Solution methods for failure analysis of massive structural elements : doctoral thesis

Stanić, Andjelka (author), Brank, Boštjan (mentor), Ibrahimbegović, Adnan (comentor)

The thesis studies: (i) the methods for failure analysis of solids and structures, and (ii) the embedded strong discontinuity finite elements for modelling material failures in quasi brittle 2d solids. As for the failure analysis, the consistently linearized path-following method with quadratic constraint equation is first presented and studied in detail. The derived path-following method can be applied in the nonlinear finite element analysis of solids and structures in order to compute a highly nonlinear solution path. However, when analysing the nonlinear problems with the localized material failures (i.e. material softening), standard path-following methods can fail. For this reason we derived new versions of the path-following method, with other constraint functions, more suited for problems that take into account localized material failures. One version is based on adaptive one-degree-of-freedom constraint equation, which proved to be relatively successful in analysing problems with the material softening that are modelled by the embedded-discontinuity finite elements. The other versions are based on controlling incremental plastic dissipation or plastic work in an inelastic structure. The dissipation due to crack opening and propagation, computed by e.g. embedded discontinuity finite elements, is taken into account. The advantages and disadvantages of the presented path-following methods with different constraint equations are discussed and illustrated on a set of numerical examples. As for the modelling material failures in quasi brittle 2d solids (e.g. concrete), several embedded strong discontinuity finite element formulations are derived and studied. The considered formulations are based either on: (a) classical displacement-based isoparametric quadrilateral finite element or (b) on quadrilateral finite element enhanced with incompatible displacements. In order to describe a crack formation and opening, the element kinematics is enhanced by four basic separation modes and related kinematic parameters. The interpolation functions that describe enhanced kinematics have a jump in displacements along the crack. Two possibilities were studied for deriving the operators in the local equilibrium equations that are responsible for relating the bulk stresses with the tractions in the crack. For the crack embedment, the major-principle-stress criterion was used, which is suitable for the quasi brittle materials. The normal and tangential cohesion tractions in the crack are described by two uncoupled, non-associative damage-softening constitutive relations. A new crack tracing algorithm is proposed for computation of crack propagation through the mesh. It allows for crack formation in several elements in a single solution increment. Results of a set of numerical examples are provided in order to assess the performance of derived embedded strong discontinuity quadrilateral finite element formulations, the crack tracing algorithm, and the solution methods.

• Language: English
• Keywords: building environment, civil engineering, thesis, finite element method, failure analysis, path-following method, localized failure, embedded discontinuity
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: [IA. Stanić]
• Year: 2017
• PID: 20.500.12556/RUL-99244
• UDC: 519.876.5:624.012:624.07(043)
• COBISS.SI-ID: 8240993
• Publication date in RUL: 09.01.2018

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.
• Licensing start date: 09.01.2018

Secondary language

• Language: Slovenian
• Title: Metode za porušno analizo masivnih konstrukcijskih elementov : doktorska disertacija

Abstract

Doktorska disertacija obravnava: (i) metode za porušno analizo trdnih teles in konstrukcij, ter (ii) končne elemente z vgrajeno močno nezveznostjo za modeliranje materialne porušitve v kvazi krhkih 2d trdnih telesih. Za porušno analizo smo najprej preučili konsistentno linearizirano metodo sledenja ravnotežne poti s kvadratno vezno enačbo (metoda krožnega loka). Metoda omogoča izračun analize nelinearnih modelov, ki imajo izrazito nelinearno ravnotežno pot. Kljub temu standardne metode sledenja poti lahko odpovedo, kadar analiziramo nelinearne probleme z lokalizirano materialno porušitvijo (mehčanje materiala). Zato smo izpeljali nove različice metode sledenja poti z drugimi veznimi enačbami, ki so bolj primerne za probleme z lokalizirano porušitvijo materiala. Ena različica temelji na adaptivni vezni enačbi, pri kateri vodimo izbrano prostostno stopnjo. Izkazalo se je, da je metoda relativno uspešna pri analizi problemov z materialnim mehčanjem, ki so modelirani s končnimi elementi z vgrajeno nezveznostjo. Druge različice temeljijo na kontroli plastične disipacije ali plastičnega dela v neelastičnem trdnem telesu ali konstrukciji. Upoštevana je tudi disipacija zaradi širjenja razpok v elementih z vgrajeno nezveznostjo. Prednosti in slabosti predstavljenih metod sledenja ravnotežnih poti z različnimi veznimi enačbami so predstavljeni na številnih numeričnih primerih. Za modeliranje porušitve materiala v kvazi krhkih 2d trdnih telesih (npr. betonskih) smo izpeljali različne formulacije končnih elementov z vgrajeno močno nezveznostjo v pomikih. Obravnavane formulacije temeljijo bodisi (a) na klasičnem izoparametričnem štirikotnem končnem elementu bodisi (b) na štirikotnem končnem elementu, ki je izboljšan z nekompatibilnimi oblikami za pomike. Nastanek in širjenje razpoke opišemo tako, da kinematiko v elementu dopolnimo s štirimi osnovnimi oblikami širjenja razpoke in pripadajočimi kinematičnimi parametri. Interpolacijske funkcije, ki opisujejo izboljšano kinematiko, zajemajo skoke v pomikih vzdolž razpoke. Obravnavali smo dva načina izpeljave operatorjev, ki nastopajo v lokalni ravnotežni enačbi in povezujejo napetosti v končnem elementu z napetostmi na vgrajeni nezveznosti. Kriterij za vstavitev nezveznosti (razpoke) temelji na kriteriju največje glavne napetosti in je primeren za krhke materiale. Normalne in tangentne kohezijske napetosti v razpoki opišemo z dvema nepovezanima, poškodbenima konstitutivnima zakonoma za mehčanje. Predlagamo novi algoritem za sledenje razpoki za izračun širjenja razpoke v mreži končnih elementov. Algoritem omogoča formacijo razpok v več končnih elementih v enem obtežnem koraku. Izračunali smo številne numerične primere, da bi ocenili delovanje izpeljanih formulacij štirikotnih končnih elementov z vgrajeno nezveznostjo in algoritma za sledenje razpoki kot tudi delovanje metod sledenja ravnotežnih poti.

• Keywords: méthode des éléments finis, analyse à rupture, méthode de continuation, rupture localisée, discontinuité forte, grajeno okolje, gradbeništvo, disertacije, metoda končnih elementov, porušna analiza, metoda sledenja ravnotežne poti, lokalizirana porušitev, vgrajena nezveznost