impact force reconstruction in composite panels

Abstract Passive sensing is a branch of structural health monitoring which aims at detecting positions and intensities of impacts occurring on aeronautical structures. Impacts are one of the main causes of damage in composite panels, limiting the application of these modern components on aircraft. In particular, impacts can cause the so called barely visible impact damage which, if not detected rapidly, can grow and lead to catastrophic failure. The determination of the impact location and the reconstruction of impact force is necessary to evaluate the health of the structure. These data may be measured indirectly from the measurements of responses of sensors located on the system subjected to the impact. The impact force reconstruction is a complex inverse problem, where the cause is to be inferred from its consequences. Inverse problems are in general ill-posed and ill-conditioned. Therefore, several techniques have been employed in the last four decades and have proven to be effective within certain limitations. Among these methods, transfer function based methods have been mainly validated for low-energy impact where the linear assumption should be valid. Nonlinearities may affect the accuracy in the reconstruction process and thus in the evaluation of damage other techniques have been adopted, such as artificial neural networks (ANN) or genetic algorithms (GA). In this study, a stiffened panel model developed in Abaqus/CAE is first validated, then numerical simulations are used to obtain data for several impacts, characterized by different impact locations and different energy (by changing the impactor mass and/or velocity). Geometrical nonlinearities of the dynamic system are considered in order to represent accurately the mechanics of the composite panel. Then the complex nonlinear behavior will be modeled through a nonlinear system identification approach, such as ANN, and an intelligent algorithm with global search capabilities, such as GA, will be used in sequence to accurately recovery the impact force peak and, therefore, properly evaluate the health status of the structure

Space tethers: parameters reconstructions and tests

In the last several years, the need for an alternative to chemical propulsive systems for low-orbit satellite deorbiting has become increasingly evident; a Tethered System can provide adequate thrust or drag without the complications of combustions and with a minimal impact on the environment. In this context, the authors are part of a team that is studying various tether applications and building a prototype of an electrodynamic tether system. The goal of this paper is to characterize tether materials in order to find valid solutions for future space tether missions. Mission requirements (e.g., the survivability to hypervelocity impacts and the capability to damp oscillations in electrodynamic tethers) influence the choice of tether parameters such as cross section geometry (round wires or tapes), materials, length, and cross section sizes. The determination of the elastic characteristics and damping coefficients is carried out through a campaign of experiments conducted with both direct stress/strain measurements and the laboratory facility SPAcecRraft Testbed for Autonomous proximity operatioNs experimentS (SPARTANS) on a low friction table at the University of Padova. In the latter case, the stiffness and damping of a flexible line were verified by applying different tensile load profiles and then measuring the tether-line dynamic response in terms of tension spike amplitude, oscillation decay, and estimation of the damping coefficient

EXPERIMENTAL VALIDATION OF A DEPLOYMENT MECHANISM FOR TAPE-TETHERED SATELLITES

The number of space debris orbiting our Earth has been continuously increasing since the beginning of the space era. The space community is converging on responsible conducts and self-regulations to address this serious problem that is degrading the near-Earth environment. In this context, green deorbiting technologies and strategies alternative to the traditional chemical propulsion are under investigation, including Electrodynamic Tethers (EDTs) because they are a promising option. To increase EDT technology maturity level, some critical points shall be addressed and experimentally evaluated, including the deployment of tape tethers, to demonstrate their reliability. This paper presents results of an experimental validation of the Deployment Mechanism (DM) proposed for the H2020 FET OPEN Project E.T.PACK \u2013 Electrodynamic Tether Technology for Passive Consumable-less Deorbit Kit. We developed a mockup that hosts the DM and other elements that are on board the tip mass of a tethered system, using off-the-shelf components. The DM is tested for the first part of the tether deployment maneuver employing the SPARTANS facility of the University of Padova. This facility includes a Testing Table where the mock-up can move with almost no friction and a Motion Capture system that provides an accurate estimation of the mock-up motion during this first part of the tether deployment maneuver

Deployment requirements for deorbiting electrodynamic tether technology

In the last decades, green deorbiting technologies have begun to be investigated and have raised a great interest in the space community. Among the others, electrodynamic tethers appear to be a promising option. By interacting with the surrounding ionosphere, electrodynamic tethers generate a drag Lorentz force to decrease the orbit altitude of the satellite, causing its re-entry in the atmosphere without using propellant. In this work, the requirements that drive the design of the deployment mechanism proposed for the H2020 Project E.T.PACK—Electrodynamic Tether Technology for Passive Consumable-less Deorbit Kit—are presented and discussed. Additionally, this work presents the synthesis of the reference profiles used by the motor of the deployer to make the tethered system reach the desired final conditions. The result is a strategy for deploying electrodynamic tape-shaped tethers used for deorbiting satellites at the end of their operational life.Open Access funding provided by Università degli Studi di Padova. This work was supported by European Union’s H2020 Research and Innovation Programme under Grant Agreement No. 828902 (E.T.PACK Project). Gonzalo Sánchez-Arriaga's work is supported by the Ministerio de Ciencia, Innovación y Universidades of Spain under the Grant RYC-2014-15357

Structural material damage: novel methods of analysis

In the classical continuum theory of solid mechanics, the mathematical framework involves partial derivatives to represent the state of deformation of a solid body. A significant drawback due to derivatives is related to the unphysical results given near the discontinuities, because they are undefined wherever a continuous field of displacements is not verified, such as in the presence of dislocations, voids, cracks, interfaces between different phases within the same body and grain boundaries. Various techniques were employed for overcoming this incapability of the classical theory in describing material behavior in such conditions; in fact, spontaneous formation and growth of discontinuities are of great importance in solid mechanics: they lead to fractures and failures of systems that must be avoided, especially in aerospace structures, primarily, for safety reasons and, secondly, for economic purposes. One of these new approaches concerns employing nonlocal theories, based on integral formulations (more precisely integro-differential formulations), defined even when non-derivable displacement fields are involved. Peridynamics is one of these theories: it was suggested by Stewart Silling in 2000 [1] in order to adopt a consistent formulation describing material behavior not only when a continuous displacement field is provided, but also whenever discontinuities are present, avoiding partial differential equations or pre-setting of conditions which can influence the results. There are two versions of peridynamic models: bond-based, which was introduced first (see [1, 2]) and state-based. In the bond-based version, forces between two material points depend solely on their relative displacement, their relative initial position, and material properties. Due to its simplicity compared to the state-based version, most of the peridynamic applications have employed bond-based Peridynamics. However, bond-based models result in several limitations (the same of other atomistic or molecular dynamics models [3], although this is a continuum theory, not a discrete one), the most important of these is the fixed value of Poisson’s ratio: 1/4 in 3D or 2D plane strain, and 1/3 in 2D plane stress (see e.g. [1, 4]). This peculiarity implies other restrictions, such as the impossibility of reproducing plastic incompressibility in an accurate way. Nevertheless, for many purposes, bond-based Peridynamics fits the requirements and gives satisfying results. State-based peridynamic models remove these restrictions by allowing the interaction (“bond”) between a pair of points to potentially depend on all other bonds connected to the two points. Moreover, there are two types of state-based peridynamic formulations: ordi- nary and non-ordinary [2, 5, 6]. In the former, the forces between two material points act along the vector connecting the points in the deformed configuration. In the latter, such characteristic is not present. The ordinary state-based formulation requires specific derivation of constitutive models, see examples of viscoelasticity and plasticity models in [7, 8]. For non-ordinary state-based formulation, two approaches have been proposed: the development of an explicit model for the peridynamic force state [2] and the development of a map thanks to which classical mechanics constitutive relations are incorporated to indirectly establish the relationship between the interaction force and the deformation. The latter approach is called correspondence model [2]. The purpose of this thesis has been the investigation of possible advantages and drawbacks of this new and unexplored theory, so to identify some guidelines for choosing parameters fundamental for the analyses and the development of models for particular structural analyses. In the first year of the PhD course, the state of the art of this theory was studied and the bond-based linear and nonlinear static solvers developed in Matlabr were analyzed, employed and improved. During the second year of PhD course, the author of this thesis has focused her attention on the second version of the theory, based on concepts of advanced mathematics. She has become familiar with it, thanks to the functional analysis course that she had attended in the first year. One of the main original contributions of the present work to the existing literature is the development of the 2D linearization of the state-based “linear peridynamic solid” model in the state-based formulation. These models are useful whenever simplifying assumptions of plane stress and plane strain can be adopted for the simulation of a system, which, otherwise, would be described by a 3D model requiring high computational resources (time and memory). Particular attention is paid to this aspect, because, being a nonlocal model, implementing a peridynamic code is, in general, more computationally expensive than a code based on a local approach. The study of the state-based version started before going abroad and the development of the 2D models was completed during the six month stay at the University of Nebraska-Lincoln in USA. Both static and dynamic codes have been developed and the relevant parameters of these models have been analyzed. These linearized models are described in chapter 1.2.2. The study of failure criteria in state-based Peridynamics and the improvement of the algorithms in Matlabr to accelerate the codes and to optimize memory resources have been the main issues of the third year research. Some failure criteria, presented in section 1.2.3, have been proposed for brittle homogeneous linear elastic materials. They are criteria based on the maximum admissible stretch: a given bond fails at a critical stretch obtained by the work required to break that bond and this work is related to the fracture energy of the material. The results are compared to experimental data both for static and for dynamic cases, in bondbased and in state-based formulations. The detailed description of the algorithms can be found in chapter 3, while the results are illustrated in chapters 4 and 5.Nella teoria classica della meccanica dei solidi, la formulazione matematica include derivate parziali, grazie alle quali si possono rappresentare stati di deformazione come funzioni degli spostamenti relativi dei nodi in cui è discretizzato il sistema continuo. Una carenza rilevante dovuto all’utilizzo delle derivate è legato ai risultati privi di significato fisico ottenuti in prossimità delle discontinuità perché le derivate non sono definite laddove manca un campo di spostamenti continuo, come può capitare in presenza di dislocazioni, vuoti, cricche, interfacce tra fasi differenti nello stesso corpo e bordi dei grani. Dato che la formazione spontanea e la crescita di discontinuità sono di grande importanza in meccanica dei solidi, diverse tecniche sono state utilizzate per superare questa incapacità della teoria di descrivere il comportamento dei materiali in tali condizioni, perché situazioni in cui le strutture sono incapaci di continuare a svolgere la propria funzione devono essere evitate, specialmente per strutture aerospaziali, in primo luogo, per ragioni di sicurezza ed, in secondo luogo, per motivi economici. Uno di questi nuovi approcci riguarda l’utilizzo di teorie non locali basate su formulazioni integrali (più precisamente formulazioni integro-differenziali), definite anche quando campi di spostamento non derivabili sono presenti. La teoria “Peridynamics” è una di queste teorie: è stata proposta da Stewart Silling nel 2000 [1] così da adottare una formulazione unica e coerente capace di descrivere i comportamenti dei materiali in corpi sia continui che discontinui, evitando l’uso di equazioni alle derivate parziali o la definizione a priori di alcune condizioni che possono influenzare (e in un certo senso favorire) dei risultati. Ci sono due versioni di modelli peridinamici: la state-based, e un suo caso particolare, la bond-based, che è stata introdotta per prima (vedi [1, 2]). Nella versione bond-based, le forze tra due punti materiali dependono unicamente dal loro spostamento relativo e dalla loro posizione relativa iniziale, oltre che dalle proprietà del materiale. Vista la sua semplicità a confronto con la seconda versione, la maggior parte delle applicazioni e degli articoli sulla Peridynamica ha adottato la formulazione bond-based. Tuttavia, i modelli nella formulazione bond-based sono caratterizzati da alcune limitazioni (le stesse dei modelli di altre teorie atomistiche e dei modelli di dinamica molecolare [3], anche se la Peridinamica è una teoria del continuo, non discreta), la più notevole di queste è il modulo di Poisson fisso: 1/4 nelle simulazioni 3D oppure in caso di deformazione piana 2D, e 1/3 nelle simulazioni in stato di tensione piana 2D (si veda per esempio [1, 4]). Questa particolarità implica altre restrizioni, come l’impossibilità di riprodurre la condizione di incomprimibilità plastica in maniera accurata. Tuttavia, per la maggior parte degli scopi, la formulazione bond-based è sufficiente e fornisce risultati approssimati soddisfacenti. I modelli della versione state-based rimuovono queste restrizioni, permettendo che le interazioni tra due punti possano dipendere da tutte le interazioni (i “bond”) connessi ad almeno uno dei due punti, tramite delle mappe avanzate chiamate “states”. Inoltre, ci sono due tipi di formulazioni state-based: la ordinary e la non-ordinary [2, 5, 6]. Nella formulazione ordinary, le forze tra due punti materiali agiscono lungo la congiungente i due punti nella configurazione deformata, mentre nella formulazione non-ordinary, questa caratteristica non è più vera. La formulazione ordinary della state-based necessita di modelli costitutivi appositamente derivati, come per esempio i modelli di viscoelasticità e platicità in [7, 8]. Per la formulazione non-ordinary della state-based, due approcci sono stati proposti: lo sviluppo di un modello esplicito per l’espressione dello state della forza peridinamica [2] e lo sviluppo di una mappa grazie alla quale le relazioni costitutive della meccanica classica sono incorporate per stabilire indirettamente la relazione tra la forza d’interazione e la deformazione. I modelli derivanti dal secondo approccio sono chiamati modelli correspondence [2]. L’argomento di questa tesi è lo sviluppo di modelli per particolari tipi di analisi e la ricerca di possibili vantaggi e inconvenienti di questa teoria nuova ed inesplorata, così da identificare alcune linee guida per la scelta di parametri fondamentali per le analisi. Durante il primo anno del corso di dottorato, lo stato dell’arte relativo a questa teoria è stato studiato e i solutori statici lineari e non lineari nella formulazione bond-based sviluppati precedentemente in ambiente Matlabr sono stati analizzati, usati e migliorati. Durante il secondo anno, l’autrice di questa tesi si è concentrata sulla seconda versione, basata su concetti di matematica avanzata con cui ha preso dimestichezza grazie al corso di analisi funzionale seguito il primo anno. Uno dei principali contributi originali alla letteratura esistente presenti in questa tesi è lo sviluppo dei modelli linearizzati 2D del modello solido lineare nella formulazione state-based. Questi modelli sono particolarmente utili quando semplificazioni di stato piano di tensione o di deformazione possono essere assunte per la simulazione di un sistema tridimensionale, che altrimenti verrebbe descritto da un modello 3D che necessiterebbe di risorse computazionali più elevate (in termini di tempo e memoria). Una particolare attenzione è richiesta per quest’aspetto, perché, essendo un approccio non locale, implementare un codice basato sulla teoria peridinamica richiede in generale più risorse computazionali di un codice basato su un approccio locale. Lo studio della versione state-based è iniziato prima di andare all’estero e lo sviluppo dei modelli 2D si è poi completato durante il soggiorno di sei mesi alla University of Nebraska-Lincoln negli Stati Uniti. Sono stati sviluppati sia un codice dinamico che uno statico. I parametri principali di questi modelli sono stati analizzati e i modelli linearizzati si possono trovare descritti nel capitolo 1.2.2. Lo studio dei criteri di frattura adottabili nella formulazione state-based e il miglioramento degli algoritmi in Matlabr per accelerare i codici e ottimizzare le risorse di memoria e gestione dei dati sono stati gli argomenti principali del terzo anno. Alcuni criteri di frattura, presentati nel capitolo 1.2.3, sono stati proposti per materiali lineari elastici omogenei e caratterizzati da frattura fragile. Sono criteri basati sul massimo allungamento: un’interazione non locale (“bond”) viene meno quando un valore critico di allungamento è raggiunto; questo valore di allungamento critico è calcolato dal lavoro richiesto per rompere il bond e questo lavoro è a sua volta legato all’energia di frattura. I risultati ottenuti sono stati confrontati con dati sperimentali per casi sia statici che dinamici, sia nella formulazione bondbased che in quella state-based. La descrizione dettagliata degli algoritmi si trova nel capitolo 3, mentre i risultati sono riportati nei capitoli 4 e 5

Mixed-mode crack patterns in ordinary state-based Peridynamics

A new nonlocal theory of continuum, called Peridynamics, was introduced in 2000. While the classical theory of solid mechanics employs spatial derivatives in order to solve the motion equation and consequently requires the derivability of the displacement field, Peridynamics employs an integral formulation of the equation of motion which leads to the possibility to analyze structures without specific techniques whenever discontinuities, such as cracks or inhomogeneities, are involved. Peridynamics has proven to be able to handle several phenomena concerning crack propagation. There are two variants of the theory, bond-based and state-based. The former is a particular case of the latter, which can also be found in two versions, the ordinary, in which the interaction force between two nodes is aligned with their current relative position, and the nonordinary, in which interaction forces can have different directions and classical models can be directly introduced in the formulation, even though in this variant numerical integration problems arise (spurious mode deformation). In this study, fracture patterns for mixed-mode crack propagation cases are investigated while varying two fundamental parameters of Peridynamics, the maximum length of interaction, called horizon, and the ratio between the grid spacing and the horizon, called m-ratio. An ordinary state-based Peridynamics formulation is adopted and numerical results are compared with experimental evidences

Artificial neural networks for impact force reconstruction on composite plates and relevant uncertainty propagation

Impacts are one of the main causes of damage in composite panels. The determination of the impact location and the reconstruction of impact force are necessary to evaluate the health of the structure. These data may be measured indirectly from the measurements of responses of sensors located on the system subjected to the impact. In this study, a composite panel model developed in Abaqus/CAE is first validated and then numerical simulations based on the model are used to obtain data for several impacts, characterized by different impact locations, different impactor velocities and masses. Subsequently, these data are used to model the complex nonlinear behavior of the composite laminate by a nonlinear system identification approach. This is based on the use of artificial neural networks, which are employed to reconstruct the impact forces and the impact locations. Finally, an analysis of uncertainty propagation of one of the employed neural networks is carried out

Artificial neural networks for impact force reconstruction on composite plates

Strane direktne investicije su iznimno važne za gospodarski razvoj zemlje. Osim što se putem njih ostvaruje dobit za matičnu državu i državu primateljicu, putem njih se šire znanja, tehnologija, a povećava se i zaposlenost te konkurentnost zemlje. Akvizicijeisto nose odreĎene prednosti prilikom preuzimanja postojećih proizvodnih pogona u vidu ekonomije opsega, stjecanja novih tehnologija i inovacija te osvajanja novih tržišta. Kao najvažnije determinante odabira pojedine strategije spominju se otvorenost tržišta, povezanost, blizina zemlje primateljice, stabilnost zemlje primateljice, zaštita investitora te kvaliteta institucija. Na temelju primjera Atlantic grupe i AD Plastika prikazalose da su determinante bile važne prilikom donošenja odluke o obliku ulaganja u odreĎenu zemlju i odreĎeni sektor. Kao najvažnije odrednice AD Plastika prilikom stranih direktnih investicija spominju se tako otvorenost tržišta, bolja povezanost i blizina zemlje primateljice. S druge strane Atlantic grupa je prilikom preuzimanja bila voĎena determinantama veličine tržišta, razvijanja inovacija, tehnološkog razvijanja i zaštite investitora.Foreign Direct Investment is extremely important for a country's economic development. While such investments gain profits for both home and recipient countries, knowledge, technology, employment and country competitiveness also increase. Acquisitions also carry certain advantages for the broader economy when taking over existing production facilities, acquiring new technologies and innovations, and entering new markets. The most important determinants when selecting an individual strategy include: openness of the market; strength of relationships; proximity and stability of the recipient country; protections for the investor, and quality of the institutions. Based on the examples of Atlantic Group and AD Plastik, it was shown that the determinants were important when deciding on the form of investment in a particular country and a particular sector. As the most important determinants for AD Plastics, foreign direct investment refers to market openness, better relationships, and the close proximity of the recipient country. Conversely, Atlantic Group was guided by the determinants of market size, development of innovations, technological development and investor protection

Examples of applications of the peridynamic theory to the solution of static equilibrium problems

Peridynamics is a recently proposed continuum theory based on a non local approach and formulated with integral equations. The theory is suitable for dealing with crack propagation in solid materials. The original peridynamic formulation regarded dynamic problems and was adapted to the static case mainly using a relaxation method by introducing a substantial amount of numerical damping in the time integration. In the present work the implementation of the theory within an implicit code for static crack propagation phenomena based on the Newton-Raphson method is presented and applied to several examples of static crack propagation equilibrium problems. Results obtained with the newly developed procedure are presented for various structural configurations, with different boundary and load conditions and quantitatively compared to published data