129 research outputs found
Corrigendum to “Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials” [Mech. Res. Commun. 126 (2022) 104001] (Mechanics Research Communications (2022) 126, (S0093641322001331), (10.1016/j.mechrescom.2022.104001))
No full textWe correct a mistake in the coefficients of a transformation matrix and accordingly update the subsequent calculations and the conclusions of our paper (Giusteri and Penta, 2022). We conclude that arrangements of spherical inclusions of isotropic materials in an isotropic matrix based on a rhomboidal cell that generates the Face-Centered Cubic lattice produce effectively isotropic composites if and only if an additional condition is satisfied. This condition entails the vanishing of a single component of the effective elasticity matrix. In spite of numerical evidence, we could not prove that this condition is always satisfied
Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands
No full textWe propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables and elements of the special Euclidean algebra. This perspective emerges naturally from the evolution equations for strands, that are one-dimensional submanifolds, of the special Euclidean group. The discretization of the corresponding equations for the three-dimensional motion of a Cosserat rod is performed, in space, by using a staggered grid. The time evolution is then approximated with a semi-implicit method. Within this approach, we can easily include dissipative effects due to both the action of external forces and the presence of internal mechanical dissipation. The comparison with results obtained with different schemes shows the effectiveness of the proposed method, which is able to provide very good predictions of nonlinear dynamical effects and shows competitive computation times also as an energy-minimizing method to treat static problems
Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands
No full textWe propose a method for the description and simulation of the nonlinear
dynamics of slender structures modeled as Cosserat rods. It is based on
interpreting the strains and the generalized velocities of the cross sections
as basic variables and elements of the special Euclidean algebra. This
perspective emerges naturally from the evolution equations for strands, that
are one-dimensional submanifolds, of the special Euclidean group. The
discretization of the corresponding equations for the three-dimensional motion
of a Cosserat rod is performed, in space, by using a staggered grid. The time
evolution is then approximated with a semi-implicit method. Within this
approach we can easily include dissipative effects due to both the action of
external forces and the presence of internal mechanical dissipation. The
comparison with results obtained with different schemes shows the effectiveness
of the proposed method, which is able to provide very good predictions of
nonlinear dynamical effects and shows competitive computation times also as an
energy-minimizing method to treat static problems.Comment: 17 pages, 9 figure
Dipendenza dal tipo di flusso e tecniche di simulazione per fluidi complessi non-Newtoniani
No full textQuesto lavoro è dedicato all’indagine dei flussi planari di fluidi complessi in geometrie non specifiche attraverso tecniche di simulazione computazionali.
In primo luogo, abbiamo sviluppato un nuovo metodo multi-scala eterogeneo che accoppia i dati su micro-scala della Dinamica Molecolare Non all’Equilibrio (NEMD) con un solutore CFD su macro-scala per ottenere una previsione data-driven di flussi planari complessi non uniformi in geometrie macroscopiche complesse. A livello del continuo, il metodo è privo di modello, poichè il tensore di Cauchy che determina l’evoluzione del moto è determinato localmente nello spazio e nel tempo dai dati NEMD. Lo sforzo di modellazione è quindi limitato all’identificazione dei potenziali di interazione adatti alla micro-scala. Il metodo è stato testato con successo su tre flussi paradigmatici di fluidi polimerici: il canale dritto, la contrazione 4:1 e il flusso oltre un foro profondo. Rispetto alle proposte precedenti, il nostro approccio tiene conto del fatto che la risposta dei fluidi polimerici può dipendere fortemente dal tipo di flusso locale e dimostriamo che questa è una caratteristica necessaria per catturare correttamente la dinamica macroscopica.
In secondo luogo, abbiamo esteso le condizioni di riproducibilità di un reticolo di punti
in R^2 sottoposto ad estensione planare (trovate da Krayinik & Reinelt [35]) al caso dei flussi misti (combinazione di simple shear ed estensione). Queste condizioni sono legate alla possibilità di estendere indefinitamente la durata temporale della simulazione e questo è molto importante per poter estrarre proprietà stazionarie del sistema. Risulta che, per ogni flusso misto fissato, dobbiamo prendere un orientazione e un rapporto d’aspetto specifico per la scatola di simulazione al fine di visualizzare un suo comportamento periodico. In corrispondenza del periodo, la scatola viene reinizializzata senza perdere alcuna proprietà fisica significativa.
In terzo luogo, l’algoritmo è stato implementato con successo nel pacchetto software
PMF, scritto in C++ e dedicato alle simulazioni NEMD di Flussi Planari Misti in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Siamo anche riusciti a realizzare una serie completa di simulazioni significative di moti misti e, per questo motivo, il software può essere uno strumento affidabile per esplorare le proprietà reologiche di questa classe di flussi.This work is devoted to the investigation of planar flows of complex fluids in non specific geometries through techniques of computer simulation.
Firstly, we developed a new heterogeneous multi-scale method that combines micro-scale data from Non-Equilibrium Molecular Dynamics (NEMD) with a macro-scale CFD solver to achieve a data-driven prediction of complex non-uniform planar flows in macroscopic complex geometries. The microscopic data were employed to reconstruct the stress tensor that determines the evolution associated with the equations of motion at the macroscopic level. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. The method has been tested successfully onto three paradigmatic flows of polymeric fluids: the straight channel, the contraction 4:1 and the flow past a deep hole. Compared to previous proposals, our approach takes into account the fact that the material response of polymeric fluids can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics.
Secondly, we have been able to extend reproducibility conditions of a lattice of points
in R^2 under planar extension (found by Krayinik & Reinelt [35]) to the case of mixed
flows (combination of simple shear and extension). These conditions are linked to the
possibility of extending indefinitely the time duration of the simulation and this is very
important to be able to extract steady properties of the system. It results that, for
each fixed homogeneous mixed flow, we must take a specific orientation and aspect ratio for the simulation box to display the periodic behavior. In correspondence to the time period, the simulation box can be re-initialized without loosing any meaningful physical property.
Thirdly, the algorithm has been successfully implemented in the PMF software package, written in C++ and devoted to NEMD simulations of Planar Mixed Flows in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). We also managed to carry out a complete set of meaningful simulations of mixed motions and, for this reason, the software can be reliable tool for exploring the rheological properties of this class of flows
Measuring <i>fN</i> force variations in the presence of constant <i>nN</i> forces: a torsion pendulum ground test of the LISA Pathfinder free-fall mode
No full textSensor noise in <math display="inline"><mrow><mi>L</mi><mi>I</mi><mi>S</mi><mi>A</mi></mrow></math> <math display="inline"><mrow><mi>P</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>f</mi><mi>i</mi><mi>n</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></math>: Laser frequency noise and its coupling to the optical test mass readout
No full textInternational audienceThe LISA Pathfinder (LPF) mission successfully demonstrated the feasibility of the technology needed for the future space borne gravitational wave observatory LISA. A key subsystem under study was the laser interferometer, which measured the changes in relative distance in between two test masses (TMs). It achieved a sensitivity of 32.0-1.7+2.4 fm/Hz, which was significantly better than the prelaunch tests. This improved performance allowed direct observation of the influence of laser frequency noise in the readout. The differences in optical path lengths between the measurement and reference beams in the individual interferometers of our setup determined the level of this undesired readout noise. Here, we discuss the dedicated experiments performed on LPF to measure these differences with high precision. We reached differences in path length difference between (368±5) μm and (329.6±0.9) μm which are significantly below the required level of 1 mm or 1000 μm. These results are an important contribution to our understanding of the overall sensor performance. Moreover, we observed varying levels of laser frequency noise over the course of the mission. We provide evidence that these do not originate from the laser frequency stabilization scheme which worked as expected. Therefore, this frequency stabilization would be applicable to other missions with similar laser frequency stability requirements
LISA Pathfinder: First steps to observing gravitational waves from space
No full textLISA Pathfinder, the European Space Agency's technology demonstrator mission for future spaceborne gravitational wave observatories, was launched on 3 December 2015, from the European space port of Kourou, French Guiana. After a short duration transfer to the final science orbit, the mission has been gathering science data since. This data has allowed the science community to validate the critical technologies and measurement principle for low frequency gravitational wave detection and thereby confirming the readiness to start the next generation gravitational wave observatories, such as LISA.
This paper will briefly describe the mission, followed by a description of the science operations highlighting the performance achieved.
Details of the various experiments performed during the nominal science operations phase can be found in accompanying papers in this volume
Capacitive sensing of test mass motion with nanometer precision over millimeter-wide sensing gaps for space-borne gravitational reference sensors
No full textWe report on the performance of the capacitive gap-sensing system of the Gravitational Reference Sensor on board the LISA Pathfinder spacecraft. From in-flight measurements, the system has demonstrated a performance, down to 1 mHz, that is ranging between 0.7 and
1.8
aF
Hz
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. That translates into a sensing noise of the test mass motion within 1.2 and
2.4
nm
Hz
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in displacement and within 83 and
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nrad
Hz
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in rotation. This matches the performance goals for LISA Pathfinder, and it allows the successful implementation of the gravitational waves observatory LISA. A
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f
tail has been observed for frequencies below 1 mHz, the tail has been investigated in detail with dedicated in-flight measurements, and a model is presented in the paper. A projection of such noise to frequencies below 0.1 mHz shows that an improvement of performance at those frequencies is desirable for the next generation of gravitational reference sensors for space-borne gravitational waves observation
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