Scale and nature of sulcification patterns

Area of Science:

• Materials Science
• Soft Matter Physics
• Mechanics of Materials

Background:

• Sulci are surface folds observed in strained soft elastomers.
• Their formation is driven by a strongly subcritical, scale-free instability.
• Understanding the underlying physics of sulcus pattern selection is crucial.

Purpose of the Study:

• To explain the nature of sulcus patterns in soft elastomers.
• To analyze the role of scale and translation symmetries in sulcus formation.
• To investigate the influence of boundary conditions on the bifurcation nature of sulcus formation.

Main Methods:

• Development of a perturbative theory.
• Conducting numerical simulations.
• Analysis of nonlinear instability as a nonlinear critical point.

Main Results:

• Sulcus formation can occur as a supercritical or weakly subcritical bifurcation.
• The specific bifurcation type depends on the boundary conditions of the compressed slab.
• An infinite number of equilibrium patterns emerge at the critical point, with the lowest energy pattern being selected.

Conclusions:

• Sulcus pattern selection in elastomers can be understood by analyzing broken symmetries at a nonlinear critical point.
• The formation process is analogous to a solid-solid phase transition.
• Boundary conditions dictate whether sulcus formation is supercritical or subcritical.