Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model

Ghosh, Somnath; Lee, Kyung-Hoon; Moorthy, Suresh

doi:10.1016/0045-7825(95)00974-4

Cited by 280 publications

(150 citation statements)

References 30 publications

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“…In the spirit of the latter, there is a direct coupling between macro model and micro models. Figure (21) gives an schematic representation of existing computational homogenization methods for bulk material [6,7,5,8], material layers (or interfaces) [13,15,14,12] and cohesive cracks [17]. This section presents computational homogenization schemes for both cohesive and adhesive cracks using the homogenization relations developed in Section 4.…”

Section: Bulk Homogenizationmentioning

confidence: 99%

“…When implemented in a finite element (FE) framework, the method is known as an FE 2 [5] scheme. Although the method is computationally expensive, it has been proved to be a valuable and flexible (due to the lack of an assumption on the macroscopic constitutive model) tool for analyzing a wide range of heterogeneous materials with complex microstructures with highly nonlinear behavior see, among others, [6,7,8] and [9] for a recent review. An open source program for homogenization problems has recently been made available [10].…”

Section: Introductionmentioning

confidence: 99%

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Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Nguyen

Lloberas-Valls

Stroeven

et al. 2011

Computer Methods in Applied Mechanics and Engineering

137

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The existence of a representative volume element (RVE) for a class of quasi-brittle materials having a random heterogeneous microstructure in tensile, shear and mixed mode loading is demonstrated by deriving traction-separation relations, which are objective with respect to RVE size. A computational homogenization based multiscale crack modelling framework, implemented in an FE 2 setting, for quasi-brittle solids with complex random microstructure is presented. The objectivity of the macroscopic response to the micro sample size is shown by numerical simulations. Therefore, a homogenization scheme, which is objective with respect to macroscopic discretization and microscopic sample size, is devised. Numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method.

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Section: Bulk Homogenizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Nguyen

Lloberas-Valls

Stroeven

et al. 2011

Computer Methods in Applied Mechanics and Engineering

137

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“…This subdomain is adaptively seeded in regions where macroscopic variables in level-0 simulations have locally high gradients of key variables. Level-1 subdomains utilize asymptotic expansion and SERVE periodicity 3,4,11 to decouple the macroscopic and micro-SERVE problems for analyzing macroscopic and microscopic variables. Macroscopic finite-element analysis is done using the HCPD constitutive model, whereas micromechanical analysis of the SERVE, e.g., in Fig.…”

Section: Homogenization-based Continuum Plasticitydamage Constitutivementioning

confidence: 99%

“…10b by using AEH. 4,26,28 The microscale problem involves identification of a SERVE and subsequent micromechanical analyses with LE-VCFEM). 35,36 Parameters of the HCP model are calibrated from homogenization of evolving variables in the SERVE of Fig.…”

Section: Dual-stage Nested Homogenization For Rate-dependent Hcp Modementioning

confidence: 99%

Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials

Ghosh

2014

JOM

Self Cite

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This article addresses two topics on multiscale modeling of heterogeneous metals and alloys. The first topic focuses on developing an adaptive hierarchical-concurrent multilevel modeling framework for ductile fracture. The microstructure of aluminum alloys, for example, is characterized by a dispersion of heterogeneities such as silicon and intermetallics in a ductile aluminum matrix. The multilevel model invokes two-way coupling, viz. hierarchical models for homogenized constitutive modeling and concurrent models with scale transition in regions of localization and damage. Adaptivity is necessary for evolving microstructural deformation and damage. A macroscopic analysis in regions homogeneity incorporates homogenization-based continuum plasticity-damage models. A microscopic analysis using locally enhanced-Voronoi cell finite-element method is required for regions of high macroscopic gradients caused by underlying localized plasticity and damage. Coupled macroscopic and microscopic analysis is conducted concurrently. Physics-based level change criteria are developed to improve accuracy and efficiency. The second topic discusses a nested dual-stage homogenization method for microstructure-based homogenized continuum plasticity models for cast aluminum alloys with large secondary dendrite arm spacing. Two distinct statistically equivalent representative volume elements are identified and used in the asymptotic expansion-based homogenization and self-consistent homogenization processes, respectively. The two-stage homogenization enables an evaluation of the overall homogenized model of a cast alloy from limited experimental data, as well as material properties of constituents like interdendritic phase and pure aluminum matrix.

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“…In techniques of this type, e.g. [58,16,61,14,57,41,42,38,8,9,62,15,28], among others, the macroscopic deformation (gradient) tensor is calculated for every material point of the macrostructure and is next used to formulate kinematic boundary conditions to be applied on the associated microstructural representative volume element (RVE). After the solution of the microstructural boundary value problem, the macroscopic stress tensor is obtained by averaging the resulting microstructural stress field over the volume of the microstructural cell.…”

Section: Introductionmentioning

confidence: 99%

The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains

Yvonnet¹,

He²

2007

Journal of Computational Physics

271

164

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To cite this version:Julien Yvonnet, Qi-Chang He. The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains. AbstractThis paper presents a new multi-scale method for the homogenization analysis of hyperelastic solids undergoing finite strains. The key contribution is to use an incremental nonlinear homogenisation technique in tandem with a model reduction method, in order to alleviate the complexity of multiscale procedures, which usually involve a large number of nonlinear nested problems to be solved. The problem associated with the Representative Volume Element (RVE) is solved via a model reduction method (Proper Orthogonal Decomposition). The reduced basis is obtained through pre-computations on the RVE. The technique, coined as Reduced Model Multiscale Method (R3M), allows reducing significantly the computation times, as no large matrix needs to be inverted, and as the convergence of both macro and micro problems is enhanced. Furthermore, the R3M drastically reduces the size of the data base describing the history of the micro problems. In order to validate the technique in the context of porous elastomers at finite strains, a comparison between a full and a reduced multiscale analysis is performed through numerical examples, involving different micro and macro structures, as well as different nonlinear models (Neo-Hookean, Mooney-Rivlin). It is shown that the R3M gives good agreement with the full simulations, at lower computational and data storage requirements.

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Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model

Cited by 280 publications

References 30 publications

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials

The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains

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