Samuel Silva Penna

A computational framework for a two-scale generalized/extended finite element method: Generic imposition of boundary conditions

Purpose This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution. Design/methodology/approach The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized. Findings The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated. Originality/value This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

A Generalized Elasto-Plastic Micro-Polar Constitutive Model

This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.

Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach

Abstract This work presents an object-oriented implementation of the G/XFEM to model the crack nucleation and propagation in structures made of either linear or nonlinear materials. A discontinuous function along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly meshing its surfaces. Different approach are explained in detail that are used to capture the crack nucleation within the model and also determine the crack propagation path for various problems. Stress intensity factor and singularity of the localization tensor (which provides the classical strain localization condition) can be used to determine the crack propagation direction for linear elastic materials and nonlinear material models, respectively. For nonlinear material model, the cohesive forces acting on the crack plane are simulated in the enrichment process by incorporating a discrete constitutive model. Several algorithms and strategies have been implemented, within an object-oriented framework in Java, called INSANE. This implementation will be presented in detail by solving different two-dimensional problems, for both linear and nonlinear material models, in order to show the robustness and accuracy of the proposed method. The numerical results are compared with the reference solutions from the analytical, numerical or experimental results, where applicable.

A computational framework for G/XFEM material nonlinear analysis

Abstract The Generalized/eXtended Finite Element Method (G/XFEM) has been developed with the purpose of overcoming some limitations inherent to the Finite Element Method (FEM). Different kinds of functions can be used to enrich the original FEM approximation, building a solution specially tailored to problem. Certain obstacles related to the nonlinear analysis can be mitigated with the use of such strategy and the damage and plasticity fronts can be precisely represented. A FEM computational environment has been previously enclosed the G/XFEM formulation to linear analysis with minimum impact in the code structure and with requirements for extensibility and robustness. An expansion of the G/XFEM implementation to physically nonlinear analysis under the approach of an Unified Framework for constitutive models based on elastic degradation is firstly presented here. The flexibility of the proposed framework is illustrated by several examples with different constitutive models, enrichment functions and analysis models.

Non-local constitutive modelling by the boundary element method

Rodrigo G. Peixoto Samuel S. Penna Gabriel O. Ribeiro Roque L. S. Pitangueira rodrigo.peixoto@dees.ufmg.br spenna@dees.ufmg.br gabriel@dees.ufmg.br roque@dees.ufmg.br Dep. de Eng. de Estruturas, Escola de Engenharia, Universidade Federal de Minas Gerais Avenida Antônio Carlos, 6627, CEP: 31270-901, Belo Horizonte, Minas Gerais, Brazil Abstract. The conventional (local) constitutive modelling of materials exhibiting strain softening behaviour is suceptive to a spurious mesh dependence caused by numerically induced strain localization. Also, for very refined meshes, numerical instabilities may be verified, mainly if the simulations are performed by the boundary element method. An alternative to overcome such difficulties is the adoption of the so called non-local constitutive models. In this approach, some internal variables of the constitutive model in a single point are averaged considering its values of the neighbouring points. In this paper, the implicit formulation of the boundary element method for physically non linear problems is used with non-local isotropic damage models. It is shown that the analysis become more stable in comparison to the case of a local application of the same models and that the results recover the desired objectiveness to mesh refinement.

Micropolar formulation for regularization of material instabilities in scalar damage models

Abstract. Strain localization is an important issue in the numerical modelling of the physically non-linear behaviour of quasi-brittle materials. Scalar damage models, and the wider class of elastic-degrading models, commonly used for the representation of quasi-brittle media, may suffer for material instabilities due to their strain-softening behaviour. When analyzed numerically with the finite element method, a set of pathological phenomena may appear, hence affecting the quality of the simulations. The micropolar continuum formulation has been showed, in the past, to be a valid alternative for the mitigation of localization issues in elasto-plastic models and, recently, also in the case of scalar damage models. This papers aims to investigate the regularization properties of the micropolar theory when applied to a scalar damage model, and to evaluate the effects of the micropolar material parameters (the Cosserat’s shear modulus and the internal bending length) on the onset of material instabilities. Analytical investigations are performed, in order to evaluate the onset of material instabilities with a proper localization indicator. Numerical simulations with the finite element method are also provided, in order to show the regularization properties of the adopted formulation.

Discontinuous failure in micropolar elastic-degrading models

The present paper investigates the phenomenon of discontinuous failure (or localization) in elastic-degrading micropolar media. A recently proposed unified formulation for elastic degradation in micropolar media, defined in terms of secant tensors, loading functions and degradation rules, is used as a starting point for the localization analysis. Well-known concepts on acceleration waves propagation, such as the Maxwell compatibility condition and the Fresnel–Hadamard propagation condition, are derived for the considered material model in order to obtain a proper failure indicator. Peculiar problems are investigated analytically in details, in order to evaluate the effects on the onset of localization of two of the additional material parameters of the micropolar continuum, the Cosserat’s shear modulus and the internal bending length. Numerical simulations with a finite element model are also presented, in order to show the regularization behaviour of the micropolar formulation on the pathological effects due to the localization phenomenon.

Sistema Gráfico Interativo para Análise de Nucleação e Propagação de Trincas

O objetivo desta dissertacao de mestrado e a implementacao computacional de um sistema graco interativo que integra pre-processador, modelos constitutivos, solucionadores de equacoes nao lineares e pos-processador para analise de nucleacao e propagacao de trincas em meios bidimensionais parcialmente frageis. A analise sicamente nao linear se inicia empregando-se o Metodo dos Elementos Finitos Padrao (MEF), atraves do qual a degradacao inicial do meio e simulada de forma distribuida por meio de metodos constitutivos baseados em degradacao elastica. O estagio limiar de nucleacao de ssuras e indicado pela singularidade do tensor acustico, caracteristica que fornece a condicao classica de localizacao de deformacoes. A presenca de trincas e simulada atraves de metodo cinematico que incorpora as descontinuidades por meio de interpolacoes enriquecidas, com base no Metodo dos Elementos Finitos Generalizados (MEFG), ao passo que a propagacao destas trincas e tambem indicada pela singularidade do tensor acustico. A relacao entre tensoes e deslocamentos no caminho da trinca e baseada em forcas coesivas atuantes no plano da trinca. Esta combinacao de metodos constitutivo e cinematico apresenta a vantagem da nao necessidade de denicao previa do caminho da trinca ou de redenicao da malha durante o processamento. Ao nal da analise, o fenomeno de nucleacao eos efeitos da presencaa de trincas, bem como suas propagacoes, podem ser visualizados utilizando os recursos do pos-processador. As implementacoes foram realizadas na plataforma INSANE (INteractive Structural ANalysis Environment)

Elementos finitos de casca do sistema computacional INSANE

This paper presents the shell finite elements of the computer system INSANE (INteractive Structural ANalysis Environment): four-node rectangular and threenode triangular, obtained by combining membrane and bending efforts, based on the Theory of Kirchhoff; a quadrilateral of four, eight and nine nodes that combines membrane, bending and shear efforts, according to the Reissner-Mindlin Theory. After summarizing the characteristics of the elements, the paper presents results of three convergence studies and two practical applications: an arch dam and a conicalcylindrical reservoir. The results are compared with analytical solutions and those obtained with the shell finite element of SAP2000.