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Micro‐inertia effects in nonlinear heterogeneous media
Author(s) -
Fish Jacob,
Filonova Vasilina,
Kuznetsov Sergey
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4322
Subject(s) - homogenization (climate) , inertia , nonlinear system , eigenstrain , continuum hypothesis , mathematics , boundary value problem , mathematical analysis , classical mechanics , physics , materials science , composite material , biodiversity , ecology , residual stress , biology , quantum mechanics
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.