Analytical computation of moderate-degree fully-symmetric cubature rules on the triangle

A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of good quality, are computed and presented.Comment: 13 pages, submitted to Journal of Computational and Applied Mathematic

A novel efficient mixed formulation for strain-gradient models.

Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues, while being simpler and computationally cheaper. The behaviour of the new elements is further demonstrated through a numerical example

Evolution of particle breakage studied using x-ray tomography and the discrete element method

Particle breakage can significantly change the fabric (size and shape of particles and contact network) of a granular material, affecting highly the material's macroscopic response. In this paper, oedometric compression tests are performed on zeolite specimens and x-ray computed micro-tomography is employed, to acquire high resolution 3D images of the specimens throughout the test. The images are processed, to describe breakage spatially and quantify it throughout the test and gain information about the mechanisms leading to particle breakage. In addition to the image processing, the discrete element method (DEM) is used to study the initiation and likelihood of particle breakage, by simulating the experimental test during the early stages of loading and using quantitative results from the images to inform and validate the DEM model. A discrete digital image correlation is used, in order to incrementally identify intact grains and simultaneously get results about the strain field within the specimen, as well as the kinematics of individual grains and fragments. In the initial stages of breakage, there is a clear boundary effect on the spatial distribution of breakage, as it is concentrated at the moving boundary (more than 90% of total breakage) and circumferentially (more than 70% of total breakage) close to the apparatus cell. The DEM model can reproduce the bulk response of the material until the point where substantial breakage governs the macroscopic response and it starts to soften. Additionally, there is an initial indication that the spatial distribution of the force network matches the localisation of breakage radially, but it does not seem to localise close to the loading platen. This analysis will enrich our understanding of the mechanisms and evolution of particle breakage

Analytical and numerical solutions in boundary value problems of materials with microstructure

This thesis deals with analytical and numerical solutions of boundary value problems in gradient elasticity, with an emphasis on three-dimensional problems. After a general overview of the relevant theoretical background, enriched with a series of observations and comments on some points which are usually not given the proper attention, the first main point presented here is the derivation of a series of analytical solutions of some simple boundary value problems. These analytical solutions represent both new problems, whose analytical treatment has not been encountered in the relevant literature, and problems whose solution has been presented before, but only for very specific cases. Of particular importance is the study of how solutions to plane strain problems may or may not apply when the respective three-dimensional problems are considered. Passing from the analytical to the numerical part of the present work, an overview is first given of the reason why the numerical treatment of gradient elasticity problems is not straightforward. The “natural” way in which the C¹ requirement appears is described, together with various possible alternative formulations. Having thus shown the importance of considering three dimensional problems and the way C¹ requirements appear, the rest of this thesis is devoted to presenting, validating and justifying the development of a three dimensional isoparametric C¹ element. Following the way the element is developed clearly indicates which are its main benefits, as well as its drawbacks. The validation of the element not only shows the correctness of its numerical behaviour, but is also an important step in demonstrating its good performance in terms of accuracy and convergence. This is further discussed in a theoretical comparison to other elements that have been previously proposed.Η διδακτορική αυτή διατριβή ασχολείται με την αναλυτική και αριθμητική επίλυση προβλημάτων συνοριακών τιμών στα πλαίσια της θεωρίας ελαστικότητος βαθμίδας, με έμφαση στα τριδιάστατα προβλήματα. Μετά από μία γενική επισκόπηση του σχετικού θεωρητικού υποβάθρου, εμπλουτισμένη με μία σειρά παρατηρήσεων και σχολίων πάνω σε ορισμένα σημεία στα οποία δε δίνεται συνήθως η δέουσα προσοχή, το πρώτο κύριο σημείο που παρουσιάζεται είναι η εύρεση μίας σειράς αναλυτικών λύσεων μερικών απλών προβλημάτων συνοριακών τιμών. Οι αναλυτικές αυτές λύσεις αντιπροσωπεύουν τόσο νέα προβλήματα, των οποίων η αναλυτική αντιμετώπιση δεν έχει βρεθεί στη σχετική βιβλιογραφία, όσο και προβλήματα των οποίων η λύση έχει παρουσιαστεί προηγουμένως, αλλά μόνο για πολύ ειδικές περιπτώσεις. Ιδιαίτερης σημασίας είναι η μελέτη του αν οι λύσεις προβλημάτων επίπεδης παραμόρφωσης μπορούν να εφαρμοστούν στα αντίστοιχα τριδιάστατα προβλήματα. Περνώντας από το αναλυτικό στο αριθμητικό μέρος της παρούσης εργασίας, δίνεται αρχικά μια γενική θεώρηση του λόγου για τον οποίο η αριθμητική αντιμετώπιση προβλημάτων ελαστικότητας βαθμίδας δεν είναι απλή. Στην συνέχεια παρουσιάζεται ο ‘φυσικός’ τρόπος με τον οποίο προκύπτει η απαίτηση για συνέχεια C¹, καθώς και διάφορες πιθανές εναλλακτικές θεωρήσεις. Έχοντας με αυτόν τον τρόπο δείξει τη σημασία της θεώρησης τριδιάστατων προβλημάτων και τον τρόπο με τον οποίο προκύπτει η απαίτηση για συνέχεια C¹, το υπόλοιπο της διατριβής ασχολείται με την παρουσίαση, τον έλεγχο και την αιτιολόγηση της ανάπτυξης ενός τριδιάστατου ισοπαραμετρικού στοιχείου με συνέχεια C¹. Ακολουθώντας την πορεία ανάπτυξης του στοιχείου φαίνονται καθαρά τα κύρια πλεονεκτήματά του, καθώς και τα μειονεκτήματά του. Ο έλεγχος του στοιχείου δε δείχνει μόνο την ορθότητα της αριθμητικής του συμπεριφοράς, αλλά είναι και ένα σημαντικό βήμα στην απόδειξη της καλής του συμπεριφοράς σε όρους ακρίβειας και ταχύτητας σύγκλισης. Το σημείο αυτό αναλύεται περαιτέρω σε μία θεωρητική σύγκριση του στοιχείου με άλλα στοιχεία που έχουν προταθεί στη βιβλιογραφία

Restaurierung antiker Tempel: Experimentelle Untersuchungen zum Ausziehverhalten von Verankerungen im Marmor

In restoration works of antique Greek temples individual marble blocks are connected together to form a single element, e.g. an architrave. Due to the demand of reversibility of the intervention, this is done in the Acropolis of Athens by means of titanium threaded bars that are inserted in the marble, in predrilled holes filled with cement mortar. This way of restoration corresponds to a partial rehabilitation of the architraves. This paper presents experimental investigations on the pull-out behaviour of such anchors. The tests are performed in specially designed equipment. Failure takes place for all tests in the interface between the mortar and the marble. It has been shown that the form of the thread influences considerably the carrying capacity. Possible limit states are introduced

Comparison of multi-sphere and superquadric particle representation for modelling shearing and flow characteristics of granular assemblies

In the current study, complex-shaped particles are simulated with the Discrete Element Method (DEM) using two different approaches, namely Multi-spheres (MS) and Superquadrics (SQ). Both methods have been used by researchers to represent the shape of real particles. However, despite the growing popularity of utilizing MS and SQ particles in DEM simulations, few insights have been given on the comparison of the macro scale characteristics arising from the two methods. In this respect, initially the characteristics of the two shape representation methods are evaluated in a direct shear test simulation. The results suggest that controlling the sharpness of the edges for SQ particles can lead to a good agreement with the results of MS particles. This way, a set of SQ and MS particles, which are numerically calibrated in the shear tester, are obtained. Furthermore, the macro-scale responses of the numerically calibrated particles are assessed during a slow shearing scenario, which is achieved through simulating quasi-static flow of the particles from a flat-bottom silo. The results for mass discharge, flow profile and wall pressure show a good quantitative agreement. These findings suggest that the numerically calibrated MS and SQ particles in the shear tester can provide similar bulk-scale flow properties. Moreover, the results highlight that surface bumpiness for MS particles and corner sharpness for SQ particles change the characteristics of particles and play a significant role in the shear strength of the material composed of these particles

Comparison of multi-sphere and superquadric particle representation for modelling shearing and flow characteristics of granular assemblies

In the current study, complex-shaped particles are simulated with the Discrete Element Method (DEM) using two different approaches, namely Multi-spheres (MS) and Superquadrics (SQ). Both methods have been used by researchers to represent the shape of real particles. However, despite the growing popularity of utilizing MS and SQ particles in DEM simulations, few insights have been given on the comparison of the macro scale characteristics arising from the two methods. In this respect, initially the characteristics of the two shape representation methods are evaluated in a direct shear test simulation. The results suggest that controlling the sharpness of the edges for SQ particles can lead to a good agreement with the results of MS particles. This way, a set of SQ and MS particles, which are numerically calibrated in the shear tester, are obtained. Furthermore, the macro-scale responses of the numerically calibrated particles are assessed during a slow shearing scenario, which is achieved through simulating quasi-static flow of the particles from a flat-bottom silo. The results for mass discharge, flow profile and wall pressure show a good quantitative agreement. These findings suggest that the numerically calibrated MS and SQ particles in the shear tester can provide similar bulk-scale flow properties. Moreover, the results highlight that surface bumpiness for MS particles and corner sharpness for SQ particles change the characteristics of particles and play a significant role in the shear strength of the material composed of these particles