A local isotropic damage coupled hyperelastic-plastic framework is formulated in principal axes where thermo-mechanical extensions are also addressed. It is shown that, in a functional setting, treatment of many damage growth models, including ones originated from phenomenological models (with formal thermodynamical derivations), micro-mechanical models or fracture criteria, proposed in the literature, is possible. Quasi-unilateral damage evolutionary forms are given with special emphasis on the feasibility of formulations in principal axes. Local integration procedures are summarized starting from a full set of seven equations which are simplified step by step initially to two and finally to one where different operator split methodologies such as elastic predictor-plastic/damage corrector (simultaneous plastic-damage solution scheme) and elastic predictor-plastic corrector-damage deteriorator (staggered plasticdamage solution scheme) are given. For regularization of the post peak response with softening due to damage and temperature, Perzyna type viscosity is devised. Analytical forms accompanied with algorithmic expressions including the consistent material tangents are derived and the models are implemented as UMAT and UMATHT subroutines for ABAQUS/Standard, VUMAT subroutines for ABAQUS/Explicit and UFINITE subroutines for MSC.Marc. The subroutines are used in certain application problems including numerical modeling of discrete internal cracks, namely chevron cracks, in direct forward extrusion process where comparison with the experimental facts show the predicting capability of the model, isoerror map production for accuracy assessment of the local integration methods, and development two novel necking triggering methods in the context of a damage coupled environment.

In the recent past, the field of scientific computing has become of more and more importance for scientific as well as for industrial research, playing a comparable role as experiment and theory do. This success of computational methods in scientific and engineering research is next to the enormous improvement of computer hardware to a large extend due to contributions from applied mathematicians, who have developed algorithms which make real life applications feasible. Examples are adaptive methods, high order discretization, fast linear and non-linear solvers and multi-level methods. The application of these methods in a large class of problems demands for suitable and robust tools for a flexible and efficient implementation. In order to play a crucial role in scientific and engineering research, besides efficiency in the numerical solution, also efficiency in problem setup and interpretation of simulation results is of utmost importance. As modeling and computing comes closer together, efficient computational methods need to be applied to new sets of equations. The problems to be addressed by simulation methods become more and more complicated, ranging over different scales, interacting on different dimensions and combining different physics. Such problems need to be implemented in a short period of time, solved on complicated domains and visualized with respect to the demand of the user. %Only a modular abstract simulation environment will fulfill these requirements and allow to setup, solve and visualize real-world problems appropriately. In this work, the concepts and the design of the C++ finite element toolbox AMDiS (adaptive multidimensional simulations) are described. It is shown, how abstract data structures and modern software concepts can help to design user-friendly finite element software, which provides large flexibility in problem definition while on the other hand efficiently solves these problems. Also systems of coupled problems can be solved in an intuitive way. In order to demonstrate its possibilities, AMDiS has been applied to several non-standard problems. The most time-consuming part in most simulations is the solution of linear systems of equations. Multi-level methods use discretization hierarchies to solve these systems in a very efficient way. In AMDiS, such multi-level techniques are implemented in the context of adaptive finite elements. Several numerical results are given which compare this multigrid solver with classical iterative methods. Besides the development of more efficient algorithms also the growing hardware capabilities lead to an improvement of simulation possibilities. Modern computing clusters contain more and more processors and also personal computers today are often equipped with multi-core processors. In this work, a new parallelization approach has been developed which allows the parallelization of sequential code in a very easy way and reduces the communication overhead compared to classical parallelization concepts.

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For \emph{isotropic} meshes many estimators are known, but they either fail when used on \emph{anisotropic} meshes, or they were not applied yet. For rectangular (or cuboidal) anisotropic meshes a modified error estimator had already been found. We are investigating error estimators on anisotropic tetrahedral or triangular meshes because such grids offer greater geometrical flexibility. For the Poisson equation a residual error estimator, a local Dirichlet problem error estimator, and an $L_2$ error estimator are derived, respectively. Additionally a residual error estimator is presented for a singularly perturbed reaction diffusion equation. It is important that the anisotropic mesh corresponds to the anisotropic solution. Provided that a certain condition is satisfied, we have proven that all estimators bound the error reliably.

The bulge test is a commonly used experiment to establish the material stress-strain response at the highest possible strain levels. It consists of a metal sheet placed in a die with a circular opening. It is clamped in place and inflated with hydraulic pressure. In this thesis, a bulge testing apparatus was designed, fabricated, calibrated and used to measure the stress-strain response of an aluminum sheet metal and establish its onset of failure. The custom design incorporates a draw-bead for clamping the plate. A closed loop controlled servohydraulic pressurization system consisting of a pressure booster is used to pressurize the specimens. Deformations of the bulge are monitored with a 3D digital image correlation (DIC) system. Bulging experiments on 0.040 in thick Al-2024-T3 sheets were successfully performed. The 3D nature of the DIC enables simultaneous estimates of local strains as well as the local radius of curvature. The successful performance of the tests required careful design of the draw-bead clamping arrangement. Experiments on four plates are presented, three of which burst in the test section as expected. Finite deformation isotropic plasticity was used to extract the true equivalent stress-strain responses from each specimen. The bulge test results correlated well with the uniaxial results as they tended to fall between tensile test results in the rolling and transverse directions. The bulge tests results extended the stress-strain response to strain levels of the order of 40%, as opposed to failure strains of the order of 10% for the tensile tests. Three-dimensional shell and solid models were used to investigate the onset of localization that precedes failure. In both models, the calculated pressure-deformation responses were found to be in reasonable agreement with the measured ones. The solid element model was shown to better capture the localization and its evolution. The corresponding pressure maximum was shown to be imperfection sensitive. / text

Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events. / text

Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013

Στις ηλεκτρικές μηχανές η θερμική ανάλυση είναι εξίσου σημαντική με την ηλεκτρομαγνητική ανάλυση, διότι η θέρμανση μίας μηχανής είναι αυτή που τελικά οριοθετεί την ονομαστική ισχύ της. Ακριβής θερμική μοντελοποίηση της μηχανής απαιτείται για την επίτευξη υψηλής απόδοσης, την ορθή σχεδίαση, την επιλογή των υλικών και του τρόπου ψύξης και τη βελτιστοποίηση κόστους. Στόχος της παρούσας διπλωματικής εργασίας είναι η μελέτη των απωλειών, ο υπολογισμός της παραγόμενης θερμότητας και η εύρεση της κατανομής θερμοκρασίας στο εσωτερικό ενός ασύγχρονου κινητήρα στη μόνιμη κατάσταση λειτουργίας του με τη μέθοδο των πεπερασμένων στοιχείων. / Thermal analysis of electrical machines is as important as electromagnetic analysis, since the machine heating actually determines the nominal power of the machine. Accurate thermal modelling is necessary in order to achieve high performance, proper design, cost optimization and selection of the most suitable materials and cooling method. The goal of this project is the study of power losses and the calculation of the produced heat and temperature distribution inside an induction motor, which operates at steady state, using the finite element method.

Οι συνεχώς αυξανόμενες απαιτήσεις για στιβαρότερες και ελαφρύτερες κατασκευές οδήγησαν στην ανάπτυξη νέων υλικών. Η αύξηση της αντοχής με την ταυτόχρονη μείωση του βάρους έχουν σαν συνέπεια τη μείωση του κόστους, όχι όμως εναντίον της αξιοπιστίας και λειτουργικότητας. Τα νέα υλικά έχουν υψηλότερες τιμές του λόγου αντοχής/βάρος σε σύγκριση με εκείνες των συμβατικών υλικών. Σαν αποτέλεσμα, χρησιμοποιούνται στη δημιουργία προηγμένων και ευφυών κατασκευών, οι οποίες ανταποκρίνονται στα πρότυπα αξιοπιστίας και λειτουργικότητας για τα οποία έχουν σχεδιαστεί. Το πεδίο εφαρμογής των προηγμένων υλικών εκτείνεται σε ένα ευρύ φάσμα κατασκευών, όπως στη βιομηχανία των αυτοκινήτων, στην αεροδιαστημική, καθώς και σε μια πληθώρα προϊόντων καθημερινής χρήσης. Η ανά χείρας διατριβή ασχολείται με την προσομοίωση και τη μελέτη των φαινομένων που σχετίζονται με τις αστοχίες και ειδικότερα με τις διαδικασίες διάρρηξης δεσμού πρόσφυσης σε υλικά με ανομοιογένειες, που κατά κύριο λόγο είναι σύνθετα υλικά. Με την εισαγωγή αντιπροσωπευτικών όγκων αναφοράς που περιγράφουν την επαναληψιμότητα της γεωμετρίας, είναι δυνατόν να επιτευχθεί μια αντικειμενική προσομοίωση, με ανεξάρτητες μεταβλητές τη διάταξη των ενισχύσεων και την κατ’ όγκο περιεκτικότητα. Διερευνώνται οι εστίες συγκέντρωσης τάσεων και παραμορφώσεων, καθώς και η αλληλεξάρτησή τους από τις ανεξάρτητες μεταβλητές του προβλήματος, όπως μεταξύ άλλων είναι η παρουσία ενδιάμεσης φάσης, η ατελής πρόσφυση κλπ. Προσομοιώνεται η αποκόλληση κατά μήκος της ενδιάμεσης φάσης, ο θρυμματισμός των ινών και αναλύεται ο τρόπος με τον οποίο αλληλεπιδρά μια θραυσμένη ίνα στις ΠΡΟΛΟΓΟΣ iii γειτονικές της. Οι προσομοιώσεις και οι αναλύσεις που πραγματοποιήθηκαν, αφορούν υλικά τα οποία έχουν εκτεταμένες ή συγκεντρωμένες ενισχύσεις και χαρακτηρίζονται από ανομοιογένειες στην περιοχή μεταξύ των ενισχύσεων και της μήτρας. Το ένα υλικό διακρίνεται από το άλλο και κατά συνέπεια η μία φάση από την άλλη, διαμέσου της διεπιφάνειας. Η τυχαία ή συστηματική διάταξη των ενισχύσεων επιβάλλει την υιοθέτηση ενός αντιπροσωπευτικού στοιχείου όγκου, το οποίο να περιλαμβάνει δύο ή και περισσότερες ομογενείς φάσεις, που διαχωρίζονται μεταξύ τους με διεπιφάνειες, οι οποίες δεν είναι τίποτα περισσότερο από ανομοιογενείς στρώσεις ενδιάμεσων φάσεων, των οποίων οι ιδιότητες μεταβάλλονται κατά την έννοια του πάχους αυτών. Οι αστοχίες υλικών όπως τα παραπάνω αποτελούν δημοφιλέστατο αντικείμενο μελέτης εξαιτίας των ιδιαίτερα καταστροφικών τους αποτελεσμάτων. Η μείωση ή και η ολοκληρωτική απώλεια της ικανότητάς του να επιτελούν το σκοπό για τον οποίο σχεδιάστηκαν, μειώνουν την αξιοπιστία τους και οδηγούν σε απροσδόκητες αστοχίες με ολέθριες συνέπειες σε ότι αφορά την ασφάλεια, τη λειτουργικότητα και το κόστος του εξοπλισμού. Η κύρια αιτία που οδηγεί σε αστοχία ένα υλικό (εκτός από τη φθορά και τη διάβρωση) είναι η παραμόρφωση, με την οποία εννοούμε τη μεταβολή στο σχήμα ενός υλικού και αφορά κυρίως τις μηχανικές αστοχίες, οι οποίες είναι και το αντικείμενο μελέτης αυτής της διατριβής. Η παραμόρφωση ως επί το πλείστον οφείλεται σε εξωτερικά φορτία και μπορεί να είναι ελαστική ή πλαστική. Η τελευταία είναι δυνατόν να οδηγήσει σε θραύση. Ένα νέο είδος μηχανικής αστοχίας είναι η αποκόλληση, η οποία εμφανίζεται στις διεπιφάνειες των προηγμένων υλικών. Σαν αποτέλεσμα, όταν τα υλικά αυτά βρεθούν κάτω από κρίσιμο συνδυασμό εντατικών καταστάσεων να εγείρεται η διάρρηξη του δεσμού πρόσφυσής και κατά συνέπεια να αποτελούν εστίες εκκίνησης ρωγμών. Όλοι οι παραπάνω λόγοι επέβαλλαν τη μελέτη της αριθμητικής προσομοίωσης διάρρηξης δεσμού πρόσφυσης σε ανομοιογενή υλικά, καταλαβαίνοντας τη σημαντικότατη συμβολή που θα έχουν τα αποτελέσματα και τα συμπεράσματα που θα προκύψουν από αυτή. Αρχικά ο αναγνώστης, στο πρώτο κεφάλαιο, έρχεται σε μια πρώτη επαφή με τα σύνθετα υλικά, τα χαρακτηριστικά τους, τις αστοχίες που εκδηλώνονται σε αυτά, τον τρόπο με τον οποίο θεωρούνται από απλά ολιγοφασικά σε πολυφασικά υλικά, ενώ εισάγεται η έννοια της ενδιάμεσης φάσης, παρουσιάζονται οι ιδιότητες της και εν συνεχεία γίνεται μια σύντομη βιβλιογραφική ανασκόπηση. Έπειτα περιγράφεται το αντικείμενο των κεφαλαίων της παρούσας διατριβής. Στο δεύτερο κεφάλαιο αναπτύσσεται η μοντελοποίηση των iv φάσεων των σύνθετων υλικών και παρουσιάζονται τα διάφορα μοντέλα της ενδιάμεσης φάσης. Στο τρίτο κεφάλαιο επεξηγείτε ο τρόπος με τον οποίο επιτυγχάνεται η τμηματική ομοιογένεια της ενδιάμεσης φάσης, πραγματοποιείται ο αντικειμενικός ορισμός του μοντέλου, εφαρμόζεται μια ημιαναλυτική διαδικασία προσέγγισης της ανομοιογένειας της ενδιάμεσης φάσης και περιγράφονται τα λεγόμενα διεπιφανειακά στοιχεία, που χρησιμεύουν στην εκκίνηση της διάρρηξης του δεσμού πρόσφυσης. Στο τέταρτο κεφάλαιο παρουσιάζονται επιλεκτικά αποτελέσματα που ελήφθησαν από τις προσομοιώσεις που πραγματοποιήθηκαν, ενώ τέλος στο πέμπτο κεφάλαιο παραθέτονται τα συνολικά συμπεράσματα αυτής της προσπάθειας και οι προοπτικές που διανοίγονται από αυτήν. / The increasing demands for the development of improved and intelligent constructions, that will meet the desired reliability and functional standards, have led to new materials of higher strength/weight ratio comparing to those of the traditional materials. The present work is focused on the study -through simulation- of phenomena related to material failures and specifically to adhesion bond breaking of inhomogeneous materials. Through the introduction of representative reference volumes describing the repetitiveness of geometry, a realistic simulation can be evaluated, in which fibers packing dimensions and volumetric composition are the independent parameters. The areas of stress and strain accumulation, as well as their dependence on the problem independent variables (as weak interphase, imperfect adhesion etc), are discussed. The debonding along interphase and fiber fragmentation are simulated, while the reaction mechanism of a broken fiber near it is analysed. The materials under study include short and long reinforcements, while presenting inhomogenities among reinforcements and fibers (interphase area). Fibers packing demand the use of a representative volume element, which is consisted of two or more homogeneous phases, separated by interfaces. Those interfaces are inhomogeneous interphase layers, whose properties vary with their thickness. The validity of the proposed simulation method is established through the accuracy, the repetitiveness and the convergence of its results. The innovations of this work are the following:  For the first time, a study of the interphase and imperfect adhesion affection to the side debonding of fiber composite materials with FEA takes place.  A parametric model is developed, contributing to the realistic solution of this kind of problems.  For the first time, the development of hybrid interphase and its introduction to FEA analysis, take place.  For the first time, the simulation of fiber fragmentation and the use of interphase elements, to this analysis, take place.  Realistic simulation is improved, as well as the result process through modern computation tools. This general model for the prediction and the failure analysis of bonds breaking can be applied to other kinds of failure problems as well, for future research.

No description available.

Gas hydrates are ice-like crystalline solids composed of a hydrogen bonded water lattice entrapping low-molecular weighted gas molecules commonly of methane. These form under conditions of relative high pressure and low temperature, when the gas concentration exceeds those which can be held in solution, both in marine and on-land permafrost sediments. Simulating the mechanisms leading to natural gas hydrate emplacement in geological environments requires the modeling of the temperature, the pressure, the chemical reactions, and the convective/diffusive flow of the reactive species. In this study, we take into account the distribution of dissolved methane, methane gas, methane hydrate, and seawater, while ice and water vapor are neglected. The starting equations are those of the conservation of the transport of momentum (Darcy’s law), energy (heat balance of the passive sediments and active reactive species), and mass. These constitutive equations are then integrated into a 2-dimentional finite element in space, finite-difference in time scheme. In this study, we are able to examine the formation and distribution of methane hydrate and free gas in a simple geologic framework, with respect to geothermal gradient, dewatering and fluid flow, the methane in-situ production and basal flux. The temperature and pressure fields are mildly affected by the hydrate emplacement. The most critical parameter in the model appears to be the methane (L+G) and hydrate (L+G+H) solubility: the decrease in methane solubility beneath the base of the hydrate stability zone (BHSZ) critically impacts on the presence of free gas at the base of the BHSZ (thus the presence of a BSR), while the sharp decrease of hydrate solubility above the BHSZ up to the sea bottom critically impact on the amount of methane available for hydrate emplacement and methane seep into the water column.