Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis

Kato, Junji; Yachi, Daishun; Terada, Kenjiro; Kyoya, Takashi

doi:10.1007/s00158-013-0994-6

Cited by 56 publications

(31 citation statements)

References 21 publications

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“…(22). In the future, we will use the PFTO model to design the material microstructures in multi-scale and multi-material problems (Kato et al, 2009;Kato et al, 2014) because the phase-field method is excellent at simulating the material microstructures. Therefore, successive simulations of an optimum material microstructure using the PFTO model and phase-field simulations to determine the process to make the optimum material microstructures should be performed.…”

Section: Discussionmentioning

confidence: 99%

Phase-field topology optimization model that removes the curvature effects

Takaki

Kato

2017

Mechanical Engineering Journal

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The conventional phase-field topology optimization (PFTO) models minimize not only the objective function but also the interface energy. In the present study, a new PFTO model, which minimizes only the objective function, is developed by removing the curvature effect from the conventional PFTO model. Simulations of elastic strain energy minimization under a constant-volume constraint condition of a cantilever are performed using the developed and conventional PFTO models. From the simulation results, we confirm that the developed PFTO model that removes the curvature effects can efficiently optimize only the objective function.

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Section: Discussionmentioning

confidence: 99%

Phase-field topology optimization model that removes the curvature effects

Takaki

Kato

2017

Mechanical Engineering Journal

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“…On the other hand, after the groundbreaking contribution of Bendsoe and Kikuchi [6] in which the homogenization method is used to design optimal topology structures several authors have dabbled into this actual research topic [1,106,128,56,22]. …”

Section: Review Of Multiscale Methodsmentioning

confidence: 99%

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Otero

Oller

Martı́nez

2016

Arch Computat Methods Eng

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Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Archives of computational methods in engineering. Abstract The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical Boundary Value Problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. firstorder and second-order, in this work an enhanced-firstorder computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macroscale BVP.

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“…The ability to design micro-scale architectures that produce a specific material behaviour is of utmost importance in this context [39,76,108]. RVE-based computational multiscale methods aiming, for instance, the optimization of certain material properties [3,54,124] have shown to offer a solid tool to assist the material design process.…”

Section: Current Trends and Perspectivesmentioning

confidence: 99%

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Blanco

Sánchez

Neto

et al. 2014

Arch Computat Methods Eng

142

113

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A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro-and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force-and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the wellknown Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force-and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.

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Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis

Cited by 56 publications

References 21 publications

Phase-field topology optimization model that removes the curvature effects

Phase-field topology optimization model that removes the curvature effects

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

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