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Pseudoelasticicy and shape memory eect due to martensitic transforma- tion of polycrystalline shape memory alloy materials are modeled in the setting of three- dimensional media. In the present work, description of rate-independent... more
Pseudoelasticicy and shape memory eect due to martensitic transforma- tion of polycrystalline shape memory alloy materials are modeled in the setting of three- dimensional media. In the present work, description of rate-independent pseudoelastic behavior and shape memory eect is presented within the context of Generalized Stan- dard Materials, using an internal variable named transformation strain tensor. Non- dierentiable but convex potentials of free energy and dissipation are dened and a special form for inelastic potential, based on the Drucker-Prager type, is proposed. The numer- ical integration of the resulting set of nonlinear ordinary dierential equations involves the implementation of a radial projection scheme so as to satisfy the existing inequality constraints. The numerical results for proportional and nonproportional load show good agreement between the mechanical model and the behavior of polycrystalline materials presenting shape memory behavior.
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... It should be remarked that this model is not able to distinguish linear and affine paths from more complex ones, although experimental observations have shown that these paths may produce distinct fatigue damage [20 ... (11). View the... more
... It should be remarked that this model is not able to distinguish linear and affine paths from more complex ones, although experimental observations have shown that these paths may produce distinct fatigue damage [20 ... (11). View the MathML source. Alternatively, Zouain and co ...
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ABSTRACT We compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis. The aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements... more
ABSTRACT We compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis. The aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them. Two of these interpolations are used in limit analysis for the first time in this article. The inequalities in the proposition are also demonstrated via numerical applications. To this end, the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements. Copyright © 2014 John Wiley & Sons, Ltd.
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Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th November 2010. Access to the website will be disrupted as follows: New York 0630 EDT to 0830 EDT; London 1130 GMT to 1330 GMT; Singapore... more
Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th November 2010. Access to the website will be disrupted as follows: New York 0630 EDT to 0830 EDT; London 1130 GMT to 1330 GMT; Singapore 1730 SGT to 1930 SGT. ...
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... e of (elastic) stress 3 Page 4. Nestor Zouain, Lavinia Borges, and José Luıs Silveira ... (3) Any virtual stress field T in the set ∆ may be sought as collecting local values of elastic stresses produced, at different instants, along... more
... e of (elastic) stress 3 Page 4. Nestor Zouain, Lavinia Borges, and José Luıs Silveira ... (3) Any virtual stress field T in the set ∆ may be sought as collecting local values of elastic stresses produced, at different instants, along a certain admissible load program (cyclic or not). ...
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... Full Text via CrossRef | View Record in Scopus | Cited By in Scopus (6). Ballard et al., 1995. P.Ballard, K. Dang Van, A. Deperrois and YV Papadopoulos , The effects of mean stress and stress concentration on fatigue under combined... more
... Full Text via CrossRef | View Record in Scopus | Cited By in Scopus (6). Ballard et al., 1995. P.Ballard, K. Dang Van, A. Deperrois and YV Papadopoulos , The effects of mean stress and stress concentration on fatigue under combined bending and twisting. Fatigue Fract. Engng. ...
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... FC Castro a , Corresponding Author Contact Information , E-mail The Corresponding Author , JA Araújo a and N. Zouain b. ... proposes that the application of multiaxial fatigue criteria in terms of the theory of critical distances... more
... FC Castro a , Corresponding Author Contact Information , E-mail The Corresponding Author , JA Araújo a and N. Zouain b. ... proposes that the application of multiaxial fatigue criteria in terms of the theory of critical distances requires the use of a distance which may be different ...
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... 508 N. Zouain ... 4 Plastic collapse of solids obeying the ISM model Elastic-plastic bodies or structures may collapse under a constant system of loads in a process where the stress distribution remains constant while the body... more
... 508 N. Zouain ... 4 Plastic collapse of solids obeying the ISM model Elastic-plastic bodies or structures may collapse under a constant system of loads in a process where the stress distribution remains constant while the body undergoes unbounded purely plastic deformation. ...
... extremely important. 6 Page 7. Lavinia Borges, Raúl Feijóo, Claudio Padra and NestorZouain 2.2.1 The algorithm In order ... the function. Whenever this stretching is very large, the matrix Pp may become illconditioned. In addition ...
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... N. Zouain ... Equation (22) defines a plastic strain rate dk as the flow produced by the compound stress µσk +σr and the thermodynamic force A. Whenever this state, associated to the load vertex k, is active (ie at the boundary of fk... more
... N. Zouain ... Equation (22) defines a plastic strain rate dk as the flow produced by the compound stress µσk +σr and the thermodynamic force A. Whenever this state, associated to the load vertex k, is active (ie at the boundary of fk = 0), it may effectively act during the critical load ...
... 208 RA Feijoo and N. Zouain 1. INTRODUCTION The aim of this work is to present the derivation of some variational formulations ... descriptions are used, the approximations induced on the material behavior are incorporated in the... more
... 208 RA Feijoo and N. Zouain 1. INTRODUCTION The aim of this work is to present the derivation of some variational formulations ... descriptions are used, the approximations induced on the material behavior are incorporated in the variational prin-ciple and may be interpreted ...
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ABSTRACT Extremum principles for structures under variable loads are considered. Classical shakedown theory is compared with the exclusive prevention of incremental collapse and also with a safety analysis for alternating plasticity. A... more
ABSTRACT Extremum principles for structures under variable loads are considered. Classical shakedown theory is compared with the exclusive prevention of incremental collapse and also with a safety analysis for alternating plasticity. A general kinematical minimum principle for incremental collapse is derived from the generalization to non-polyhedral load domains of the König critetion. A mixed principle for incremental collapse, and also a static principle, are proposed. A numerical procedure for the computation of the safety factor against incremental collapse is developed on the basis of these theoretical results.
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RESUMEN As formulasoes variacionais que caracterizam a Análise Limite sáo apresentadas em tres versóes: Estática, Cinemática e Mista. SZo propostas discretizacóes pelo MEF para cada uma das formulasoes, reduzindo o problema de Análise Limite a um problema de Programacáo Linear. Uma placa com enta...more
Pseudoelasticicy and shape memory eect due to martensitic transforma- tion of polycrystalline shape memory alloy materials are modeled in the setting of three- dimensional media. In the present work, description of rate-independent... more
Pseudoelasticicy and shape memory eect due to martensitic transforma- tion of polycrystalline shape memory alloy materials are modeled in the setting of three- dimensional media. In the present work, description of rate-independent pseudoelastic behavior and shape memory eect is presented within the context of Generalized Stan- dard Materials, using an internal variable named transformation strain tensor. Non- dierentiable but convex potentials of free energy and dissipation are dened and a special form for inelastic potential, based on the Drucker-Prager type, is proposed. The numer- ical integration of the resulting set of nonlinear ordinary dierential equations involves the implementation of a radial projection scheme so as to satisfy the existing inequality constraints. The numerical results for proportional and nonproportional load show good agreement between the mechanical model and the behavior of polycrystalline materials presenting shape memory behavior.
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A analise limite de estruturas de material elasto-plastico e considerada em geral e objetivando o calculo da carga de colapso plastico em cascas. Como aplicacao sao desenvolvidos metodos numericos para analise limite de cascas... more
A analise limite de estruturas de material elasto-plastico e considerada em geral e objetivando o calculo da carga de colapso plastico em cascas. Como aplicacao sao desenvolvidos metodos numericos para analise limite de cascas axissimetricas. A analise limite e essencialmente um problema de otimizacao. Em consequencia a apresentacao dos fundamentos e a geracao dos metodos de resolucao se faz utilizando a teoria e os algoritmos da programacao matematica. As equacoes constitutivas sao estabelecidas em variaveis generalizadas e tambem sao definidos os conceitos de tensoes e deformacoes plasticamente admissiveis. O fenomeno de colapso plastico e caracterizado matematicamente para em seguida se estabelecer os teoremas estatico e cinematico de carga limite propor cional como principios de maximo e minimo respectivamente. Aplicando os teoremas fundamentais de colapso plastico e mediante a utilizacao do metodo dos elementos finitos e da programacao linear sao desenvolvidos dois metodos nume...
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In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by... more
In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by ASME or European Standards must be precluded. Those modes are the alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case). Shakedown theory is a tool that permit us to assure that those kinds of failures will be avoided. However, in practical applications, very large nonlinear optimization problems are generated. Due to this facts, only in recent years have been possible to obtain algorithms sufficiently accurate, robust and efficient, for dealing with this class of problems. In this paper, one of these shakedown algorithms, developed for dealing with elastic ideally-plastic structures, is enhanced to include limited kinematic hardening, a more realistic material behavior. This is done in the continuo...
Research Interests: Engineering and Shakedown
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... 1. Introduction. Inelastic structures submitted to variable loads may undergo one of the following types of failure modes: alternating plasticity (plastic shakedown), incremental collapse (ratcheting), or instantaneous collapse... more
... 1. Introduction. Inelastic structures submitted to variable loads may undergo one of the following types of failure modes: alternating plasticity (plastic shakedown), incremental collapse (ratcheting), or instantaneous collapse (plastic collapse). ...
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ABSTRACT The continuum-based (CB) finite element approach has been demonstrated to be a good choice for the modeling of long thin structures, providing very good results. In this technique, the element formulation starts from the... more
ABSTRACT The continuum-based (CB) finite element approach has been demonstrated to be a good choice for the modeling of long thin structures, providing very good results. In this technique, the element formulation starts from the classical continuum formulation. Then, assumptions on the motion and on the stress state of the elements are made so that they behave like structural elements, e.g. beams and shells. Therefore, this methodology seems to be a simpler way for developing structural elements than the use of classical theories. In this paper the CB approach is used for the development of a multilayer three-node beam element for the solution of 2D linear elastic problems and limit analysis using direct methods. The element displacements/velocities are quadratic along the element axis and linear through the thickness. Bilinear interpolation functions are used to interpolate the stress fields on each element layer. Continuity of the stresses through the element thickness can be also enforced. Different materials can be defined on each element layer, allowing to model composite. The use of mixed formulation allows the easy application of the element proposed herein on the solution of plasticity problems using direct methods. The examples provided include simulations of linear elastic and limit analysis problems. The results are used to verify the robustness and accuracy of the element.
Two approaches to the solution of contact problems with friction in elasticity and plasticity are presented. In the first one, the solution is sought by alternating two simpler problems: (1) frictionless contact and (2) friction with... more
Two approaches to the solution of contact problems with friction in elasticity and plasticity are presented. In the first one, the solution is sought by alternating two simpler problems: (1) frictionless contact and (2) friction with given normal stress. For linear elasticity successive relaxation with projection is used. In the second approach, a constitutive relationship for normal and tangential reactions at the contact surface is introduced. A quasi-Newton method with a linear complementary solver at the element level can be used. Numerical examples are presented.
Page 1. 6th World Congress on Structural and Multidisciplinary Optimization Rio de Janeiro, 30 May - 03 June 2005, Brazil Minimum norm ellipsoids as a measure in high-cycle fatigue criteria Nestor Zouain Mechanical Engineering ...