Improving the reliability of material databases using multiscale approaches

This article addresses the propagation of constitutive uncertainties between scales occurring in the multiscale modelling of fibre-reinforced composites. The amplification of such uncertainties through upward or downward transitions by a homogenisation model is emphasized and exemplified with the Mori-Tanaka model. In particular, the sensitivity to data uncertainty in the inverse determination of constituent parameters based on downward transitions is stressed on an example. Then a database improvement method, which exploits simultaneously the available information on constitutive uncertainties at all scales instead of just propagating those associated with one scale, is presented and shown to yield substantial reductions in uncertainty for both the constitutive parameters and the response of structures. The latter finding is demonstrated on two examples of structures, with significant gains in confidence obtained on both

Sprzężone i niesprzężone równania konstytutywne liniowej sprężystości i lepkosprężystości materiałów ortotropowych

The study concerns the linear elastic and viscoelastic constitutive modelling of homogeneous orthotropic solid bodies. The considerations are based on well-known coupled standard/inverse constitutive equations of elasticity. The author has derived new uncoupled standard/inverse constitutive equations of elasticity, new uncoupled standard/inverse constitutive equations of viscoelasticity, and new coupled standard/inverse constitutive equations of viscoelasticity of orthotropic materials. A homogeneous orthotropic material is deseribed by 9 elastic and 18 viscoelastic constants, clearly interpreted physically. Simpler materials, i.e. monotropic and isotropic solid bodies, are also considered. In addition, the separation of shear and bulk strains in the uncoupled constitutive equations of elasticity has been examined numerically for exemplary materials.Praca dotyczy modelowania konstytutywnego jednorodnych ortotropowych ciał stałych w zakresie linowym, sprężystym i lepkosprężystym. Podstawą rozważań są znane sprzężone standardowe/odwrotne równania konstytutywne liniowej sprężystości tych materiałów. Wyznaczono niesprzężone standardowe/odwrotne równania konstytutywne liniowej sprężystości, sformułowano niesprzężone standardowe/odwrotne równania konstytutywne liniowej lepkosprężystości, a następnie wyznaczono sprzężone standardowe/odwrotne równania konstytutywne liniowej lepkosprężystości ortotropowych ciał stałych. Jednorodny materiał ortotropowy opisano za pomocą 9 stałych sprężystości i 18 stałych lepkosprężystości z podaniem przejrzystej interpretacji fizycznej tych stałych. Rozważono również przypadki szczególne materiału monotropowego i izotropowego. Dodatkowo, przetestowano numerycznie rozdzielenie odkształceń postaciowych i objętościowych w przypadku niesprzężonych równań konstytutywnych sprężystości materiałów ortotropowych i monotropowych

Wpływ losowych nierówności toru na drgania wybranego układu most zespolony / nawierzchnia kolejowa / pociąg szybkobieżny

A theory of the quasi-exact physical and mathematical modelling of the composite (steel–concrete) bridge / ballasted track structure / high-speed train system (BTT) was developed, including viscoelastic suspensions of rail-vehicles on two-axle bogies, the non-linear Hertz contact stiffness and one-sided contact between the wheel sets and the rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, the approach slabs, and random track irregularities. Based on this theory, advanced computer algorithms for the BTT numerical modelling were written and a computer program to simulate the vertical vibrations of the BTT systems was developed. The bridge subject to the preliminary dynamic analysis and designed according to Polish standards has a 15.00 m span length. The bridge was loaded by the German ICE-3 high-speed train moving at the critical (180 and 270 km/h) and the maximum (300 km/h) operating speeds.Opracowano quasi-ścisłą teorię modelowania jednowymiarowego (1D), fizycznego i matematycznego, układu most zespolony / nawierzchnia kolejowa podsypko-wa / pociąg szybkobieżny (BTT), przy uwzględnieniu lepkosprężystych zawieszeń pojazdów szynowych na dwuosiowych wózkach jezdnych, nieliniowej sztywności kontaktowej Hertza i jednostronnego kontaktu między zestawami kołowymi a szynami, cech lepkosprężystych i bezwładnościowych mostu, lepko sprężystej nawierzchni kolejowej na moście i poza mostem, płyt przejściowych i losowych nierówności toru. Na podstawie tej teorii opracowano zaawansowane algorytmy komputerowe modelowania numerycznego układów BTT oraz program komputerowy do symulacji drgań pionowych tych układów. W ramach wstępnych badań dynamicznych rozważono most zaprojektowany zgodnie z polskimi normami, o rozpiętości teoretycznej przęsła 15,00 m, oznaczony kodem SCB-15. Most obciążono niemieckim pociągiem szybkobieżnym ICE-3, poruszającym się z prędkością krytyczną (270 km/h) i maksymalną (300 km/h)

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 3: Deterministic and random vibrations of exemplary system

Based on the one-dimensional quasi-exact physical and mathematical modelling of a composite (steel-concrete) bridge/track structure/high-speed train system (BTT), developed in Part 2, advanced computer algorithms for the BTT numerical modelling and simulation as well as a computer programme to simulate vertical vibrations of BTT systems are developed. The exemplary bridge under numerical quasi-static and dynamic analysis, designed according to Polish standards, has a 15.00 m span length and belongs to the SCB series-of-types developed in Part 1. The bridge is loaded by a German ICE-3 high-speed train moving at the resonant and maximum operating speeds. A continuously welded ballasted track structure adapted to high operating velocities is applied. The output quantities include: time-histories of the vertical deflection of the main beams at the midspan, time-histories of the longitudinal normal stress in the bottom fibres of the main beams at the midspan, time-histories of the vertical acceleration of the bridge deck at the midspan, time-histories of the vertical accelerations of the suspension pivots in car-bodies, time-histories of the dynamic pressures of the wheel sets of moving rail-vehicles. The design quantities, understood as the extreme values of the output quantities, are used to verify the design conditions. The basic random factor, i.e. vertical track irregularities of the track, is taken into consideration. Basic statistics of the design quantities treated as random variables are calculated and taken into account in the design conditions

Numerical modelling and validation of 12.7 MM FSP impact into ALFC shield - ARMOX 500T steel plate system

The study develops a methodology for numerical modelling and simulation of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield – ARMOX 500T steel plate system. The ALFC shield is composed of the ALF energyabsorbing subsystem and a 10 mm-thick 99,7% Al2O3 alumina ceramic layer. The ALF subsystem is designed to absorb blast wave impact energy induced by explosive materials up to 10 kg TNT. The ceramic layer is designed to stop fragments from IED explosion. The 5 mm-thick Armox 500T steel plate constitutes the body bottom segment of a light armoured vehicle. The ALF subsystem has the following layered structure: Al2024 aluminium alloy plate, SCACS hybrid laminate plate, ALPORAS aluminium foam, SCACS hybrid laminate plate. The layers are joined with Soudaseal 2K chemoset glue. SCACS hybrid laminate contains the following components: VE 11-M modified vinylester resin (matrix), SWR800 S-glass plain weave fabric, Tenax HTA40 6K carbon plain weave fabric, Kevlar 49 T 968 aramid plain weave fabric. The total thickness of the ALFC shield amounts to 90 mm. Proof ground tests of a 12.7 mm 13.4 g FSP fragment impact into the ALFC shield - ARMOX 500T steel plate system have been performed at impact velocity 715 m/s and used for experimental validation of numerical modelling and simulation. In the numerical modelling, the aluminium alloy plate and Armox 500T steel plate are working in the elasto-plastic range according to Johnson-Cook model. The 99.7% Al2O3 alumina ceramic is working in elasto-short range according to JH-2 Johnson-Holmquist model. The simulations correspond to large displacements, large deformations and potential contact among all the components of the system. In FE mesh, the 8-node 24 DOF hexahedral finite elements with single integration point have been used. Failure criteria governing ad-hoc erosion of finite elements have been applied. The FEM modelling, simulation and postprocessing have been carried out using Catia, HyperMesh, LS-DYNA and LS-PrePost systems. The simulation results in the form of displacement/penetration contours and the FSP final deformation have been compared with the experimental results

Model reologiczny HWKK dla żywic

A rheological model for epoxy and polyester resins, denoted with the symbol HWKK, has been developed and positively validated for selected loading programmes. This model describes the first-rank reversible creep of amorphous tyermohardened polymers with good accuracy. The mechanical HWKK model consists of four elements connected in series, formulated by Hooke, Wilczyński and Kelvin. Constitutive equations of viscoelasticity for the HWKK model have been formulated, with fractional and normal exponential functions used as the generating ones. An algorithm for identification of the material constants, based on creep experiments of bar samples uniaxially tensioned, has been developed. The material constants have been identified for epoxy and polyester resins.Opracowano nowy model reologiczny żywicy epoksydowej i poliestrowej, oznaczony symbolem HWKK. Przeprowadzono walidację tego modelu dla wybranych programów obciążenia, uzyskując pozytywne wyniki. Model HWKK opisuje z dobrą dokładnośćią pełzanie pierwszorzędowe odwracalne polimerów amorficznych termoutwardzalnych. Model ten jest odwzorowany przez cztery elementy mechaniczne połączone szeregowo typu Hooke'a, Wilczyńskiego i Kelvina. Sformułowana równania konstytutywne lepkosprężystości i modelu HWKK stosując jako funkcje tworzące jedną funkcję wykładniczą ułamkową oraz dwie funkcje wykładnicze zwykłe. Opracowano algorytm identyfikacji stałych materiałowych opisujących model HWKK, bazujący na eksperymentach pełzania próbek prętowych rozciąganych osiowo. Stałe te zidentyfikowano dla żywicy epoksydowej i poliestrowej

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 1: Series-of-types of steel-concrete bridges

A new series-of-types of single-span simply-supported railway composite (steel-concrete) bridges, with a symmetric platform, has been designed according to the Polish bridge standards. The designed bridges/viaducts are located on the main railways of the classification coefficient k = +2. A ballasted track structure adapted to high operating speeds has also been designed. The ultimate limit states and the limit states corresponding to the bridges undertaken are collected and discussed. The bridges have been designed in accordance with contemporary art engineering, with geometric and material optimization, avoiding overdesign. A new methodology of numerical modelling and simulation of dynamic processes in composite bridge/ballasted track structure/high speed train systems, developed in Part 2 and Part 3, has been applied and implemented in a problem-oriented computer programme. A new approach to predicting forced resonances in those systems is formulated and tested numerically. It has been proved that in the case of typical structural solutions of bridges and ballasted track structures, it is necessary to introduce certain limitations for operating speeds of trains

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 2: Physical and mathematical modelling

A theory of one-dimensional physical and mathematical modelling of the composite (steel-concrete) bridge/track structure/highspeed train system is developed including viscoelastic suspensions of rail-vehicles with two two-axle bogies each, non-linear Hertz contact stiffness and one-sided contact between wheel sets and rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, approach slabs, and random vertical track irregularities. Compared to the state-of-the-art, the physical model developed in the study accurately reproduces dynamic processes in the considered system. Division of the system into the natural subsystems, a method of formulation of the equations of motion partly in implicit form and the finite element method are applied. Vibrations in the vertical plane of symmetry are described by more than nine matrix equations of motion with constant coefficients. Couplings and non-linearity are hidden in the generalized load vectors. The equations of motion are integrated using the implicit Newmark average acceleration method with linear extrapolation of the interactions between the subsystems