The energy density of martensitic thin films via dimension reduction

@inproceedings{Freddi2004TheED,
  title={The energy density of martensitic thin films via dimension reduction},
  author={Lorenzo Freddi and Roberto Paroni},
  year={2004}
}
A variational limit defined on the space of bi-dimensional gradient Young measures is obtained from three-dimensional elasticity via dimension reduction. The obtained limit problem uniquely determines the energy density of the thin film. Our result might be used to compute the microstructure in membranes made of phase transforming material. 

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References

Publications referenced by this paper.
Showing 1-10 of 30 references

Variational models for microstructure and phase transitions., Calculus of variations and geometric evolution problems (Cetraro

S. Müller
Lecture Notes in Math. vol. 1713, • 1996
View 4 Excerpts
Highly Influenced

The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity

H. Le Dret, A. Raoult
J. Math. Pures Appl. 74 • 1995
View 4 Excerpts
Highly Influenced

Theory of diffusionless phase transitions

R. D. James, D. Kinderlehrer
Lecture Notes in Physics vol. 344, Springer • 1989
View 4 Excerpts
Highly Influenced

A theory of thin films of martensitic materials with applications to microactuators

K. Bhattacharya, R. D. James
J. Mech. Phys. Solids 47 • 1999
View 5 Excerpts
Highly Influenced

Proposed experimental tests of a theory of fine microstructure and the two well problem

J. M. Ball, R. D. James
Phil. Trans. R. Soc. London A. 338 • 1992
View 6 Excerpts
Highly Influenced

A version of the fundamental theorem for Young measures

J. M. Ball
PDE’s and continuum models of phase transitions, Lecture Notes in Physics vol. 359, Springer • 1989
View 6 Excerpts
Highly Influenced

Semicontinuity

G. Buttazzo
relaxation and integral representation in the calculus of variations, Pitman Res. Notes Math. Ser., vol. 207, Longman • 1989
View 3 Excerpts
Highly Influenced

Semicontinuity problems in the calculus of variations

E. Acerbi, N. Fusco
Arch. Rational Mech. Anal. 86 • 1984
View 3 Excerpts
Highly Influenced

A 3D-1D Young measure theory of an elastic string, to appear in Asymptot

L. Freddi, R. Paroni
2004
View 1 Excerpt

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