D. Chrupalla¹, J. Kreikemeier¹, S. Berg², L. Kärger³, M. Doreille⁴, T. Ludwig⁴, E. Jansen², R. Rolfes², A.Kling¹

CMC-Computers, Materials & Continua, Vol.32, No.3, pp. 159-176, 2012, DOI:10.3970/cmc.2012.032.159

Abstract In this paper, a loose coupling multiscale modeling technique for the detailed numerical analysis of critical areas in composite structures is presented. It is used to describe the global (macroscopic) behaviour of composite structures taking into account the effects of local phenomena. This is done by indirectly connecting the global and local FE-models. Prescribed displacements are assigned to the local boundaries in the transition from the global to local modeling level. The local-to-global transition is realized by assigning averaged local stresses to the respective global Gauss points and by updating the global tangent stiffness operator. To illustrate the feasibility of… More >

Filip Putar¹, Jurica Sorić^1,*, Tomislav Lesičar¹, Zdenko Tonković¹

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 123-156, 2019, DOI:10.32604/cmes.2019.06562

Abstract A novel multiscale algorithm based on the higher-order continuum at both micro- and macrostructural level is proposed for the consideration of the quasi-brittle damage response of heterogeneous materials. Herein, the microlevel damage is modelled by the degradation of the homogenized stress and tangent stiffness tensors, which are then upscaled to govern the localization at the macrolevel. The C¹ continuity finite element employing a modified case of Mindlin’s form II strain energy density is derived for the softening analysis. To the authors’ knowledge, the finite element discretization based on the strain gradient theory is applied for the modeling of damage evolution… More >

Hao Dong¹, Yufeng Nie^1,2, Zihao Yang¹, Yang Zhang¹, Yatao Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.5, pp. 395-419, 2016, DOI:10.3970/cmes.2016.111.395

Abstract In this paper, we discuss the numerical accuracy of asymptotic homogenization method (AHM) and multiscale finite element method (MsFEM) for periodic composite materials. Through numerical calculation of the model problems for four kinds of typical periodic composite materials, the main factors to determine the accuracy of first-order AHM and second-order AHM are found, and the physical interpretation of these factors is given. Furthermore, the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed, and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions. Finally, numerical experiments verify that MsFEM is… More >

Y. T. Wu¹, Y. F. Nie², Z. H. Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 297-325, 2014, DOI:10.3970/cmes.2014.099.297

Abstract Four representative multiscale methods, namely asymptotic homogenization method (AHM), heterogeneous multiscale method (HMM), variational multiscale (VMS) method and multiscale finite element method (MsFEM), for elliptic problems with multiscale coefficients are surveyed. According to the features they possess, these methods are divided into two categories. AHM and HMM belong to the up–down framework. The feature of the framework is that the macroscopic solution is solved first with the help of effective information computed in local domains, and then the multiscale solution is resolved in local domains using the macroscopic solution when necessary. VMS method andMsFEM fall in the uncoupling framework. The… More >

Louis C. Foucard¹, John Pellegrino¹, Franck J. Vernerey^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.1, pp. 101-127, 2014, DOI:10.3970/cmes.2014.098.101

Abstract Many colloidal-sized particles encountered in biological and membranebased separation applications can be characterized as soft vesicles such as cells, yeast, viruses and surfactant micelles. The deformation of these vesicles is expected to critically affect permeation by accommodating pore shapes and sizes or enhancing the adhesion with a pore surface. Numerical and theoretical modelings will be critical to fully understand these processes and thus design novel filtration membranes that target, not only size, but deformability as a selection criterion. The present paper therefore introduces a multiscale strategy that enables the determination of the permeability of a fibrous network with respect to… More >

Marcin Kamiński^1,2, Bernd Lauke²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 411-440, 2013, DOI:10.3970/cmes.2013.093.411

Abstract The main aim in this paper is a computational study devoted to the sensitivity gradients and probabilistic moments of the effective elastic parameters for the rubber-filled polymers. The methodology is based on least squares recovery of the polynomial functions relating the effective tensor components and the given input design/random parameters. All numerical experiments are provided with respect to Young’s moduli of the elastomer constituents. Computational analysis is possible thanks to the application of the Response Function Method, which is enriched in our approach with the weighting procedures implemented according to the Dirac-type distributions. The homogenized elasticity tensor components are derived… More >

V. Sansalone^1,∗, V. Bousson², S. Naili¹, C. Bergot², F. Peyrin³, J.D. Laredo², G. Haïat¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.5, pp. 387-410, 2012, DOI:10.3970/cmes.2012.087.387

Abstract This paper investigates the effects of the heterogeneous distribution of the Haversian Porosity (HP) and Tissue Mineral Density (TMD) on the elastic coefficients of bone in the human femoral neck. A bone specimen from the inferior femoral neck was obtained from a patient undergoing standard hemiarthroplasty. The specimen was imaged using 3-D synchrotron micro-computed tomography (voxel size of 10.13 mm), leading to the determination of the anatomical distributions of HP and TMD. These experimental data were used to estimate the elastic coefficients of the bone using a three-step homogenization model based on continuum micromechanics: (i) At the tissue scale (characteristic… More >

Lianhua Ma¹, Bernard F. Rolfe², Qingsheng Yang^1,3, Chunhui Yang^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.2, pp. 131-158, 2011, DOI:10.3970/cmes.2011.079.131

Abstract For fluid-filled closed cell composites widely distributed in nature, the configuration evolution and effective elastic properties are investigated using a micromechanical model and a multiscale homogenization theory, in which the effect of initial fluid pressure is considered. Based on the configuration evolution of the composite, we present a novel micromechanics model to examine the interactions between the initial fluid pressure and the macroscopic elasticity of the material. In this model, the initial fluid pressure of the closed cells and the corresponding configuration can be produced by applying an eigenstrain at the introduced fictitious stress-free configuration, and the pressure-induced initial microscopic… More >

Marco Dondero¹, Adrián P. Cisilino^1,2, J. Pablo Tomba¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 225-246, 2011, DOI:10.3970/cmes.2011.078.225

Abstract This paper introduces a numerical methodology for the design of random micro-heterogeneous materials with functionally graded effective thermal conductivities (ETC). The optimization is carried out using representative volume elements (RVEs), a parallel Genetic Algorithm (GA) as optimization method, and a Fast Multipole Boundary Element Method (FMBEM) for the evaluation of the cost function. The methodology is applied for the design of foam-like microstructures consisting of random distributions of circular insulated holes. The temperature field along a material sample is used as objective function, while the spatial distribution of the holes is the design variable. There are presented details of the… More >

J. Cugnoni¹, M. Galli²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 165-186, 2010, DOI:10.3970/cmes.2010.066.165

Abstract With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is… More >