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.