High-order three-scale computational method for dynamic thermo-mechanical problems of composite structures with multiple spatial scales

Dong, Hao; Zheng, Xiaojing; Cui, Junzhi; Nie, Yufeng; Yang, Zhiqiang; Yang, Zihao

doi:10.1016/j.ijsolstr.2019.04.017

Cited by 20 publications

(18 citation statements)

References 23 publications

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“…Practically, the perforated domain may be quite complicated with more than two scales and cavities with different sizes may be encountered rather the uniform size considered in this paper. Thus it is interesting to apply the three‐scale asymptotic analysis 33 for such structure and the homogenized coefficients can be derived successively. More attention should be paid for the integrations on each cavity boundary.…”

Section: Discussionmentioning

confidence: 99%

“…Cui and Cao 30,31 proposed the Second‐Order Two‐Scale (SOTS) method to give out the second‐order asymptotic expansions systematically, focused on the practical computations to reflect precisely the original highly oscillating solutions. Following this idea, variations of the SOTS expansions are developed and some featured works involve the SOTS model for the heat conduction problem in curvilinear coordinates, 32 two‐scale and three‐scale asymptotic expansions for the dynamic thermo‐mechanical problem, 33,34 reduced asymptotic expansion method for the thermal‐mechanical problem with nonlinear materials, multi‐scale expansions and algorithm for the 3‐D Maxwell equations 35 and so forth. The spectral analysis for such heterogeneous materials can be also performed by this approach.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain

et al. 2021

Math Methods in App Sciences

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A second‐order asymptotic analysis method is developed for the Steklov eigenvalue problem in periodically perforated domain. By the two‐scale expansions of the eigenfunctions and eigenvalues, the first‐ and second‐order cell functions defined on the representative cell are obtained successively, the homogenized elliptic eigenvalue problem is formulated, and effective coefficients are derived. The first‐ and second‐order correctors of the eigenvalues are expressed in terms of the integrations of the cell functions and homogenized eigenfunctions. The error estimations of the expansions of eigenvalues are established, and the corresponding finite element algorithm is proposed. Numerical examples are carried out, and both qualitative and quantitative comparisons with the solutions by classical finite element computations are performed. It is demonstrated that this asymptotic model is effective to capture the local details of the eigenfunctions by considering the second‐order expansion terms, and the algorithm presented in this work is efficient to obtain the accurate spectral properties of the porous material at lower cost.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain

et al. 2021

Math Methods in App Sciences

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“…In general, the AHM makes it possible to obtain an effective characterization of the heterogeneous system or phenomenon under study by encoding the information available at the microscale into the so-called effective coefficients. In particular, multiscale AHM take advantage of the information available at the smaller scales of a given heterogeneous medium to predict the effective properties at its larger scales, see, for instance, [36][37][38][39]. This, in turn, dramatically reduces the computational complexity of the resulting boundary problems.…”

Section: Introductionmentioning

confidence: 99%

Effective Complex Properties for Three-Phase Elastic Fiber-Reinforced Composites with Different Unit Cells

et al. 2021

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The development of micromechanical models to predict the effective properties of multiphase composites is important for the design and optimization of new materials, as well as to improve our understanding about the structure–properties relationship. In this work, the two-scale asymptotic homogenization method (AHM) is implemented to calculate the out-of-plane effective complex-value properties of periodic three-phase elastic fiber-reinforced composites (FRCs) with parallelogram unit cells. Matrix and inclusions materials have complex-valued properties. Closed analytical expressions for the local problems and the out-of-plane shear effective coefficients are given. The solution of the homogenized local problems is found using potential theory. Numerical results are reported and comparisons with data reported in the literature are shown. Good agreements are obtained. In addition, the effects of fiber volume fractions and spatial fiber distribution on the complex effective elastic properties are analyzed. An analysis of the shear effective properties enhancement is also studied for three-phase FRCs.

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“…In particular, multiscale asymptotic homogenization methods take advantage of the information available at the smaller scales of a given heterogeneous medium to predict the effective properties at its larger scales (see e.g. Lukkassen and Milton [3]; Penta and Gerisch [4]; Ram ırez-Torres et al [5]; Ram ırez-Torres et al [6]; Yang et al [7]; Dong et al [8]). This homogenization procedure requires the solution of cell problems with input data corresponding to the homogenized material properties resulting in previous steps.…”

Section: Introductionmentioning

confidence: 99%

“…An additional overview of reiterated homogenization is presented in Trucu, Chaplain, and Marciniak-Czochra [15] via a three-scale convergence approach where the asymptotic parameters independently approach zero. More recently, in Dong et al [8]; Yang et al [7,16], the authors study the properties of thermo-mechanical, non-aging and aging viscoelastic composites with multiple spatial scales by using a three-scale asymptotic expansion and a periodic layout of the heterogeneities in the structures. They also provide a finite element algorithm based on inverse Laplace transform and the three-scale asymptotic homogenization to obtain the numerical results.…”

Section: Introductionmentioning

confidence: 99%

A hierarchical asymptotic homogenization approach for viscoelastic composites

Cruz-González

Ramírez-Torres

Rodrı́guez-Ramos

et al. 2020

Mechanics of Advanced Materials and Structures

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Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method. In this approach, we consider the assumption of a generalized periodicity in the different structural levels and their characterization through the socalled stratified functions. The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization by using the correspondence principle and the Laplace-Carson transform. Considering isotropic components and a perfect contact at the interfaces between the constituents, analytical solutions, in the Laplace-Carson space, are found for the local problems and the effective coefficients are computed. An interconversion procedure between the effective relaxation modulus and the effective creep compliance is carried out for obtaining information about both viscoelastic properties. The numerical inversion to the original temporal space is also performed. Finally, we exploit the potential of the approach and study the overall properties of a hierarchical viscoelastic composite structure representing the dermis.

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High-order three-scale computational method for dynamic thermo-mechanical problems of composite structures with multiple spatial scales

Cited by 20 publications

References 23 publications

Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain

Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain

Effective Complex Properties for Three-Phase Elastic Fiber-Reinforced Composites with Different Unit Cells

A hierarchical asymptotic homogenization approach for viscoelastic composites

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