Scaling of the Energy for Thin Martensitic Films

Nirmalendu Chaudhuri, Stefan Müller
2006 SIAM Journal on Mathematical Analysis  
We study the scaling behaviour of thin martensitic films. Specifically we consider an elastic energy with two SO(3) invariant wells which are strongly incompatible in the sense of Matos andŠverák, but whose two-dimensional projections are compatible. We show that in a thin film of thickness the energy per unit height scales like h. This scaling lies in between the classical membrane theory (where the energy per unit height is of order 1) and the Kirchhoff bending theory, which corresponds to a
more » ... h corresponds to a scaling of h 2 .
doi:10.1137/04061581x fatcat:h5cc7m6rpvbvdouexmhfw7ddea