The Relaxation of Two-well Energies with Possibly Unequal Moduli

@inproceedings{Chenchiah2007TheRO,
  title={The Relaxation of Two-well Energies with Possibly Unequal Moduli},
  author={Isaac Vikram Chenchiah and Kaushik Bhattacharya},
  year={2007}
}
The elastic energy of a multiphase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution, and optimal design. Mathematically, the problem is to determine the relaxation under fixed phase fraction of a multiwell energy. This paper addresses two such problems in the geometrically linear setting… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 54 REFERENCES

Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions

  • G. Allaire, R. V. Kohn
  • Q. Appl. Math. 12(4), 643–674
  • 1993
Highly Influential
24 Excerpts

On a certain variational problem of phase equilibrium

  • K. A. Lurie, A. V. Cherkaev
  • Material instabilities in continuum mechanics
  • 1986
Highly Influential
13 Excerpts

Calcul des variations et homogénéisation [Calculus of variations and homogenization

  • F. Murat, L. Tartar
  • Collection de la Direction des Études et…
  • 1983
Highly Influential
7 Excerpts

The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites

  • A. V. Cherkaev, L. V. Gibiansky
  • Proc. R. Soc. Edinb. Sect. A 122(1–2), 93–125
  • 1992
Highly Influential
5 Excerpts

Elastic materials with two preferred states

  • A. C. Pipkin
  • Q. J. Mech. Appl. Math. 44(1), 1–15
  • 1991
Highly Influential
5 Excerpts

Optimal use of the translation method and relaxations of variational problems

  • N. B. Firoozye
  • Commun. Pure Appl. Math. 44, 643–678
  • 1991
Highly Influential
4 Excerpts

The relaxation of a double-well energy

  • R. V. Kohn
  • Contin. Mech. Thermodyn. 3, 193–236
  • 1991
Highly Influential
5 Excerpts

A survey on compensated compactness

  • F. Murat
  • Cesari) Longman Scientific and Technical,
  • 1987
Highly Influential
4 Excerpts

Microstructures of composites of extremal rigidity and exact bounds on the associated energy density

  • L. V. Gibiansky, A. V. Cherkaev
  • Technical Report 1115,
  • 1987
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…