A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials

Terada, Kenjiro; Kato, Junji; Hirayama, Norio; Inugai, Takenori; Yamamoto, Koji

doi:10.1007/s00466-013-0872-5

Cited by 80 publications

(75 citation statements)

References 30 publications

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“…One of the main driving forces behind the advancement of multiscale techniques is the pressing need for more accurate computational tools for prediction of material response in situations where the macroscale effects of complex micro-scale mechanisms cannot be easily captured by the conventional phenomenological modelling approach. In this context, computational RVE-based methods can be used either in the simulation of macroscopic structures by a coupled multiscale approach (often referred to as FE 2 ) or as a basis for the development of new phenomenological models, or calibration of material parameters of existing models, by means of so-called numerical material testing [32,38,94,113,119,120,129]. An interesting application in this context is the development of constitutive laws for micromorphic materials [27,28,31,50,51].…”

Section: Current Trends and Perspectivesmentioning

confidence: 99%

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Blanco

Sánchez

Neto

et al. 2014

Arch Computat Methods Eng

142

113

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A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro-and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force-and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the wellknown Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force-and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.

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Section: Current Trends and Perspectivesmentioning

confidence: 99%

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Blanco

Sánchez

Neto

et al. 2014

Arch Computat Methods Eng

142

113

View full text Add to dashboard Cite

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“…Numerical material testing, which is a term coined by the authors , is nothing but microscopic analysis within the framework of computational homogenization and can be recognized as homogenization analysis in the context of mutliscale analysis. Because the purpose of the testing is to evaluate the macroscopic material properties for realistic composite materials and is exactly the same as actual material testing, we prefer to using NMT rather than VT sometimes used in the literature .…”

Section: Homogenizationmentioning

confidence: 99%

“…A representative volume element (RVE), which contains enough information of micro‐scale heterogeneities, is used to characterize the macroscopic material behavior of composite materials. Homogenization analysis with FEM conducted on a RVE can be regarded as numerical material testing (NMT) or numerical plate testing (NPT) , in which a periodic or in‐plane periodic microstructure (unit cell) is employed as a RVE and used to resemble a specimen. Because the NMT, is also referred to as the virtual testing (VT) in the literature , is usually a finite element analysis (FEA) for the periodic boundary conditions (PBCs) on the displacement fields, the reliability of macroscopic material characterization is determined by the setting for the numerical models of unit cells.…”

Section: Introductionmentioning

confidence: 99%

On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis

Matsubara

Terada

2016

Numerical Meth Engineering

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Summary The treatments of heterogeneities and periodic boundary conditions are explored to properly perform isogeometric analysis (IGA) based on NURBS basis functions in solving homogenization problems for heterogeneous media with omni‐directional periodicity and composite plates with in‐plane periodicity. Because the treatment of the combination of different materials in IGA models is not trivial especially for periodicity constraints, the first priority is to clearly specify points at issue in the numerical modeling, or equivalently mesh generation, for IG homogenization analysis (IGHA). The most awkward, but important issue is how to generate patches for NURBS representation of the geometry of a rectangular parallelepiped unit cell to realize appropriate deformations in consideration of the convex‐hull property of IGA. The issue arises from the introduction of overlapped control points located at angular points in the heterogeneous unit cell, which must satisfy multiple point constraint (MPC) conditions associated with periodic boundary conditions (PBCs). Although two measures may be conceivable, we suggest the use of multiple patches along with double MPC that imposes PBCs and the continuity conditions between different patches simultaneously. Several numerical examples of numerical material and plate tests are presented to demonstrate the validity of the proposed strategy of IG modeling for IGHA. Copyright © 2016 John Wiley & Sons, Ltd.

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“…A first straightforward approach, inspired by classical experimental identifications procedures, uses virtual tests on RVEs through numerical computations to identify empirical macroscopic constitutive laws (see, e.g., recent contributions in Terada et al, 2013Terada et al, , 2014. However, classifying such procedures as homogenization is questionable.…”

Section: Decoupled Computational Homogenization Methodsmentioning

confidence: 99%

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Geers

Kouznetsova

Matouš

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

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A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials

Cited by 80 publications

References 30 publications

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

On the treatments of heterogeneities and periodic boundary conditions for isogeometric homogenization analysis

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

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