Análise não linear de meios parcialmente frágeis via abordagem global-local do Método dos Elementos Finitos Generalizados
Anelize Borges Monteiro
Doctoral dissertation - 2019
Abstract (in Portuguese)
O Método dos Elementos Finitos Generalizados (MEFG) foi desenvolvido com o intuito de superar algumas limitações inerentes ao Método dos Elementos Finitos(MEF), relacionadas, por exemplo, à descrição do comportamento de fenômenos que envolvem mudanças na geometria, como devido à propagação de defeitos, presença de grandes deformações ou ainda na descrição de elevados gradientes das variáveis de estado. Em síntese, no MEFG há o enriquecimento do espaço da solução polinomial de MEF com informações conhecidas a priori tendo como base o conceito da Partição da Unidade (PU). Certos obstáculos da análise não linear podem ser amenizados com o emprego do MEFG e as frentes de dano e de plasticidade podem ser representadas com precisão. Dentro deste contexto, especialmente para problemas com a identificação de fenômenos localizados, foi proposta a abordagem global-local para o MEFG (MEFG global-local). O sucesso de sua aplicação para problemas da Mecânica da Fratura Linear Elástica já se encontra comprovado, porém sua extensão para a simulação do colapso de estruturas constituídas de materiais parcialmente frágeis ainda é um campo vasto a ser pesquisado. Neste trabalho, é proposta uma estratégia baseada na abordagem global-local do Método dos Elementos Finitos Generalizados para descrever o processo de deterioração de meios parcialmente frágeis dentro do contexto da Mecânica do Dano Contínuo. A solução numérica usada para enriquecer o problema global, representado por uma malha grosseira, é obtida através de análise fisicamente não linear realizada somente na região local onde ocorre a propagação do dano, representada por modelos constitutivos adequados. Com a descrição da região danificada incorporada ao problema global, por intermédio das funções de enriquecimento global-local, e a obtenção do estado de danificação mapeado a partir do modelo local, procede-se com a análise da região global. Exemplos numéricos bidimensionais são apresentados com o objetivo de ilustrar e avaliar o desempenho da abordagem proposta.
Estratégia multiescala para descrição micromórfica do contínuo a partir do contínuo clássico
Leandro Lopes da Silva
Doctoral dissertation - 2019
Abstract not available.
Estratégias baseadas na participação da unidade para simulação do comportamento de meios parcialmente frágeis
Débora Coelho Cordeiro Pinheiro
Doctoral dissertation - 2019
Abstract (in Portuguese)
Nos Métodos da Partição da Unidade a aproximação é construída com base em funções de Partição da Unidade (PU) enriquecidas pela sua multiplicação por funções especialmente escolhidas para o tipo de solução a ser descrita. O emprego de uma base extrínseca adicional tem por objetivo o aumento da consistência da aproximação ou melhora da aproximação com base na inclusão de funções que contemplem aspectos da solução do problema conhecidos a priori. O enriquecimento extrínseco é uma das principais vantagens dos métodos ditos da Partição da Unidade e sua eficácia está ligada a escolha adequada das funções de enriquecimento. Para algumas classes de problemas, a construção de funções de enriquecimento analíticas adequadas pode não ser possível. Neste contexto, surge um procedimento para construção de funções de enriquecimento para métodos que empregam a PU, a chamada abordagem global-local aplicada ao GFEM. Na tese aqui proposta, a solução numérica usada para enriquecer o problema global será obtida via Métodos sem Malha. Espera-se que o fenômeno local seja melhor descrito pelas funções de MM enquanto que o comportamento global continuará sendo descrito pelo GFEM. Este projeto de tese está inserido no contexto geral da análise não-linear de meios parcialmente frágeis. Especificamente, no trabalho aqui enunciado, visa-se a aplicação de uma abordagem global-local associada a Métodos Sem Malha na plataforma computacional INSANE (Interactive Structural Analysis Enviroment). Este trabalho será construído a partir de recursos já disponibilizados na plataforma tais como o framework de modelos constitutivos, as implementações de métodos sem malha e da abordagem global-local via GFEM, entre outros.
Failure analysis of quasi-brittle media using the micropolar continuum theory, elastic-degrading constitutive models, and smoothed point interpolation methods
Doctoral dissertation - 2018
The present thesis address the issue of localization (or discontinuous failure) in quasibrittle materials modelled as elastic-degrading media, using two different regularization strategies, applied individually as well as in a combined form: a regularization at the formulation level with the micropolar continuum theory, and a regularization at the numerical level using smoothed point interpolation meshfree methods. In order to allow the representation of quasi-brittle media with the micropolar continuum model, a unified monodissipative formulation for elastic degradation in micropolar media, defined in terms of secant tensors, loading functions and degradation rules, has been proposed, also deriving a number of scalar damage models within its general scheme. A peculiar compact representation for micropolar media has been introduced, in order to guarantee a formal compatibility between classic and micropolar constitutive models. Taking advantage of this compatibility, the micropolar models have been implemented within an existing object-oriented constitutive models framework originally conceived for classic media, characterized by its independence on the underlying numerical method and analysis model adopted during an analysis. Well-known concepts of acceleration waves propagation, such as the Maxwell compatibility condition and the Fresnel–Hadamard propagation condition, have been derived for the proposed micropolar formulation, in order to obtain a proper localization indicator as a both analytical and numerical tool for the evaluation of the regularization effects induced by the micropolar material parameters. Existent smoothed point interpolation methods, originally developed for classic elasticity and elasto-plasticity, have been extended to the case of elastic degradation in classic media. The peculiar weakened-weak form which they are based on, has been also extended to the micropolar continuum, considering both elasticity and elastic degradation. These methods have been implemented within the same object-oriented project of the micropolar constitutive models framework. A number of simulations regarding problems of numerical and induced localization in damage models, allowed to point out the regularization effects of the micropolar theory in finite element analyses, as well as the regularization effects of smoothed point interpolation methods in classic elastic-degrading models. Both these strategies were capable to individually regularize the behaviour of a number of analyses. Furthermore, their combination allowed to improve the results in the cases where the use of just one of them wasn’t sufficient. The same results were obtained with another set of simulations performed using two different real experimental tests as a basis for the discrete models. In this case, beside the regularization of material instabilities, is was also possible to observe a certain capability of the smoothed point interpolation methods to provide mesh-objective results during the analyses.
Crack propagation modeling in plane structures using two-scale Generalized/Extended Finite Element Method
Doctoral dissertation - 2017
Finite Element Method (FEM) has been widely used for the numerical modeling of structural/mechanical problems. Use of computer-based FEM programs was greatly facilitated with the development of pre- and post-processors rich interactive graphics capabilities, allowing users with basic knowledge of geometry to easily work with them. However, modeling of discontinuous fields with a standard finite element approximation presents challenges like restrictions on the finite element mesh to align with the discontinuity and the need for remeshing as the discontinuity evolves. The generalized or extended FEM (G/XFEM) was proposed as a numerical method to solve some of these challenges. The G/XFEM method enriches the standard finite element shape functions locally with enrichment functions which are based on the physics associated with the problem.
The goal of this thesis is to fracture modeling in thin-walled structure, specifically Plate structures, by extending the available capabilities of the G/XFEM method implemented in INSANE (INteractive Structural ANalysis Environment) in-house code, a computational environment developed by the Department of Structural Engineering (DEEs) at the Federal University of Minas Gerais (UFMG), which has been implemented using Object Oriented Programming (OOP). A stable version of G/XFEM is implemented to have a well-conditioning systems of equations. Then, the crack propagation strategy is applied to plane stress/strain and Reissner-Mindlin problems using classical and two-scale G/XFEM. These whole implementations and design are explained in detail and their robustnesses and accuracies are examined by solving various structural problems
Análise de degradação material, bifurcação e transição entre descontinuidades fracas e fortes através do Método dos Elementos de Contorno
Rodrigo Guerra Peixoto
Doctoral dissertation - 2016
The implicit formulation of the boundary element method is applied to bidimensional problems of material failure involving, sequentially, inelastic dissipation with softening in continuous media, bifurcation and transition between weak and strong discontinuities. The bifurcation condition is defined by the singularity of the localization tensor, also known, for historical reasons, as acoustic tensor. The weak discontinuities are associated to strain localization bands of finite width, which become increasingly narrow until to collapse in a surface with discontinuous displacement field, called strong discontinuity surface. Continuum constitutive models are adopted to represent the material behaviour in all of these steps, taking into account the adaptations that come from the strong discontinuity analysis for the post-bifurcation phases. The methodology is generic enough to treat any type of material instability and, according with the constitutive model adopted, the discontinuities may represent slip lines in geomechanics, shear bands in ductile materials or cracks in brittle (or quasi-brittle) materials. However, in this thesis, only the last case was considered, from the adoption of an isotropic damage model. The crack propagation across the solid domain is done by an automatic cells generation algorithm and, in this context, the fracture process zone in the crack tip became totally represented by the cells in the continuum damage regime and the cells with weak discontinuities.
Análise não-linear de estruturas de concreto por meio do Método Element Free Galerkin
Ramon Pereira da Silva
Doctoral dissertation - 2012
Softening behavior materials such as concrete, rocks and geomaterials, are initially modeled as a continuum, elastic, isotropic and homogeneous medium. However, this class of materials is inherently heterogeneous. Nonetheless, as the loads are applied, and the deformations thereof,such materials no longer exhibit the same initial behavior. The numerical simulation of such materials, in particular performing a physically nonlinear Finite Element Method (FEM) analysis, often leads to numerically induced localization problems. Furthermore, a reasonable accurate FEM discretization usually restricts the material’s randomspatial characteristics to the geometry of the finite elements employed. Also, taking into account, for instance, material discontinuities, usually requires expensive remeshing operations to track the cracking path. In order to overcome such difficulties, much work has been devoted into the development of constitutive modelling, where some parameter associated to the finite element’s geometric dimensions introduced into the formulation. This, however, renders an artificial modelling, which is physically inconsistent. One of the contributions of this Thesis was presenting a computational implementation of a meshless method while reusing the maximum possible legacy code INSANE, a software platform originally developed for the FEM. Another contribution was a novel form of calculating the predictor and corrector incremental loading factor used in the nonlinear solver, in which the nodal parameters associated to theMLS approximation are used instead of the nodal displacements. The numerical experiments performed throughtout this work suggest that when performing a physically nonlinear analysis using the EFG, one should take the same caution measures usually taken when using the FEM in the same circunstances. Also, it was detected that, from all of the possible parameters necessary to the EFG, the choices of the size of the domain of inuence, the numerical integration scheme and the polinomialbasis used, are fundamental to performing a physically nonlinear analysis.
Formulação multipotencial para modelos de degradação elástica: unificação teórica, proposta de novo modelo, implementação computacional e modelagem de estruturas de concreto
Samuel Silva Penna
Doctoral dissertation - 2011
This thesis presents a theoretical and computational framework for constitutive models based on elastic degradation. Classical models to deal with material’s media degradation are addressed in the context of the theoretical and computational proposal. In addition, smeared cracking model’s are reformulated, considering multiple uncoupled loading functions and a generalized degradation rule. To illustrate the potentiality of the created theoretical and computational framework, some damage models, founded in the literature, are implemented as well as a classical plasticity model. Also is proposed a new damage model with multiple loading functions. The created computational system takes advantage of the object-oriented programming paradigm, enabling to implement the proposal unified theoretical framework, independently of the applied numerical method. However, only the Finite Element Method (FEM) is used in the validation of this unified theory and the constitutive models inserted on it. Several application examples are presented, in order to illustrate the modeling possibilities provided by the constitutive models library gathered in this work. The new proposed damage model is validated by examples that compare their results with experimental results or obtained with other models, available in the literature.
Formulações de modelos constitutivos de microplanos para contínuos generalizados
Jamile Salim Fuina
Doctoral dissertation - 2009
This work describes the non-linear analysis of the quasi-brittle media through the Finite Elements Method, targeting to define appropriate kinematic and static descriptions to these medias.
The limitations of the classical continuum theory, as well as those of the local constitutive models, on the representation of strain localization problems, are pointed out. In addition, are proposed thermodynamically consistent formulations that gather the advantages of the Microplanes model for considering the material’s anisotropic behavior together with the Generalized Continuums, that have intrinsic characteristic lengths, being able to describe materials which need to have its microstructure highlighted for the understanding of the structural behavior.
Initially, the microplane constitutive model is formulated for the Cosserat continuum and, in one second phase, a refinement of the proposed model is presented, with the use of the microstretch continuum.
The implementations of the proposed constitutive model are discussed, as well as of those taken as reference, and also all the necessary tools to the complete solution of the nonlinear problem. These implementations are included in the numerical core of the INSANE computing system, a software developed at the Structures Engineering Department of UFMG, that uses the object-oriented programming approach.
Numerical simulations are presented. The analysis of the results is followed by a discussion of the adequacy of classic theories and proposed models.