Hierarchical model reduction at multiple scales

Filonova

Кузнецов

2012

Self Cite

SUMMARY The manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large. We develop a general purpose computational framework, which is valid for nonlinear problems and requires standard C 0 continuous formalism. The fine‐scale inertia effect is accounted for by formulating a quasi‐dynamic unit cell problem where the fine‐scale inertia effect is represented by so‐called inertia induced eigenstrain. The solution of the nonlinear quasi‐dynamic unit cell problem gives rise to the modification of either coarse‐scale mass matrix in the implicit solvers or internal force in the explicit solvers. Similarly to the classical homogenization theory, scale‐separation is assumed, but higher order homogenization is not pursued to avoid higher order coarse‐scale gradients, higher order continuity, and higher order boundary conditions. Numerical examples for both the one‐dimensional model problem and three‐dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed. Copyright © 2012 John Wiley & Sons, Ltd.

“…Consider the following definition of f μ

f_{i}^{μ} (bold-italicx MathClass-punc, bold-italicy MathClass-punc, t) MathClass-rel= {MathClass-op\int}_{Θ} g_{i}^{kl} (bold-italicy MathClass-punc, \overset{bold-italicy}{true}) μ_{kl}^{normalf} ((), bold-italicx MathClass-punc, \overset{bold-italicy}{true} MathClass-punc, t) normald \overset{Θ}{true} MathClass-punc,

which corresponds to the fine‐scale displacement decomposition

u_{i}^{(1)} (bold-italicx MathClass-punc, bold-italicy MathClass-punc, t) MathClass-rel= H_{i}^{kl} (bold-italicy) ϵ_{kl}^{normalc} (bold-italicx MathClass-punc, t) MathClass-bin+ {MathClass-op\int}_{Θ} g_{i}^{kl} ((), bold-italicy MathClass-punc, \overset{bold-italicy}{true}) μ_{kl}^{normalf} ((), bold-italicx MathClass-punc, \overset{bold-italicy}{true} MathClass-punc, t) normald \overset{Θ}{true} MathClass-punc,

where

g_{i}^{kl}

is y − periodic tensor function with normalization condition 〈 g 〉 Θ = 0 .…”

Section: Residual‐free Dispersive Homogenizationmentioning

confidence: 99%

\begin{matrix} leftalign \\ rightalign-odd u_{i}^{MathClass-open(1 MathClass-close)} MathClass-open(x, y, t MathClass-close) & align-even = H_{i}^{kl} MathClass-open(y MathClass-close) ϵ_{kl}^{c} MathClass-open(x, t MathClass-close) + \sum_{α = 1}^{n} S_{i}^{kl (α)} MathClass-open(y MathClass-close) μ_{kl}^{MathClass-open(α MathClass-close)} (x, t) & rightalign-label (51a) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd S_{i}^{kl MathClass-open(α MathClass-close)} MathClass-open(y MathClass-close) & align-even = \int_{Θ} g_{i}^{kl} (y, y ̃) N^{MathClass-open(α MathClass-close)} (y ̃) d Θ ̃ & rightalign-label (51b) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd \end{matrix}

…”

Section: Residual‐free Dispersive Homogenizationmentioning

confidence: 99%

Micro‐inertia effects in nonlinear heterogeneous media

Filonova

Кузнецов

2012

Self Cite

“…The ROH adopts a piecewise constant approximation of eigenfields (eigenstrains and eigentemperature gradients) over each phase as schematically shown in Figure . For more details, we refer to References for the case of a single physical process. ROH for two physical process, such as a mechanical problem coupled with an oxidation damage in ceramics and titanium or degradation due to moisture ingression in polymers, was studied in References , respectively.…”

Section: Roh Frameworkmentioning

confidence: 99%

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Yuan

Aitharaju

2019

Self Cite

Summary We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo‐chemo‐mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale‐multiphysics approach. To address the enormous computational complexity involved, a reduced‐order homogenization was originally developed for a single physics problem is employed. The proposed reduced‐order two‐scale thermo‐chemo‐mechanical model has been validated for predicting part distortion beam strength in three‐point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.

“…, hereafter referred as the NIAR report. A nonlinear two‐scale analysis has been conducted using the reduced order homogenization method For validation, a nonintrusive stochastic multiscale solver based on the sparse grid collocation approach is employed.…”

Section: Numerical Studiesmentioning

confidence: 99%

An adaptive stochastic inverse solver for multiscale characterization of composite materials

McAuliffe

2016

Self Cite

Summary We present an adaptive variant of the measure‐theoretic approach for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin‐hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC‐12K‐31E and epoxy #2510 material system from the National Institute for Aviation Research report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open‐hole laminates. Copyright © 2016 John Wiley & Sons, Ltd.