A double incremental variational procedure for elastoplastic composites with combined isotropic and linear kinematic hardening

Lucchetta, Antoine; Auslender, François; Bornert, Michel; Kondo, Djimédo

doi:10.1016/j.ijsolstr.2018.09.012

Cited by 15 publications

(35 citation statements)

References 28 publications

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“…On the other hand, if this non-convex free-energy density is replaced by the convex density wfalse^false(ε¯boldu,αfalse¯false(1false)boldu,α~false(1false)false)=μ1−c[(εfalse¯−(1−c)α¯(1))2+(false(3/2false)c εfalse¯−(1−c)α~(1))2], keeping the reduced dissipation potential (2.3) and reinterpreting the effective internal variable α~false(1false) as a signed quantification of the inelastic strain fluctuations so that it is allowed to become negative, the spurious transients no longer occur and the exact response for general deformation programmes ε¯false(tfalse) is obtained. This replacement of the reduced free-energy density—henceforth referred to as ‘convexification’—is equivalent to the algorithmic correction devised by Idiart & Lahellec [6], Boudet et al [10] and Lucchetta et al [11] on the basis of exploiting the existence of multiple stationary points in the approximate incremental functionals of Lahellec & Suquet [1,12]. Unfortuna...…”

Section: Results For Particulate Systemsmentioning

confidence: 99%

Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

2020

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The mean-field homogenization scheme proposed by Lahellec & Suquet (2007 Int. J. Solids Struct. 44 , 507–529 ( doi:10.1016/j.ijsolstr.2006.04.038 )) and revisited in a companion paper (Idiart et al . 2020 Proc. R. Soc. A 20200407 ( doi:10.1098/rspa.2020.0407 )) is applied to random mixtures of a viscoelastic solid phase and a rigid phase. Two classes of mixtures with different microstructural arrangements are considered. In the first class the rigid phase is dispersed within the continuous viscoelastic phase in such a way that the elastic moduli of the mixture are given exactly by the Hashin–Shtrikman formalism. In the second class, both phases are intertwined in such a way that the elastic moduli of the mixture are given exactly by the Self-Consistent formalism. Results are reported for specimens subject to various complex deformation programmes. The scheme is found to improve on earlier approximations of common use and even recover exact results under several circumstances. However, it can also generate highly inaccurate predictions as a result of the loss of convexity of the free-energy density. An auspicious procedure to partially circumvent this issue is advanced.

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Section: Results For Particulate Systemsmentioning

confidence: 99%

Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

2020

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“…No entanto, em uma situação real de processamento de materiais metálicos nem sempre será observada uma relação monotônica ou encruamento progressivo [4,5] entre a resistência mecânica e a deformação plástica, devido à existência de carregamentos mecânicos complexos, os quais combinam diferentes modos de deformação plástica, alterando, por exemplo, o encruamento de um material metálico.…”

Section: Rotaunclassified

Estudo da conformabilidade do aço inoxidável AISI 409 sob rotas complexas de deformação

Morais¹,

Corrêa²,

Lopes³

2021

Tecnol. Metal. Mater. Min.

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Publicado pela ABM. Este é um artigo publicado em acesso aberto (Open Access) sob a licença Creative Commons Attribution, que permite uso, distribuição e reprodução em qualquer meio, sem restrições desde que o trabalho original seja corretamente citado.a ResumoNas diversas operações de conformação é necessária a combinação de diferentes esforços mecânicos até que sejam alcançadas a forma e as dimensões de um produto. A severidade dessas mudanças no modo de deformação pode ocasionar modificações inesperadas no comportamento mecânico de um material, restringindo o uso do mesmo em processos industriais. Considerando essa abordagem, este trabalho apresenta o estudo da conformabilidade do aço inoxidável ferrítico AISI 409 sob duas rotas de processamento mecânico, com o objetivo de analisar a evolução da resistência mecânica e da ductilidade desse aço. Neste caso, chapas do aço AISI 409 foram submetidas a uma combinação de tensões compressivacisalhante (laminação), tração e cisalhamento (de modo direto e reverso) de forma a promover mudanças severas no modo de deformação plástica. Os resultados revelaram a influência da quantidade de pré-deformação efetiva (variando de 3,88% a 16,50%), do estado inicial do material (recozido e laminado a frio), do modo de deformação plástica (laminação, tração e cisalhamento) no endurecimento e na ductilidade do aço AISI 409, exibindo ainda transientes na taxa de encruamento associados com o modo de pré-deformação em laminação a frio. Palavras-chave: Aço AISI 409; Cisalhamento; Trajetória de deformação.

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“…Propagation of cracks in such strengthened materials is described, for instance in [ 8 , 9 , 10 ]. Isotropic and kinematic hardening of modern, e.g., composite materials are the topic of, for instance, [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

et al. 2020

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In exact analyses of bodies in the elastic–plastic regime, the behavior of the material above critical stress values plays a key role. In addition, under cyclic stress, important phenomena to be taken into account are the various types of hardening and the design of the material or structure. In this process, it is important to define several groups of characteristics. These include, for instance, the initial area of plasticity or load which defines the interface between elastic and plastic deformation area. The characteristics also include the relevant law of plastic deformation which specifies the velocity direction of plastic deformation during plastic deformation. In the hardening condition, it is also important to determine the position, size and shape of the subsequent loading area. The elasto-plastic theory was used for the analysis of special compliant mechanisms that are applied for positioning of extremely precise members of the Compact Linear Collider (CLIC), e.g., cryomagnets, laser equipment, etc. Different types of deformation hardening were used to simulate the behavior of particular structural elements in the elastic–plastic regime. Obtained values of stresses and deformations may be used in further practical applications or as default values in other strain hardening model simulations.

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A double incremental variational procedure for elastoplastic composites with combined isotropic and linear kinematic hardening

Cited by 15 publications

References 28 publications

Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

Estudo da conformabilidade do aço inoxidável AISI 409 sob rotas complexas de deformação

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

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