Bounds and estimates on the effective properties for nonlinear composites

Peter Wall

Applications of Mathematics (2000)

  • Volume: 45, Issue: 6, page 419-437
  • ISSN: 0862-7940

Abstract

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In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior.

How to cite

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Wall, Peter. "Bounds and estimates on the effective properties for nonlinear composites." Applications of Mathematics 45.6 (2000): 419-437. <http://eudml.org/doc/33070>.

@article{Wall2000,
abstract = {In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior.},
author = {Wall, Peter},
journal = {Applications of Mathematics},
keywords = {homogenization; effective properties; variational methods; nonlinear composites; homogenization; effective properties; variational methods; nonlinear composites},
language = {eng},
number = {6},
pages = {419-437},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bounds and estimates on the effective properties for nonlinear composites},
url = {http://eudml.org/doc/33070},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Wall, Peter
TI - Bounds and estimates on the effective properties for nonlinear composites
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 6
SP - 419
EP - 437
AB - In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle together with the bounds presented by Lukkassen, Persson and Wall in 1995. Moreover, we also present some examples where the bounds are so tight that they may be used as a good estimate of the effective behavior.
LA - eng
KW - homogenization; effective properties; variational methods; nonlinear composites; homogenization; effective properties; variational methods; nonlinear composites
UR - http://eudml.org/doc/33070
ER -

References

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