Elasto-Plastic Analysis of Composite Materials Using the Homogenization Method. 1st Report. Formulation.

賢二郎, 寺田; 康平, 弓削; 昇, 菊池

doi:10.1299/kikaia.61.2199

Cited by 26 publications

(8 citation statements)

References 7 publications

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“…3 Terada et al proposed a formulation to track the nonlinear behavior of the whole structure by the homogenization method under the assumption of large deformation and small strain. 4 Terada et al assumed an anisotropic hyperelastic constitutive law as a macro-material model for fiber-reinforced composites with periodic microstructures, and also proposed a method to identify the material parameters of the assumed macrostructure through analysis of the microstructure by applying numerical material experiments based on the homogenization method. 5 Carbone and Codegone incorporated the homogenization method into problems arising in civil engineering, and obtained the mechanical properties of a periodic masonry structure composed of bricks and mortar using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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In this paper, we propose a solution to a shape optimization problem for the strength design of periodic microstructures in multiscale structures. Two maximum stress minimization problems are addressed: minimization of maximum microstructural stress and minimization of maximum macrostructural stress.The homogenization method is used to bridge the macrostructure and the microstructure and to calculate local microstructural stress. By replacing the maximum stress value with a Kreisselmeier-Steinhauser function, the difficulty of nondifferentiability of maximum stress is avoided. Each strength design problem is formulated as a distributed parameter optimization problem subject to an area constraint including the whole microstructure. The shape gradient functions for both problems are derived using Lagrange's undetermined multiplier method, the material derivative method, and the adjoint variable method. The H 1 gradient method is used to determine the unit cell shapes of the microstructure, while reducing the objective function and maintaining smooth design boundaries. In the numerical examples, the optimal shapes obtained for minimization of the maximum local stress of the microstructure and the macrostructure are compared and discussed. The results confirm the effectiveness of the microstructure shape optimization method for the two strength design problems of multiscale structures.

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Section: Introductionmentioning

confidence: 99%

Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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“…The homogenization method 7) was proposed to simultaneously represent non-uniform deformations on two different scales. Extended investigations of the homogenization method have been reported, e.g., an extension to the elastoplastic problem 8) and the rate-form large deformation 9) , application to the boundary element method 10) , and establishment of an implicit method process 11) . In the conventional homogenization method, namely, the first-order homogenization method (1st-HM), the microscopic virtual work for the macroscopic strain is estimated by solving the periodic boundary problems given to the microstructure.…”

Section: Introductionmentioning

confidence: 99%

Computational Evaluation of Micro- to Macroscopic Non-Uniform Deformation Behavior of Polycrystalline Materials Using Second-Order Homogenization Method

Uchida

Sakamoto

Kaneko

2021

J. Soc. Mat. Sci., Japan

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“…The crystallographic homogenization method has been utilized as one of the effective numerical techniques [1][2][3][4][5]. The crystallographic homogenization method has been utilized as one of the effective numerical techniques [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Parallel Computing of Multi-scale Finite Element Sheet Forming Analyses Based on Crystallographic Homogenization Method

Kuramae¹,

Okada²,

Tam³

et al. 2005

AIP Conference Proceedings

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Since the multi-scale finite element analysis (FEA) requires large computation time, development of the parallel computing technique for the multi-scale analysis is inevitable. A parallel elastic/crystalline viscoplastic FEA code based on a crystallographic homogenization method has been developed using PC cluster. The homogenization scheme is introduced to compute macro-continuum plastic deformations and material properties by considering a polycrystal texture. Since the dynamic explicit method is applied to this method, the analysis using micro crystal structures computes the homogenized stresses in parallel based on domain partitioning of macro-continuum without solving simultaneous linear equations. The micro-structure is defined by the Scanning Electron Microscope (SEM) and the Electron Back Scan Diffraction (EBSD) measurement based crystal orientations.In order to improve parallel performance of elastoplasticity analysis, which dynamically and partially increases computational costs during the analysis, a dynamic workload balancing technique is introduced to the parallel analysis. The technique, which is an automatic task distribution method, is realized by adaptation of subdomain size for macro-continuum to maintain the computational load balancing among cluster nodes. The analysis code is applied to estimate the polycrystalline sheet metal formability.

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Elasto-Plastic Analysis of Composite Materials Using the Homogenization Method. 1st Report. Formulation.

Cited by 26 publications

References 7 publications

Shape optimization method for strength design problem of microstructures in a multiscale structure

Shape optimization method for strength design problem of microstructures in a multiscale structure

Computational Evaluation of Micro- to Macroscopic Non-Uniform Deformation Behavior of Polycrystalline Materials Using Second-Order Homogenization Method

Parallel Computing of Multi-scale Finite Element Sheet Forming Analyses Based on Crystallographic Homogenization Method

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