Applicability of micro–macro decoupling scheme to two-scale analysis of fiber-reinforced plastics

Summary This study presents an isogeometric framework for incorporating representative volume element–based multiscale models into computational homogenization. First‐order finite deformation homogenization theory is derived within the framework of the method of multiscale virtual power, and Lagrange multipliers are used to illustrate the effects of considering different kinematical constraints. Using a Lagrange multiplier approach in the numerical implementation of the discrete system naturally leads to a consolidated treatment of the commonly employed representative volume element boundary conditions. Implementation of finite deformation computational strain‐driven, stress‐driven, and mixed homogenization is detailed in the context of isogeometric analysis (IGA), and performance is compared to standard finite element analysis. As finite deformations are considered, a numerical multiscale stability analysis procedure is also detailed for use with IGA. Unique implementation aspects that arise when computational homogenization is performed using IGA are discussed, and the developed framework is applied to a complex curved microstructure representing an architectured material.

Section: B-splines and Nurbsmentioning

confidence: 99%

A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis

Alberdi

Zhang

Khandelwal

2018

“…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%

“…In general, the targets of the NMT are not limited to linear problems. However, for nonlinear cases, the macroscopic constitutive equations, which resembles the NMT results, have to be assumed first with reference to the material models used for the constituent materials in a unit cell, and then the parameters must be identified with an alternative route; see . That is, when elastic‐plastic materials are used for the constituent materials, the macroscopic material behavior must be elastic‐plastic, but possibly exhibit anisotropy and some effects of residual stresses .…”

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%

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

Matsubara

Terada

2016

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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.

“…The so-called multi-scale analysis to solve the two-scale BVP is often referred to as Accepted Article decoupling method is amenable to various nonlinear material models and geometrical nonlinear problems; see Terada et al [29] for application to inelastic materials.…”

Section: Introductionmentioning

confidence: 99%

Micro‐macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis

Kato

Yachi

Kyoya

et al. 2017

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SUMMARYThe present study proposes a method of micro-macro concurrent topology optimization for a two-phase nonlinear solid to minimize the end compliance of its macrostructure undergoing large deformation. In order to reduce the computational costs to solve a two-scale boundary value problem (BVP) under geometrically nonlinear setting, we employ the so-called method of decoupling multi-scale structural analysis, in which the micro-and macroscopic BVPs are decoupled in terms of the homogenization process. An isotropic hyperelasticity model is employed for the constitutive model for microstructures, while an orthotropic one is assumed to represent the macroscopic material behavior. Owing to this decoupling framework, the micromacro concurrent optimization problem can be split into two individual problems at the micro-and macroscales for the sake of algorithmic simplicity. Also, a two-scale adjoint sensitivity analysis can be performed within the framework of computational homogenization. It is verified from a series numerical examples that the proposed method is capable of computing the optimal structures at both micro-and macro-scales, according to the level of applied load.