Pattern Selection in Biaxially Stressed Solids

We analyze the morphological instability of the surface of a solid which is subject to a biaxial stress. The stability calculation reveals a new favored pattern: a diamond morphology. This occurs if the stress is tensile in one direction and compressive in the orthogonal one and the ratio exceeds a certain value. A nonlinear analysis shows that the bifurcation is subcritical and hints to a nontrivial competition between tilted stripes and diamonds. This study opens a new line of inquiries in the field of stress-induced pattern selection.

Figure 1

Stressed solid in contact with its melt.

Figure 2

Phase diagram of the biaxially stressed solid (see text).

Figure 3

Elastic part of the chemical potential as a function of $\theta$ for different values of ${\sigma }_{0Y}$ at constant ${\sigma }_{0X}$. Dashed lines and dotted lines correspond to a shear stress, respectively, below and above the transition.