reasonable computational cost also for large supercells describing lattices with defects, e.g. grain boundaries or twin boundaries. Large supercells are also required for description of alloys with chemical disorder by the supercell-based quasirandom structures (SQS). Further directional optimization of SQS (do-SQS) supercell is necessary to obtain proper matrix of elastic constants that will reflect the symmetry of the simple ordered lattice. Using of the stress-strain method and do-SQS approach will be demonstrated for Ni3Si and Ni3Al intermetallics, CoCrNi high entropy alloy and Ni2MnGa magnetic shape memory alloy.
PondÄ›lĂ 9. prosince 2019, 13:00, posluchĂˇrna B
Application of the method of localized Lagrange multipliers to the partitioned solution of large-scale structural dynamic systems: The AFETI algorithm
Prof. JosĂ© GonzĂˇlez, Universidad de Sevilla, Ĺ panÄ›lsko
In this talk, we will discuss about classical and new numerical techniques used for parallel/partitioned computations in structural mechanics and also multi-physics or coupled-field problems. In this field, methods based on classical Lagrange multipliers, like the two-level FETI-DP method, have been de facto the preferred parallel algorithms in solid and structural mechanics for decades. However, as we will see, classical Lagrange multipliers also present some limitations. The method of localized Lagrange multipliers (LLM) is a more general coupling technique, that introduces an explicit definition of the problem interface and brings some important advantages. Under this LLM framework, new partitioned algorithms like AFETI-C method are derived from variational principles. AFETI-C uses a combination of rigid-body modes and dominant substructural deformation modes in enforcing the interface force equilibrium equation as constraint conditions. In addition, a regularization of heterogeneities of partitioned systems is appended to AFETI-C that makes it competitive with FETI-DP. These methods, their derivation and their performance will be described, providing a full understanding of the potential of LLM in the solution of coupled problems.
PĂˇtek 6. prosince 2019, 11:00, posluchĂˇrna Klub
Cavitation and separation during water entry and exit
Alexander Korobkin, Professor in Applied Mathematics
First part of the presentation will explain the pressure distributions over the wetted surfaces of a parabolic contour in 2D and an elliptic paraboloid in 3D for oblique water impact. The pressures are calculated by the Wagner model of water entry with focus on zones of the wetted surface, where the hydrodynamic pressure is below the ambient pressure, and the zones, where the pressure approaches the vapour pressure. When the zones of low hydrodynamic pressure approach the contact line of the body surface, the surrounding air flows into this area separating the liquid surface from the body and leading to ventilation. Several models of ventilation and cavitation for 2D problem of oblique impact of rigid and elastic plates will be introduced. The nonlinear 2D problem of oblique impact of an elliptic cylinder onto a thin liquid layer with multiple bouncing of the cylinder from water will be presented. The second part of the presentation is about the water exit problems including the problem of an elastic disc lifted from water surface. The corresponding exit models will be applied to the 3D problem of a rigid ellipsoid gliding on water surface. Comparison of the obtained results with 3D CFD results will be shown. Our exit model of elastic bodies will be compared with the experimental results for large accelerations of the body lifting.
StĹ™eda 4. prosince 2019, 10:00, posluchĂˇrna B
Properties of open thermodynamic systems as the consequence of their stability
Prof. FrantiĹˇek MarĹˇĂk, DrSc., Ăšstav termomechaniky AV ÄŚR, ZĂˇpadoÄŤeskĂˇ univerzita, a Fakulta tÄ›lesnĂ© vĂ˝chovy a sportu Univerzity Karlovy
The presented concept deals with production of entropy generated by the nonequilibrium processes in consequence of the mass and energy transfer. Often used concept of endoreversible thermodynamics is based on non-realistic conjecture that the entire entropy production is realized at the system boundary. In this contribution, the open system in the thermodynamically non-equilibrium state is assumed. Production of entropy is generated due to the non-equilibrium processes accompanied by the energy conversion. The non-equilibrium steady state is maintained by a negative entropy flux. The stability conditions of the state with the minimum of entropy production are used to replace the endoreversibility concept.
This theory is applied to three different open non-equilibrium systems.
i) Efficiency of thermal machines and chemical reactors.
Hydrogen fuel cell with polymer electrolyte membrane are studied in details. The transport coefficients for reactants inlet, i.e. hydrogen and air, and for the products outlet, i.e. water, are connected with the actual electric efficiency. The calculated efficiency qualitatively and quantitatively corresponds to the experimentally obtained values. The further research shall focus on the relation of the parameters characterizing the membrane and transport of reactants and products to the power output.
ii) Energetic limitations of population growth.
Entropy production is characterized by general form of chemical reaction based on the mass action law. This law is usable for description of dynamics of population biology, e.g. cells, species. Moreover, this law can be even used to study dynamics of ecological systems. The reproduction process is spontaneous process with increase of entropy. The entropy increase is compensated by the negative entropy flux from the Sun. From the thermodynamic point of view, the sex reproduction is more advantageous as the cellular division because of it is reached by the lower Gibbs free enthalpy. This is probably the reason why sex reproduction is evolutionarily more advantageous.
iii) Dynamics of ecological system with migration.
Influence of reproduction and migration dynamics is evident on example of two competitive ecological systems (in general two auto catalytic reactions) of type predator and prey. The migration decreases the frequency of dynamical state of system. Due the migration this dynamical state can change to the stationary state, when time period is high enough. In principle, it is a diffusion reaction system in which a stationary spatial change of concentrations can occur. An example may be the presence of colored stripes on the body of some animals, such as cats, some fish, hornets, and the like.
PĂˇtek 15. listopadu 2019, 10:00, posluchĂˇrna B
Model reduction for the FEM of solids applied to the Rayleigh-Ritz computation of the free vibration spectrum
Prof. Petr Krysl, University of California, San Diego
Modal expansion is a workhorse used in many engineering analysis algorithms. One example is the coupled boundary element-finite element computation of the backscattering target strength of underwater elastic objects. To obtain the modal basis, a free-vibration (generalized eigenvalue) problem needs to be solved. This tends to be expensive when there are many basis vectors to compute. In the above mentioned backscattering example it could be many hundreds or thousands. Excellent algorithms exist to solve the free-vibration problem, and most use some form of the Rayleigh-Ritz (RR) procedure. The key to an efficient RR application is a low-cost transformation into a reduced basis. In this work we show how a cheap a priori transformation can be constructed for solid-mechanics finite element models based on the notion of coherent nodal clusters. The inexpensive RR procedure leads to not insignificant speedups of the computation of an approximate solution to the free vibration problem.
StĹ™eda 13. listopadu 2019, 13:00, posluchĂˇrna B
Non-coaxiality between two tensors: Application to stress rate decomposition and non-coaxial invariants
Prof. Yannis F. Dafalias, Ăšstav termomechaniky AV ÄŚR
Given a stress tensor and its rate, what are the analytical expressions of the parts of the stress-rate tensor that are (a) coaxial with the stress; (b) non-coaxial with the stress; (c) proportional with the stress; (d) non-proportional but coaxial with the stress; (e) orthogonal and coaxial with the stress and (f) orthogonal and non-coaxial with the stress? To answer the foregoing questions the coaxial and totally non-coaxial parts of a tensor in regard to another reference tensor are derived in closed analytical form based on representation theorems of tensor-valued isotropic functions. In the process a new interpretation is obtained for a singular case of representation theorems. The particular application of rotational shear is presented where analytical expressions are obtained for the parts of a stress rate tensor that induce (1) change of stress principal axes at fixed principal stress values, and (2) change of stress principal values at fixed stress principal axes such that the deviatoric stress orbit is circular on the Ď€-plane. Additional application in mechanics are discussed such as the definition and role of invariants related to the non-coaxial and orthogonal parts.
ĂšterĂ˝ 5. listopadu 2019, 10:00, posluchĂˇrna A
Notes on Experimental Research on Transonic Compressor Blade Cascades
Dr. David Ĺ imurda, Ăšstav termomechaniky AV ÄŚR
Despite ever increasing capabilities of CFD, experimental research on compressor blade cascades still plays important role in design and operation of gas turbines and other turbomachinery. This is true particularly in case of first stages of todayâ€™s large output gas turbine compressors and aircraft engine fans which operate at transonic range of relative inlet velocities. However, due to specific features of the flow past compressor cascades at transonic regimes, namely unstarted supersonic flow, experimental modelling is relatively complicated. Aim of the lecture will be to point out main difficulties connected with the cascade tests arising from the nature of compressor cascade flow and to provide ways of dealing with these problems.
ĂšterĂ˝ 22. Ĺ™Ăjna 2019 v 12:00, posluchĂˇrna A
The Energy-Sampling Stabilization of Nodally Integrated Continuum Elements for Dynamic Analyses
Prof. Petr Krysl, University of California, San Diego
Nodally integrated elements exhibit spurious modes in dynamic analyses (such as in modal analysis). Previously published methods involved a heuristic stabilization factor, which may not work for a large range of problems, and a uniform amount of stabilization was used over all the finite elements in the mesh. The method proposed here makes use of energy-sampling stabilization. The stabilization factor depends on the shape of the element and appears in the definition of the properties of a stabilization material. The stabilization factor is non-uniform over the mesh, and can be computed to alleviate shear locking, which directly depends on the aspect ratios of the finite elements. The nodal stabilization factor is then computed by volumetric averaging of the element-based stabilization factors. Energy-sampling stabilized nodally integrated elements (ESNICE) tetrahedral and hexahedral are proposed. We demonstrate on examples that the proposed procedure effectively removes spurious (unphysical) modes both at lower and at higher ends of the frequency spectrum. The examples shown demonstrate the reliability of energy-sampling in stabilizing the nodally integrated finite elements in vibration problems, just sufficient to eliminate the spurious modes while imparting minimal excessive stiffness to the structure. We also show by the numerical inf-sup test that the formulation is coercive and locking-free.
PondÄ›lĂ 21. Ĺ™Ăjna 2019 v 10:00, posluchĂˇrna B
Lessons to be learned from German Attempts to Reduce Atmospheric CO2-Emissions
Prof. Dr-Ing. Roland Span, Ruhr University Bochum, NÄ›mecko
With the goal to limit the increase of the average global temperature to 1.5 to 2 K, the governments of almost all developed countries agreed to drastically reduce atmospheric CO2 emissions. Though the common political will is clearly declared, concepts how the emission of greenhouse-gas emissions can be drastically reduced are very different and seem only partly realistic and appropriate. In this context Germany has launched the â€śEnergiewendeâ€ť program. This program relies essentially on a drastic increase in renewable power-production with wind and sun being the main energy sources and on reduced energy consumption in industry, private households, and traffic. Even though the availability of both wind and sun is rather limited in Germany, the program can so far be considered a success with regard to renewable power-production. The increase in renewable power-productions exceeded the politically formulated goals. However, currently the further increase is slowed down by different political measures, because a number of (mostly non-technical) limitations became obvious, that have not been addressed properly. And the required energy savings in the different sectors could not be realizedto date. Aspects of sectorial coupling have not been considered properly and problems in the areas of mobility and heat supply were underestimated. The presentation will briefly address the observed limitations and will formulate a number of theses derived from these findings. Not all of the factors influencing the further development of renewable power-production in Germany are relevant in other countries as well, but still the derived theses may serve as a starting point for general discussions on options for energy systems with largely reduced atmospheric CO2-emissions.
StĹ™eda 2. Ĺ™Ăjna 2019 v 10:30, posluchĂˇrna B
High Strain-rate Experiments Using Hopkinson Bar: Application on Cellular Metals and Additively Manufactured Auxetic Structures
Ing. TomĂˇĹˇ FĂla, Fakulta dopravnĂ ÄŚVUT
Cellular solids, such as metal foams, hybrid foams, 3D printed lattices or additively manufactured auxetic structures are complex lightweight cellular materials with high energy absorption capabilities and possible functionally graded material properties. Thus, mechanical behavior of the materials under the representative loading conditions (i. e., dynamic impact, blast) has to be well understood. In this study, results of several experimental campaigns covering high-strain rate testing of cellular solids using conventional Split Hopkinson Pressure Bar (SHPB) and direct impact Open Hopkinson Pressure Bar (OHPB) are presented. High-speed imaging together with custom digital image correlation (DIC) technique are introduced as vital techniques for a complex experimental analysis of the materials at high strain-rates. Examples covering the evaluation of the displacement and strain fields, different methods for evaluation of Poissonâ€™s ratio, and the analysis of the digital image correlation reliability are shown. Comparison of the digital image correlation results with the other methods (e. g. strain-gauges), its limitations and the actual challenges in this field are discussed. Overview of the experiments conducted at low and elevated temperatures observed using high-speed thermal imaging will be provided as well.
StĹ™eda 2. Ĺ™Ăjna 2019 v 10:00, posluchĂˇrna B
Digital image correlation: from static tests to X-ray tomography and high strain-rate loading
Prof. OndĹ™ej JirouĹˇek, Fakulta dopravnĂ ÄŚVUT
In the short lecture an overview of digital image correlation (DIC) applied to strain measurement of samples loaded in mechanical tests in general will be given. Examples of using the method in several engineering applications will be given, extension of the method that enables to use it in 3D (using time-lapse tomography) will be introduced and examples of experiments performed on a wide range of materials, ranging from trabecular bone samples, whole bone samples (vertebral bodies) to metallic foams will be presented. A special attention will be given to high-strain rate loading using Split Hopkinson Pressure Bar technique.