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Cross-section modeling of the non-uniform corrosion due to chloride ingress using the positional finite element method

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2020年第10期42卷 1-18页

作者： Ramos, Everton Souza Carrazedo, Rogerio Univ Sao Paulo Sao Carlos Sch Engn Dept Struct Engn Sao Carlos SP Brazil

In this paper, we propose an original and alternative FEM strategy to simulate the expansion and damage in cross sections of concrete elements due to non-uniform corrosion associated with chloride ingress. The strategy embed two-dimensional particle elements in two-dimensional matrix elements to simulate the stress distribution in the steel/concrete interface. This approach is different from the usual ones in which the steel rebar is replaced by forces and the contribution of the reinforcement stiffness is neglected. The reinforced concrete cross section is made by the composition of matrix and particle elements by means of nodal correspondence. This ensures that the number of degrees of freedom is not affected by the reinforcement, which makes the technique highly economical from the numerical point of view. A damage model contributes to the process of concrete degradation due to corrosion. The numerical applications ensure the accuracy of the developed model, showing its applicability in the analysis of non-uniform corrosion propagation in cross sections of reinforced concrete structures.

关键词： Non-uniform corrosion Pitting corrosion Rust layer positional finite element method Embedded particles

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Modeling the creep behavior of GRFP truss structures with positional finite element method

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2018年第2期15卷

作者： Rabelo, Joao M. G. Becho, Juliano S. Greco, Marcelo Cimini, Carlos A., Jr. Univ Fed Minas Gerais Escola Engn Programa Posgrad Engn Estruturas Belo Horizonte MG Brazil

This paper presents the development of a formulation, based on positional finite element method, to describe the viscoelastic mechanical behavior of space trusses. The numerical method used was chosen due to its efficiency in the applications concerning nonlinear numerical analyses. The formulation describes the positional variation over time under constant stress state (creep). The objective is to provide a way to quantify the creep behavior for space truss structures and thus contribute to the encouragement of GFRP usage in such structural components. Time-dependent behavior of such materials is one the most important factors for their use in design of structures, demanding studies about the deformations expected within the operational life of the structural systems. To perform this study, the proposed methodology considers a standard solid rheological model to describe stress-strain time-dependent law. This model is implemented in the formulation for quantify the total strain energy. The effects of the model parameters in the mechanical response of the structure with accentuated geometric nonlinearity were presented. In this analysis, it was possible to identify the influence of the elastic and the viscous moduli on the creep response. Model calibration was performed using test data obtained from literature and a GFRP transmission line tower cross-arm was simulated to predict the evolution of displacements under real operational loads. From the results, it was possible to observe a fast evolution of displacements due to the creep effect in the first 7,500 h. This increase was close to 0.6% in relation to the displacement obtained in the elastic behavior. The presented methodology provided a simple and efficient way to quantify the creep phenomenon in viscoelastic GFRP composites truss structures, as can be seen in the developed analyses.

关键词： Creep positional finite element method Rheological Model Nonlinear Analysis GFRP

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Nonlinear analysis of plane frames considering hyperelastic models through the finite element positional method

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2024年第8期21卷

作者： dos Santos, Leandro Maciel, Daniel Nelson Barros, Rodrigo Neto, Joel Araujo do Nascimento da Silva Filho, Jose Neres Univ Fed Rio Grande do Norte UFRN Ctr Tecnol Natal RN Brazil Univ Fed Rio Grande do Norte UFRN Escola Ciencias & Tecnol Natal RN Brazil

Computational mechanics has become an essential tool in engineering, just as the use of hyperelastic materials has seen remarkable growth in everyday applications. Therefore, it is fundamental to study hyperelastic models that represent the behavior of these materials, such as elastomers and polymers. With that in mind, the Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh models were implemented in a computational code in FORTRAN using the positional finite element method with Reissner kinematics and the Newton-Raphson method for nonlinear analysis of plane frames with samples of elastomers added with different percentages of carbon black. Ultimately, it was concluded that the Yeoh and Ogden models presented coherent values and that the use of the formulation for nonlinear analysis of plane frame performs well after the modifications proposed by this work. These modifications consisted of adding the first and second strain invariants of the simple shear formulation to include the consideration of distortion in the specific strain energy of hyperelastic models.

关键词： Computational mechanics Hyperelastic models positional finite element method Plane structures Plane frames

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positional finite element formulation for two-dimensional analysis of elasto-plastic solids with contact applied to cold forming processes simulation

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2020年第5期42卷 1-17页

作者： Carvalho, Pericles R. P. Coda, Humberto B. Sanches, Rodolfo A. K. Univ Sao Paulo Sao Carlos Sch Engn Dept Struct Engn Sao Carlos SP Brazil

In this work, we develop a position-based finite element formulation for elasto-plastic solids under contact situation. The proposed positional formulation employs a total Lagrangian description and naturally considers geometric nonlinearities. The employed elasto-plastic model is derived from the dissipation inequality, using the thermodynamic conjugacy between the plastic strain rate and the so-called Mandel stress. The formulation is based on the Kroner-Lee decomposition, in which the deformation gradient is multiplicatively split into its elastic and plastic parts. We apply the backward Euler method to solve the plastic evolutions and von Mises yield criterion to define the elastic limit. The adopted kinematic hardening model is a finite strain generalization of the Armstrong-Frederick law, which uses the objective Jaumann derivative for the evolution equation and the concept of back stress tensor as an internal variable. For the elastic parcel of strains, we adopt a neo-Hookean constitutive law. With respect to the 2D application, plane strain and plane stress approximations are considered, where the latter is solved numerically by a local Newton-Raphson numerical procedure. Regarding the contact problem, a classical node-to-segment algorithm is applied, considering both frictionless and frictional cases, with the introduction of Lagrange multipliers in order to enforce contact constraints. Representative numerical examples are used to validate and show the possibilities of the proposed formulation in macroscale simulation of metal cold forming manufacturing processes.

关键词： positional finite element method Elasto-plasticity Large strain Contact Cold forming

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A total Lagrangian position-based finite element formulation for free-surface incompressible flows

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finite elementS IN ANALYSIS AND DESIGN 2020年 169卷 103348-000页

作者： Avancini, Giovane Sanches, Rodolfo A. K. Univ Sao Paulo Sao Carlos Sch Engn Dept Struct Engn Ave Trabalhador Saocarlense 400 BR-13566590 Sao Carlos SP Brazil

In this work, we propose a position-based finite element formulation for incompressible Newtonian flows under total Lagrangian description. Such formulation is different from the traditional finite element approach used in fluid dynamics by using current nodal positions as main variable instead of nodal velocities. The variational form of the governing equations is derived by applying the stationary total mechanical energy principle written in terms of current positions. To introduce full incompressibility, we use equal-order mixed finite elements combined to a pressure stabilizing Petrov-Galerkin technique, circumventing Ladyzhenskaya-Babuska-Brezzi conditions. This leads to a method directly applicable to finite strain incompressible flow problems that, if combined to re-meshing techniques, is capable of simulating more complex problems, resulting into a suitable tool for free-surface flows analysis in general. The efficiency and robustness of the proposed approach is demonstrated with numerical studies and comparison of obtained results to numerical and experimental data from literature.

关键词： Free-surface incompressible flows Total Lagrangian description positional finite element method Moving-boundary flows

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Flexible Multibody Dynamics finite element Formulation Applied to Structural Progressive Collapse Analysis

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2017年第1期14卷 52-71页

作者： Kuche Sanches, Rodolfo Andre Coda, Humberto Breves Univ Sao Paulo Escola Engn Sao Carlos BR-05508 Sao Paulo Brazil

This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis.

关键词： Multibody dynamics positional finite element method geometric nonlinear analysis Lagrange multipliers progressive collapse

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Development of Sliding Connections for Structural Analysis by a Total Lagrangian FEM Formulation

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2016年第11期13卷 2059-2087页

作者： Siqueira, Tiago Morkis Coda, Humberto Breves Univ Sao Paulo Dept Struct Engn Escola Engn Sao Carlos BR-05508 Sao Paulo Brazil

In this study a total lagrangian 2D finite element formulation is used to model plane frames developing large displacements and rotations considering sliding connections. This kind of connections is usually called prismatic and cylindrical joints. In order to be self-containing, the steps of the development of a frame finite element of any approximation order that considers the influence of shear strain by means of a generalized Reissner kinematics is presented. The adopted degrees of freedom are positions and rotations. Using positions as degrees of freedom simplifies the total lagrangian description and enables a comprehensive presentation of the proposed connections. Revolute connections are considered by direct degrees of freedom matching. Prismatic connections are modelled by the Lagrange multiplier technique that constrains positions and rotation of a sliding node to the varying position and rotation of a path element. Cylindrical joints are introduced in similar way by Lagrange multipliers releasing the sliding node rotation. The principle of stationary potential energy is used to write the non-linear equilibrium equation including the Lagrange multiplier influence. To solve the non-linear equation a Taylor expansion is carried out and the Newton-Raphson procedure is employed. The frame element is considered elastic, following the Saint-Venant-Kirchhoff constitutive model. Selected examples are used to validate the formulation and to show its possibilities of application.

关键词： positional finite element method Sliding connections Lagrange multipliers

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On fluid-shell coupling using an arbitrary Lagrangian-Eulerian fluid solver coupled to a positional Lagrangian shell solver

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APPLIED MATHEMATICAL MODELLING 2014年第14期38卷 3401-3418页

作者： Kuche Sanches, Rodolfo Andre Coda, Humberto Breves Fed Technol Univ Parana Civil Bldg Dept Pato Branco Parana Brazil Univ Sao Paulo Sch Engn Sao Carlos Dept Struct Engn Sao Carlos SP Brazil

In this work, we develop a partitioned algorithm for three-dimensional geometric non-linear fluid-structure interaction analysis using the finite element method. The fluid solver is explicit and its time integration based on characteristics, which automatically introduces stabilising terms on stream direction. The Navier-Stokes equations are written using the arbitrary Lagrangian-Eulerian (ALE) description, in order to accept moving boundaries and coupling with Lagrangian shell elements. The structure is modelled using a novel finite element method formulation for geometric non-linear shell dynamics. Such shell formulation, so-called positional formulation, is based on the minimum potential energy theorem, written regarding nodal positions and generalised unconstrained vectors, not displacements and rotations. These characteristics avoid the use of large rotation approximations. The coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell positions and velocities. The efficiency and robustness of the proposed approach is demonstrated by examples. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Fluid-structure interaction positional finite element method Geometric non-linear analysis Shell Arbitrary Lagrangian-Eulerian (ALE) description

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Alternative positional FEM applied to thermomechanical impact of truss structures

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finite elementS IN ANALYSIS AND DESIGN 2010年第11期46卷 1008-1016页

作者： Carrazedo, Rogerio Coda, Humberto Breves Univ Sao Paulo Sao Carlos Sch Engn BR-13566590 Sao Carlos SP Brazil

This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors' numerical solutions and experimental results. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Thermo-elasto-plasticity Additive decomposition positional finite element method

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