Homogenization of stratified thermoviscoplastic materials
Authors:
Nicolas Charalambakis and François Murat
Journal:
Quart. Appl. Math. 64 (2006), 359399
MSC (2000):
Primary 74Q15, 74Q10, 35B27; Secondary 74C10, 74F05, 35Q72, 35M20, 35K55
Published electronically:
May 22, 2006
MathSciNet review:
2243868
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Abstract: In the present paper we study the homogenization of the system of partial differential equations posed in , , completed by boundary conditions on and by initial conditions on and . The unknowns are the velocity and the temperature , while the coefficients , and are data which are assumed to satisfy This sequence of onedimensional systems is a model for the homogenization of nonhomogeneous, stratified, thermoviscoplastic materials exhibiting thermal softening and a temperaturedependent rate of plastic work converted into heat. Under the above hypotheses we prove that this system is stable by homogenization. More precisely one can extract a subsequence for which the velocity and the temperature converge to some homogenized velocity and some homogenized temperature which solve a system similar to the system solved by and , for coefficients , and which satisfy hypotheses similar to the hypotheses satisfied by , and . These homogenized coefficients , and are given by some explicit (even if sophisticated) formulas. In particular, the homogenized heat coefficient in general depends on the temperature even if the heterogeneous heat coefficients do not depend on it.
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 J. Aboudi, M. Pindera, and S.M. Arnold, Higherorder theory for functionally graded materials, Composite Part B (Engineering) 30 (1999), 777832.
 2.
 J. Aboudi, M. Pindera, and S.M. Arnold, Higherorder theory for periodic multiphase materials with inelastic phases, Int. J. Plasticity 19 (2003), 805847.
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 Y. Bansal and M.J. Pindera, A second look at the higherorder theory for periodic multiphase materials, J. Appl. Mech. 72 (2005), 177195.
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 R.C. Batra and B.M. Love, Adiabatic shear bands in functionally graded materials, J. Thermal Stresses 27 (2004), 11011123.
 5.
 T. Baxevanis, T. Katsaounis, and A. Tzavaras, A finite element method for computing shear band formation, in Proceedings of the International Hyperbolic Conference (Osaka 2004), Yokohama Publ., Yokohama, to appear.
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 J. Hodowany, G. Ravichandran, A.J. Rosakis, and P. Rosakis, Partition of plastic work into heat and stored energy in metals, J. Exp. Mech. 40 (2000), 113123.
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 17.
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Additional Information
Nicolas Charalambakis
Affiliation:
Department of Civil Engineering, Aristotle University, GR 54124 Thessaloniki, Greece
Email:
charalam@civil.auth.gr
François Murat
Affiliation:
Laboratoire JacquesLouis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France
Email:
murat@ann.jussieu.fr
DOI:
http://dx.doi.org/10.1090/S0033569X06010173
PII:
S 0033569X(06)010173
Keywords:
Homogenization,
thermoviscoplastic materials
Received by editor(s):
December 1, 2005
Published electronically:
May 22, 2006
Article copyright:
© Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.
