A new approach for physically nonlinear analysis of continuum damage mechanics problems using the generalized/extended finite element method with global-local enrichment.
H.A.S. Monteiro, L. Novelli, G.M. Fonseca, R.L.S. Pitangueira, F.B. Barros
Engineering Analysis With Boundary Elements , v. 113 , p. 277-295 , 2020
The Generalized/Extended Finite Element Method (G/XFEM) is a numerical technique suitable to solve a wide range of continuum mechanics problems. It applies hierarchical nodal enrichment strategies within the Finite Element Method framework, allowing more flexibility in the numerical solution of boundary value problems (BVP) and being a powerful mesh-reduced method that takes advantage of the state-of-art of the standard FEM. One of the enrichment mechanisms is the so-called global-local enrichment (G/XFEMGL), in which the solution of a refined local BVP generates enrichment functions for the global domain. In this context, this work presents a new two-scale nonlinear strategy, associated with the G/XFEMGL, able to solve the material nonlinear analysis of continuum damage mechanics problems, in which quasi-brittle media degrade and soften, using a versatile mesh refinement strategy. A comprehensive description of the proposed strategy is registered and the aforementioned computational technique is validated throughout a set of plane stress numerical experiments that employ smeared crack constitutive model formulations, with well-known stress-strain laws. The results indicate that the implemented methodology could be used to solve a reasonable range of problems with considerable flexibility.
Damage propagation using novel G/XFEM strategies: computational aspects and numerical investigations
Anderson Renato Vobornik Wolenski, Anelize Borges Monteiro, Samuel Silva Penna, Roque Luiz da Silva Pitangueira, Felício Bruzzi Barros
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 42 , 2020
The nonlinear modelling of concrete structures demands strain-softening models that correctly represent the nucleation and propagation of damage. The typical concentration of such degrading phenomena in limited parts of the structure results in the strain localization that can be highly affected by the numerical algorithm used to solve the softening behaviour in concrete material. Finite Element discretization based on models from the continuum damage mechanics has not been able to overcome the numerical localization induced, anticipating the failure of the analysed problem. The Generalized/eXtended Finite Element Method is investigated here as an alternative to the standard Finite Element Method aiming to efficiently simulate the concrete strain-softening phenomenon. The enrichment strategy of the G/XFEM is used to obtain the nonlinear structural response using coarse meshes combined with different constitutive models from the continuum damage mechanics. Experimental results available in the literature are numerically reproduced and compared with equivalent approaches using FEM. Pathological behaviours that affect the quality of the results are evaluated. The possibility of using several combinations of different numerical methods and constitutive models is ensured by a framework for computational mechanics that encloses the G/XFEM implementation.
Elastoplastic constitutive modeling for concrete: a theoretical and computational approach
Danilo Bento Oliveira, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Revista Ibracon de Estruturas e Materiais , v. 13 , p. 171-182 , 2020
This article presents a study of the plasticity model applicability to concrete in a theoretical framework that generalizes the formulation of constitutive models for physically nonlinear analysis of structures. In this sense, the theoretical framework for the computational implementation of the plasticity mathematical theory is described, detailing the models formulations capable to describe the inelastic behavior of concrete. The loading surfaces associated to Drucker Prager and Ottosen criterion are highlighted. Furthermore, the Cutting Plane return mapping algorithm, necessary to the integration of constitutive relations that govern the behavior of the material in the context of computational plasticity, is described. Finally, numerical simulations are presented, such as the direct tension loading and three-point bending tests. The results of these simulations are compared with those from the literature to verify the model stability and accuracy.
Numerical technique for strain localization analysis considering a Cartesian parameterization
Lucas A. F. Fioresi, Roque L. S. Pitangueira, Samuel S. Penna
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 42 , 2020
This paper presents a numerical technique for strain localization analysis in nonlinear material models considering a Cartesian parameterization. As a result of material’s natural heterogeneity, degradation often occurs in a small and weaker portion of the body. This concentration of irreversible phenomena is commonly referred as strain localization. From a kinematic standpoint, strain localization is associated with weak discontinuities that occur during physically nonlinear structural analysis. In a numerical simulation, it is linked with the loss of ellipticity of differential equations governing the boundary value problem. Singularity of the acoustic tensor is considered the classical condition for strain localization. It can be approached via analytical formulations or numerical techniques. Such a parameterization was utilized to define the normal direction to the discontinuity surface. Localization analysis was performed at material level after the convergence of each step in a set of nonlinear analyses. After the simulations, valuable information is available to regularization methods.
2-D fracture mechanics problems by SGFEM
Thaianne S. de Oliveira, Felício B. Barros, Gabriela M. Fonseca, Roque L.S. Pitangueira
Engineering Analysis With Boundary Elements , v. 108 , p. 279-294 , 2019
In this paper, an extensive investigation is done on Stable Generalized Finite Element Method (SGFEM) performance through the analysis of 2-D fracture mechanics problems. Condition number, Stress Intensity Factors (SIFs), global and local measures of the energy norm are used to study SGFEM conditioning and accuracy. Computational time is also briefly discussed. The method is compared with the standard Generalized/eXtended Finite Element Method (G/XFEM). Numerical experiments corroborate and complement the knowledge available in the literature so far, and demonstrate SGFEM accuracy in 2-D cracked problems. Modified Heaviside Functions, combined with other enrichment functions, are also studied in the simulations. A simple and yet generic implementation for SGFEM is described, under the Object Oriented strategy, in a open source software. The implementation can be used in 2-D and 3-D problems, and it allows to generalize the implementation of any type of enrichment function under the SGFEM approach.
A computational framework for the constitutive modeling of nonlinear micropolar media
Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 41 , 2019
Despite the large number of applications with micropolar models, the aspects of their implementation have been rarely addressed in the literature. In the present paper, a strategy for the computational modeling of micropolar media with elasto-plasticity and elastic degradation is investigated. The proposed strategy is based on the Object-Oriented Paradigm (OOP) and on the use of tensor objects. The presence of tensor objects inside the code allows to obtain a constitutive models framework that, with respect to existent implementations, is independent on both the adopted analysis model and numerical method. The OOP, with its properties of abstraction, inheritance, and polymorphism, leads to a framework highly modular and easy to expand. The theoretical basis is a compact tensorial representation for the micropolar equations that makes them formally identical to the ones of the classic continuum theory. This compatibility has been here extended to their computational expressions, making possible to use the same code structure for both the continuum models, taking advantage of existing implementations of classic constitutive models.
A non-local damage approach for the boundary element method
R.G. Peixoto, S.S. Penna, R.L.S. Pitangueira, G.O.Ribeiro
Applied Mathematical Modelling , v. 69 , p. 63-76 , 2019
The conventional (local) constitutive modelling of materials exhibiting strain softening behaviour is susceptive to a spurious mesh dependence caused by numerically induced strain localization. Also, for 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 these approaches, 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 in solid mechanics is used with a non-local isotropic damage model and a very simple averaging scheme, over internal cells, is introduced. It is shown that the analysis become more stable in comparison to the case of a local application of the same model and that the results recover the desired objectiveness to mesh refinement.
G-space theory and weakened-weak form for micropolar media: Application to smoothed point interpolation methods
Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Engineering Analysis with Boundary Elements , v. 101 , p. 318-329 , 2019
The concepts of G-space and weakened-weak form already available for the classic continuum model are extended to the case of the micropolar theory, in order to allow the use of smoothed point interpolation methods for the analysis of micropolar media. A new G-space, defined as a cartesian product of standard G-spaces, is introduced in order to represent both the displacement and the microrotation fields of a micropolar medium. Based on this G-space, a micropolar weakened-weak form is formulated, and the existence and uniqueness of its solution are proven.
A boundary element method formulation for quasi-brittle material fracture analysis using the continuum strong discontinuity approach
R. G. Peixoto, G. O. Ribeiro, R. L. S. Pitangueira
Engineering Fracture Mechanics , v. 202 , p. 47-74 , 2018
The implicit formulation of the boundary element method is applied to bi-dimensional 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. Weak discontinuities are related 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. To associate such steps to the fracture process in quasi-brittle materials, an isotropic damage constitutive model is used to represent the behaviour in all of them, considering the adaptations that come from the strong discontinuity analysis for the post-bifurcation steps. The crack propagation across the domain is done by an automatic cells generation algorithm and, in this context, the fracture process zone in the crack tip became totally represented.
A progressive cells activation algorithm for physically non-linear BEM analysis
Rodrigo G. Peixoto, Gabriel O. Ribeiro, Roque L. S. Pitangueira
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 40:112 , 2018
A drawback of the boundary element method (BEM) to analyse solid non-linear problems is the necessity to discretize, not only the boundaries, but also the domain in internal cells. Such discretization is required to evaluate the domain integrals involving the inelastic (initial) fields and represents a loss of one of the most remarkable features of the BEM, which is the reduction of the problem’s dimension by one order. However, only regions where the dissipative effects take place need to be divided in cells, allowing optimization of the non-linear solution algorithms. In this paper, one of these optimization attempts is present in which the cells are progressively activated, augmenting the corresponding matrices, as the inelastic region develop and grow. In addition, the implicit formulation of the BEM with a unified constitutive modelling framework is used in order that different material behaviours may be addressed by a single numerical structure. Three numerical examples are presented: two involving ductile material behaviour, modelled with the elastoplastic von Mises associative constitutive model, and another to simulate quasi-brittle behaviour by an isotropic damage constitutive model.
An overview of the numerical modeling and computer programming disciplines of an undergraduate Civil Engineering course and the Insane project experience
Humberto Alves da Silveira Monteiro, Roque Luiz da Silva Pitangueira
Mecánica Computacional , v. XXXVI. Number 32 , p. 1039-1048 , San Miguel de Tucumán, Argentina , 2018
The world witnesses the progressive advancement of computing, whether it is in the raising power of data processing and storage, in the enhancement of modeling tools or in the improvement of the capacity to exchange information and knowledge. Today science seems to be dependent on informatics, and because of its nature, the Engineering (or the Exact Sciences, in a more general way) shares this connection even more. A need for understanding some real phenomena and the relentless search for rules that explain the behavior of physical systems drive the modern engineer to develop proper computational mechanisms that could handle the analysis of complex (mathematical) problems. Therefore, the appropriate training of engineering students regarding programming and numerical methods skills should be considered if a society wants to fully use its technological resources. In that sense, this work shares a brief overview of the numerical modeling and computer programming disciplines of the undergraduate civil engineering course of the Federal University of Minas Gerais, Brazil, towards a basic diagnosis and a critical appraisal of the curriculum. Trying to fill some gaps in the academic formation process, the INSANE (INteractive Structural ANalysis Environment) project was created; an interactive environment of structural analysis conceived to be used as a didactic resource in undergraduate and graduate courses of engineering, as well as a platform of high-level scientific research on numerical methods. Throughout the years, INSANE has contributed to the training of many students, either enabling programming proficiency or in-depth learning of finite element method formulations.
Análisis global-local de medios lineales utilizando el Método de Elementos Finitos Generalizados
Humberto A. da Silveira Monteiro, Gabriela Marinho Fonseca, Larissa Novelli, Roque L. da Silva Pitangueira, Felício Bruzzi Barros
Mecánica Computacional , v. XXXVI. Number 32 , p. 1539-1368 , San Miguel de Tucumán, Argentina , 2018
The Generalized Finite Element Method (GFEM) is a relatively new numerical method, developed in the mid-1990s. By using concepts of its precursors, the GFEM applies strategies of some meshless formulations within the Finite Element Method (FEM) framework, allowing more flexibility for the numerical solution of boundary value problems (BVP), and being efficient, for example, in those problems that have some kind of discontinuity. This work presents the result of a computational implementation of an already known enrichment strategy: the global-local enrichment, in which the solution of a refined local BVP numerically generates enrichment functions for the global domain. A brief example of application of the technique for linear problems in plane state is presented. The work has been executed in the INSANE system (INteractive Structural ANalysis Environment), a free software developed in the Department of Structural Engineering of the Federal University of Minas Gerais, Brazil.
Crack propagation using the continuum strong discontinuity approach by the BEM: some numerical remarks
Tiago S. Mendonça, Rodrigo G. Peixoto, Gabriel O. Ribeiro
Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 40:520 , 2018
Some numerical remarks regarding the crack evolution in failure analysis by the BEM using cells with embedded strong discontinuities are addressed in this work. A comparative study between the generation of these cells at any iteration or only after a step convergence is firstly performed. Moreover, an analysis is carried out related to the cells size growth throughout the iterative-incremental process. As reference, some classical problems whose experimental results are available in the literature are used for the numerical analysis which is performed considering the implicit formulation of the boundary element method together with the continuum strong discontinuity approach. It was verified that the results are coincident for different numbers of steps considered in the simulations when cells are generated during any iteration, showing step size independence in this case, while the same is not true for the case of cells generated only after step convergence, in which a large number of steps are required for a good accuracy. Finally, it is shown that a small increase in cell size throughout the analysis contributes to the reduction in numerical processing time without significantly affecting the results accuracy.
Fracture analysis in plane structures with the two-scale G/XFEM method
Mohammad Malekan, Felicio B.Barros, Roque L.S.Pitangueira
International Journal of Solids and Structures , v. 155 , p. 65-80 , 2018
Generalized or extended finite element method (G/XFEM) uses enrichment functions that holds a priori knowledge about the problem solution. These enrichment functions are mostly limited to two-dimensional problems. A well-established solution for problems without any specific types of analytically derived enrichment functions is to use numerically-build functions in which they are called global-local enrichment functions. These functions are extracted from the solution of boundary value problems defined around the region of interest discretized by a fine mesh. Such solution is used to enrich the global solution space through the partition of unity framework of the G/XFEM. Here it is presented a two-scale/global-local G/XFEM approach to model crack propagation in plane stress/strain and Reissner–Mindlin plate problems. Discontinuous functions along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly represent its geometries. Under the linear elastic fracture mechanics approach, the stress intensity factor (obtained from a domain-based interaction energy integral) can be used to either determine the crack propagation direction or propagation status, i.e., the crack can start to propagate or not. The proposed approach is presented in detail and validated by solving several linear elastic fracture mechanics problems for both plane stress/strain and Reissner–Mindlin plate cases to demonstrate its the robustness and accuracy.
Nonlinear analysis of concrete structures using GFEM enrichment strategy with a microplane constitutive model
A. R. V. Wolenski, A. B. Monteiro, S. S. Penna, R. L. S. Pitangueira, F. B. Barros
Revista Ibracon de Estruturas e Materiais , v. 11, no. 3 , p. 523-534 , São Paulo , 2018
One of the most widespread methods to the nonlinear analysis of structures is the Finite Element Method (FEM). However, there are phenomena whose behavior is not satisfactorily simulated by the standard FEM and this fact has quickened the development of new strategies such as the Generalized Finite Element Method (GFEM), understood as a variation of the FEM. In parallel, nonlinear analysis of concrete structures requires the use of constitutive models that represents the nucleation and propagation of cracks. In this paper it is used an anisotropic constitutive model, based on the microplane theory, which is able to represent the behavior of concrete structures, together with the GFEM approach. These resources are incorporated on the INSANE system (INteractive Structural ANalysis Environment), used in the numerical simulations presented here to demonstrate the feasibility of using the GFEM enrichment strategy, in the nonlinear analysis of concrete structures, with validation made from comparisons with experimental results available in the literature.
Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method
Mohammad Malekan, Felício B. Barros
Computational Mechanics , v. 62, Issue 10 , p. 783–801 , 2018
Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner–Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.
Sistema gráfico interativo para ensino de análise estrutural através do Método dos Elementos Finitos
Renata Nicoliello Moreira Albuquerque, Roque Luiz da Silva Pitangueira
Revista de Ensino de Engenharia , v. 37 , p. 76-87 , 2018
This work refers to the expansion of INSANE (INteractive Structural Analysis Environment): a computational system for finite element method (FEM) structural analysis discrete models, in Java language and object-oriented programming (OOP). The expansion work consists in an interactive graphic application to assist the FEM teaching for structural engineering. A study of the diverse approaches for FEM in engineering courses is presented, identifying its generalities and the possibilities that INSANE offers to facilitate learning process. It is argued, then, available suggestions in literature for characterization of stages for the solution of FEM problems. It is an analysis seeking to identify key interactions required for display of the numerical nucleus computer system to the user, so that it can display information relating to the resolution of the MEF models, thereby facilitating the understanding of the theory. Such approach allows the graphical, interactive and didactic presentation of the processing of FEM models. The resources of the new graphical interface are presented through examples and the possibilities of enrichment of the learning process are shown.
Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models
Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
International Journal for Numerical Methods in Engineering , p. 1-27 , 2018
The nonlocal character embedded in the formulation of smoothed point interpolation methods is exploited, in order to regularize the behavior of the simulations of scalar damage problems affected by strain localization. The use of these methods is made possible by the extension of the weakened weak form that they are based on to the case of elastic‐degrading media, with specific focus on the scalar damage case. The provided numerical simulations emphasize the regularization effects of this class of meshfree methods and the improved mesh objectivity with respect to the standard finite element method. Different strategies for support node selection are considered, pointing out the role played by the size of the support domains regarding the regularization effects.
Strain localization analysis in material nonlinear models
Lucas A. F. Fioresi, Roque L. S. Pitangueira, Samuel S. Penna, Humberto A. S. Monteiro
Mecánica Computacional , v. XXXVI. Number 32 , p. 1527-1536 , San Miguel de Tucumán, Argentina , 2018
This paper presents a strain localization analysis in nonlinear models detached from constitutive models. The proposed implementation was performed on the INteractive Structural ANalysis Environment (INSANE) platform, an open source project developed by the Structural Engineering Department of the Federal University of Minas Gerais. Strain localization is associated with weak discontinuities and materials instabilities that occur during physically nonlinear structural analysis. Singularity of the acoustic tensor is considered the classical condition for strain localization and it can be calculated regardless of constitutive model selection. Localization analysis consists in searching for a unit vector which defines the direction at which the acoustic tensor becomes singular. This unit vector points towards the normal direction of the discontinuity surface in the body, which is created by the localization phenomenon. Localization analysis can be approached as a minimization problem of the acoustic tensor determinant. With parametrization techniques, it is possible to obtain the unit vector associated with the singularity. Strain localization analysis should be performed in each integration point (Gauss point), at each step of an incremental nonlinear analysis. At the end of localization analysis, one expects to detect points of material instabilities and use them as references for multiscale structural analysis.
Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach
Mohammad Malekan, Leandro L. Silva, Felicio B. Barros, Roque L. S. Pitangueira, Samuel S. Penna
Advances in Engineering Software , v. 115 , p. 168-193 , 2018
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 a two-scale generalized/extended finite element method: generic imposition of boundary conditions
Mohammad Malekan, Felicio Barros, Roque Luiz da Silva Pitangueira, Phillipe Daniel Alves, Samuel Silva Penna
Engineering Computations , v. 34, Issue 3 , p. 988-1019 , 2017
This paper presents a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having a 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 using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.
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 analysis 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.
The generalization done for boundary conditions is very important since 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 employed and the accuracy, robustness and computational efficiency are demonstrated.
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 since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problem simultaneously and solving plate problems using global-local G/XFEM is another contributions of this work.
A computational framework for constitutive modelling
Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Computers & Structures , v. 187 , p. 1-23 , 2017
The field of computational constitutive modelling for engineering applications is an active research tread in academia. New advanced models and formulations are constantly proposed. However, when dealing with implementation aspects, often the main concern is to provide a minimal environment to show a certain model and its applications, with implementations made from scratch. Though advanced, usually such implementations lack of generality and are well-suited for a certain numerical method while not compatible with other ones, making it difficult to reuse the code in other contexts. The Object-Oriented Paradigm (OOP) to programming have been widely applied in the last years for the realization of numerous academic numerical simulation softwares, due to its fundamental properties of abstraction, inheritance and polymorphism that allow the creation of programs well-suited for an easy collaboration between developers with expertise in different fields of engineering and mechanics. As showed in this paper, the same properties can be effectively extended also to the constitutive aspects of a model. The application of the OOP to the constitutive modelling of a wide range of materials of engineering interest is investigated, aiming to the creation of a computational framework for constitutive models that is fully independent on the other components of a code and easy to expand.
A computational framework for G/XFEM material nonlinear analysis
A.B. Monteiro, A.R.V. Wolenski, F.B. Barros, R.L.S. Pitangueira, S.S. Penna
Advances in Engineering Software , v. 114 , p. 380-393 , 2017
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.
An enhanced tensorial formulation for elastic degradation in micropolar continua
Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Applied Mathematical Modelling , v. 41 , p. 299-315 , 2017
In the past, a lot of applications of the micropolar (or Cosserat) continuum theory have been proposed, especially in the field of granular materials analysis and for strain localization problems in elasto-plasticity, due to its regularization properties. In order to make possible the application of the micropolar theory to different constitutive models and to extend its regularization properties also to damage models, in this work a general formulation for elastic degradation based on the micropolar theory is proposed. Such formulation is presented in a unified format, able to enclose different kinds of elasto-plastic, elastic-degrading and damage constitutive models. A peculiar tensor-based representation is introduced, in order to guarantee the conformity with analogous theories based on the classic continuum, in such a way as to make possible the application to the micropolar theory of theoretical and numerical resources already defined for the classic theory. Peculiar micropolar scalar damage models are also proposed, and derived within the new general formulation.
Discontinuous failure in micropolar elastic-degrading models
Lapo Gori, Samuel S. Penna, Roque L. da Silva Pitangueira
International Journal of Damage Mechanics , 2017
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.
High regularity partition of unity for structural physically non-linear analysis
D.C.C. Pinheiro, F.B. Barros, R.L.S. Pitangueira, S.S. Penna
Engineering Analysis with Boundary Elements , v. 83 , p. 43-54 , 2017
Meshfree techniques, such as hp-Clouds and Element Free Galerkin Methods, have been used as attractive alternatives to finite element method, due to the flexibility in constructing conforming approximations. These approximations can present high regularity, improving the description of the state variables used in physically non-linear problems. On the other hand, some drawbacks can be highlighted, as the lack of the Kronecker-delta property and numerical integration problems. These drawbacks can be overcome by using a Ck, k arbitrarily large, partition of unity (PoU) function, built over a finite element mesh, but with the approximate characteristic of the meshfree methods. Here, this procedure is for the first time investigated to simulate the non-linear behavior of structures with quasi-brittle materials. The smeared crack model is adopted and numerical results, obtained with different kinds of polynomial enrichments, are compared with the experimental results.
Imposition of Dirichlet boundary conditions in Element Free Galerkin Method through an object-oriented implementation
Samira Hosseini, Mohammad Malekan, Roque L. S. Pitangueira, Ramon P. Silva
Latin American Journal of Solids and Structures , v. 14, no. 6 , Rio de Janeiro , 2017
One of the main drawbacks of Element Free Galerkin (EFG) method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.
The Strong Discontinuity Approach as a limit case of strain localization in the implicit BEM formulation
R. G. Peixoto, G. O. Ribeiro, R. L. S. Pitangueira, S. S. Penna
Engineering Analysis with Boundary Elements , v. 80 , p. 127-141 , 2017
The Implicit Formulation of the Boundary Element Method (BEM) is used to deal with physically non-linear 2D-problems in solids. An isotropic damage constitutive model, equipped with a strain softening rule, is applied to increasingly narrow bandwidths, determined by mesh refinement, showing the typical post-peak mesh-dependence behaviour. The Continuum Strong Discontinuity Approach (CSDA), characterized by the introduction of discontinuous jumps in the displacement field together with an equilibrium verification (using continuous constitutive models) on the discontinuity line, is also applied to the implicit formulation of the BEM. By a simple numerical example, it is shown that, beyond the mesh independence, the CSDA results represent the limit case of a zero localization bandwidth. Moreover, to demonstrate the accuracy of the CSDA, other three examples involving concrete fracture are presented and the obtained results are compared with experimental or analytical data available in the literature.
A solution strategy for non-linear implicit BEM formulation using a unified constitutive modelling framework
R.G. Peixoto, F.E.S. Anacleto, G.O. Ribeiro, R.L.S. Pitangueira, S.S. Penna
Engineering Analysis with Boundary Elements , v. 64 , p. 295-310 , 2016
A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.
An object-oriented class organization for global-local Generalized Finite Element method
Malekan, Mohammad; Barros, Felício Bruzzi; Pitangueira, Roque Luiz da Silva; Alves, Phillipe D.
Latin American Journal of Solids and Structures , v. 13, No. 13 , p. 2529-2551 , Rio de Janeiro , 2016
This paper shows and discusses a generic implementation of the global-local analysis toward generalized finite element method (GFEMgl). This implementation, performed into an academic computational platform, follows the object-oriented approach presented by the authors in a previous work for the standard version of GFEM in which the shape functions of finite elements are hierarchically enriched by analytical functions, according to the problem behavior. In global-local GFEM, however, the enrichment functions are constructed numerically from the solution of a local problem. This strategy allows the use of a coarse mesh even when the problem produces complex stress distributions. On the other hand, a local problem is defined where the stress field presents high gradients and it is discretized using a large number of elements. The results of the local problem are used to enrich the global problem which improves the approximate solution. The great advantage is allowing a well-refined description of the local problem, when necessary, avoiding an overburden for the computation of the global solution. Details of the implementation are presented and important aspects of using this strategy are highlighted in the numerical examples.
A generalized elasto-plastic micro-polar constitutive model
Lapo Gori, Roque Luiz da Silva Pitangueira, Samuel Silva Penna, Jamile Salim Fuina
Applied Mechanics and Materials , v. 798 , p. 505-509 , 2015
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.
Experimental and finite element analysis of bond-slip in reinforced concrete
Wolenski, Anderson Renato Vobornik, Castro, Saulo Silvestre, Penna, Samuel Silva, Pitangueira, R. L. S.
Revista IBRACON de Estruturas e Materiais , v. 8, N. 6 , p. 787-799 , São Paulo , 2015
The modeling of reinforced concrete structures has taken advantage of the increasing progress on Computational Mechanics, in such way that complex phenomena, such as cracking and crushing, creep, reinforcement yielding, steel-concrete bond loss, can be modeled in a reasonable realistic way, using the proper set of numerical and computational resources. Among several options, the ones based on the Finite Element Method (FEM) allow complex analysis simulations of reinforced concrete structures, including the interaction of different nonlinear effects. This paper deals with the nonlinear finite element analysis of the bond-slip between reinforcing steel and concrete, taking into account an experimental study previously performed. The FEM analysis presented uses a combination of resources where the material behavior of concrete is described by the Microplane Constitutive Model, and an embedded reinforcement model is used to represent steel inside the concrete and take into account the effect of bond-slip. The FEM models were created using the INSANE (INteractive Structural ANalysis Environment) computational system, open source software that has a set of FEM tools for nonlinear analysis of reinforced concrete structures. The correlations between numerical-experimentals results and several parameters validate the proposed combination of resources and identifies the significance of various effects on the response.
An object-oriented approach to the Generalized Finite Element Method
Alves, Phillipe D., Barros, Felício Bruzzi, Pitangueira, Roque Luiz da Silva
Advances in Engineering Software , v. 59 , p. 1-18 , 2013
The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.
An object-oriented tridimensional self-regular boundary element method implementation
Anacleto, F.E.S., Ribeiro, T.S.A., Ribeiro, G.O., Pitangueira, R.L.S. ; Penna, S.S.
Engineering Analysis with Boundary Elements , v. 37, Issue 10 , p. 1276-1284 , 2013
The object-oriented design used to implement a self-regular formulation of the boundary element method is presented. The self-regular formulation is implemented to four integral equations: the displacement boundary integral equation, and the Somigliana’s integral identities for displacement, stress and strain. The boundary-layer effect that arises in the classical BEM on the transition from interior to boundary points is eliminated and thus special integration schemes to treat nearly singular integrals become unnecessary. The self-regular formulations lead to very accurate results. Comparisons of displacements, stress and strain obtained from analytical solutions and the numerical results for bidimensional and tridimensional elastostatics problems are presented, and the self-regular formulation shows strong stability. The implemented code is open-source and is available under the GNU General Public License.
Estudo comparativo de modelos de fissuração distribuída para estruturas de concreto
Samuel Silva Penna, Roque Luiz da Silva Pitangueira, Jamile Salim Fuina
Semina: Ciências Exatas e Tecnológicas , v. 34, N. 2 , p. 211-228 , Londrina , 2013
The article shows how the constitutive modeling of concrete has evolved since the initial attempts to characterize the medium cracked as continuous, moving from smeared cracking, damage and microplane models, until the current tendency to design different models according to a single theoretical framework. A generic formulation for smeared cracking models, including fixed and rotational models, as well as degradation in tension and in compression, is provided. Using this formulation, three models are generated by specifying the laws of degradation. A comparative study of models, based on computer simulations of a beam subjected to shear at four points, is presented. The results are compared, between themselves and with experimental results, providing a critical analysis of the models.
A comparison of two microplane constitutive models for quasi-brittle materials
Fuina, J.S., Pitangueira, R.L.S., Penna, S.S.
Applied Mathematical Modelling , v. 35, Issue 11 , p. 5326-5337 , 2011
This article presents a comparison of two microplane constitutive models. The basis of the microplane constitutive models are described and the adopted assumptions for the conception of these models are discussed, with regard to: decomposition of the macroscopic strains into the microplanes, definition of the microplane material laws, including the choice of variables that control the material degradation, and homogenization process to obtain the macroscopic quantities. The differences between the two models, with respect to the employed assumptions, are emphasized and expressions to calculate the macroscopic stresses are presented. The models are then used to describe the behavior of quasi-brittle materials by finite element simulations of uniaxial tension and compression and pure share stress tests. The results of the simulations permit to compare the capability of the models in describing the post critical strain-softening behavior, without numerically induced strain localization.
Abordagem orientada a objetos para implementação computacional de elementos finitos de placa
Samir Silva Saliba, Samuel Silva Penna, Roque Luiz Pitangueira
Cadernos de Engenharia de Estruturas (Online) , v. 13, N. 60 , p. 37-54 , São Carlos , 2011
This article presents a software for structural analysis of plates that provides a variety of finite elements, based on the theories of Kirchhoff and Reissner-Mindlin. These theories are briefly discussed, highlighting differences and particularities relevant to software design. The implementation of the system, conducted under the paradigm of object-oriented programming, is then presented through Unified Modelling Language (UML) diagrams that describe the main classes and interfaces used. For purposes of illustration and validation of the resources available, some numerical simulations are presented. Finally, the importance of the system to study the issue and the possibilities of its expansion are discussed.
Elementos finitos de casca do sistema computacional INSANE
Flávio Henrique Ajeje, Samuel Silva Penna, Roque Luiz da Silva Pitangueira
Rem: Revista Escola de Minas , v. 64, N. 4 , p. 399-405 , Ouro Preto , 2011
This paper presents the shell finite elements of the computer system INSANE (INteractive Structural ANalysis Environment): four-node rectangular and three-node 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 conical-cylindrical reservoir. The results are compared with analytical solutions and those obtained with the shell finite element of SAP2000.
Contínuos Generalizados: de Voigt à modelagem de materiais parcialmente frágeis
Jamile Salim Fuina, Roque Luiz da Silva Pitangueira, Samuel Silva Penna
Semina: Ciências Exatas e Tecnológicas , v. 31 , p. 119-130 , Londrina , 2010
This article discusses the use of the generalized continuum theories to incorporate the effects of the microstructure in the nonlinear finite element analysis of quasi-brittle materials and, thus, to solve mesh dependency problems. A description of the problem called numerically induced strain localization, often found in Finite Element Method material non-linear analysis, is presented. A brief historic about the Generalized Continuum Mechanics based models is presented, since the initial work of Voigt (1887) until the more recent studies. By analyzing these models, it is observed that the Cosserat and microstretch approaches are particular cases of a general formulation that describes the micromorphic continuum. After reporting attempts to incorporate the material microstructure in Classical Continuum Mechanics based models, the article shows the recent tendency of doing it according to assumptions of the Generalized Continuum Mechanics. Finally, it presents numerical results which enable to characterize this tendency as a promising way to solve the problem.
Um modelo para propagaςão de fissuras no concreto baseado no Método dos Elementos Finitos Estendido
Kelson Pothin Wolff, Roque Luiz Pitangueira, Samuel Silva Penna
Mecánica Computacional , v. XXIX , p. 10131-10153 , 2010
Abstract (in Portuguese)
O artigo trata da implementação computacional de um modelo capaz de descrever o comportamento do concreto sujeito à ﬁssuração. Utilizam-se relações constitutivas baseadas no modelo de ﬁssuras coesivas para representar a região ﬁssurada do concreto, enquanto o restante do volume nãoﬁssurado é representado como linearmente elástico. Tais relações constitutivas são, então, combinadas com as hipóteses do Método dos Elementos Finitos Estendido, formando um modelo que, introduzindo um salto no campo de deslocamentos do Método dos Elementos Finitos Padrão, para representar a descontinuidade provocada neste campo pela ﬁssura, é capaz de descrever a propagação da mesma. O critério de propagação é baseado no limite de resistência à tração do material e a geometria da ﬁssura é deﬁnida por um conjunto de segmentos lineares. O modelo assim concebido permite que a ﬁssura se propague livremente pela malha convencional, atravessando o domínio e a interface dos elementos ﬁnitos. O modelo foi implementado no núcleo numérico do sistema computacional INSANE (Interactive Structural Analysis Environment), permitindo simular problemas de propagação de ﬁssuras em peças de concreto submetidas a tração axial, ﬂexão e compressão diametral. Os resultados são obtidos dentro da faixa de resposta esperada. A principal diﬁculdade encontrada relaciona-se com o critério de propagação escolhido, que não se mostra adequado para predição da direção correta de propagação da ﬁssura quando a análise alcança níveis elevados de tensão.