Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

Guedes, J. M.; Kikuchi, Noboru

doi:10.1016/0045-7825(90)90148-f

Cited by 1,191 publications

(576 citation statements)

References 11 publications

(6 reference statements)

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“…9,10) One of the merits of the homogenization method is strict dynamics theory and the method can reflect the correlations between macro and micro scale. 3) To analyze the microscopic fracture of composite materials such as coke, the correlations must be taken into consideration. The microstructure of actual materials deforms by macroscopic load or thermal expansion and these microscopic behaviors affects on macroscopic behavior as macroscopic property.…”

Section: Application Of Homogenization Methods To Cokementioning

confidence: 99%

“…2) Fundamental researches are hardly performed in regard to the effect of these microstructures on coke size and strength. Recently, the homogenization method, 3) which enables us to analyze macroscopic and microscopic behavior simultaneously, was applied for the understanding the fracture mechanism in coke, and then the finite element method was used to solve the partial differential equations derived by the homogenization method. Dealing with the microstructure such as pores, their distribution and micro cracks was not enough because the finite element cell to express the microstructure was too simple.…”

Section: Introductionmentioning

confidence: 99%

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A New Estimation Method of Coke Strength by Numerical Multiscale Analysis

et al. 2003

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The homogenization method is proposed as new numerical approach to understand the fracture mechanism of the microscopic behavior in coke because the evaluations of the strength has been still difficult for the improvement of coke qualities in coke making process. The conditions for the stress concentration and relaxation effect are investigated by homogenization method. These results show that the distribution of micro cracks and pores in coke is important factor for the microscopic fracture. Also, the digital image technique is applied to the actual coke with the complicated microstructure and the improvement mechanism of coke strength by the carbon deposition is clarified by using homogenization method. The effect of carbon deposition on the coke strength is illustrated from the stress distribution while calculating the homogenized elastic modulus. Although the stress concentration between large pores is caused in the case of carbon deposited coke, the maximum stress becomes smaller than the tensile strength of coke because of large homogenized elastic modulus. As a result, the microscopic fracture does not easily occur for carbon deposited coke.

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Section: Application Of Homogenization Methods To Cokementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Estimation Method of Coke Strength by Numerical Multiscale Analysis

et al. 2003

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“…The evolution of the nonlocal phase static damage at a given time can be expressed as (25) where ; the operator denotes the positive part, i.e. ; the phase deformation history parameter is determined from the evolution of the phase damage equivalent strain, denoted by (26) where represents the threshold value of damage equivalent strain prior to the initiation of phase damage; is defined as the square root of the phase damage energy release rate [39] (27) Since is assumed to be a positive definite fourth order tensor it follows that and consequently, must hold due to the energy dissipation inequality in (24).…”

Section: Fatigue Damage Cumulative Lawmentioning

confidence: 99%

“…By integrating (10) over and making use of (13), we have (18) where and (19) The constitutive equating for the phase average field can be expressed as (20) where is the phase average stress, and the overall homogenized stress field turns into (21) where is the volume fractions for phase in RVE satisfying . The phase free energy density corresponding to the nonlocal constitutive equation (20) is given as (22) and the corresponding phase damage energy release rate and the energy dissipation inequality [9][39] applied to the phase average field can be expressed as (23) (24) It should be noted that the nonlocal character of the phase average damage and the constitutive equation (20) has been proved in [20]. This important feature validates our homogenization theory for simulating the damage evolution in composite materials [1] [37].…”

Section: Figure 1 Macroscopic and Microscopic Structuresmentioning

confidence: 99%

Computational mechanics of fatigue and life predictions for composite materials and structures

Fish

2002

Computer Methods in Applied Mechanics and Engineering

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A multiscale fatigue analysis model is developed for brittle composite materials. The mathematical homogenization theory is generalized to account for multiscale damage effects in heterogeneous media and a closed form expression relating nonlocal microphase fields to the overall strains and damage is derived. The evolution of fatigue damage is approximated by the first order initial value problem with respect to the number of load cycles. An efficient integrator is developed for the numerical integration of the continuum damage based fatigue cumulative law. The accuracy and computational efficiency of the proposed model for both low-cycle and high-cycle fatigue are investigated by numerical experimentation. IntroductionIn recent years several fatigue models have been developed within the framework of continuum damage mechanics (CDM) [10][12] [29][35] [36]. Within this framework, internal state variables are introduced to model the fatigue damage. The degradation of material response under cyclic loading is simulated using constitutive equations which couple damage cumulation and mechanical responses. The microcrack initiation and growth are lumped together in the form of the evolution of damage variables from zero to some critical value. Most of the existing CDM based fatigue damage models are based on the classical (local) continuum damage theory even though it is well known that the accumulation of damage leads to strain softening and loss of ellipticity in quasi-static problems and hyperbolicity in dynamic problems (see, for example, [45] revealed the intrinsic links between the nonlocal CDM theory and fracture mechanics providing a possibility for building a unified framework to simulate crack initiation, propagation and overall structural failure under cyclic loading.When applying the CDM based fatigue model to life prediction of engineering systems, the coupling between mechanical response and damage cumulation poses a major computational challenge. This is because the number of cycles to failure, especially for high-cycle fatigue, is usually as high as tens of millions or more, and therefore, it is practically not feasible to carry out a direct cycle-by-cycle simulation for the fully coupled models even with today's powerful computers. An efficient integrator, or the so-called

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“…An extensive body of literature is devoted to study this technique among which we refer to Refs. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Reviews of the different multiscale approaches can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

178

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

Cited by 1,191 publications

References 11 publications

A New Estimation Method of Coke Strength by Numerical Multiscale Analysis

A New Estimation Method of Coke Strength by Numerical Multiscale Analysis

Computational mechanics of fatigue and life predictions for composite materials and structures

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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