Natural Erosion of Sandstone as Shape Optimisation

Area of Science:

• Geomorphology
• Mechanical Engineering
• Computational Science

Background:

• Natural arches and pillars exhibit complex shapes suggesting intelligent design.
• Recent studies propose negative feedback between stress and erosion as the cause.
• Friction between rock particles is fundamental to these erosional processes.

Purpose of the Study:

• To analyze the negative feedback mechanism in natural erosion.
• To connect erosion processes with shape and topology optimization.
• To confirm the hypothesis using numerical simulations.

Main Methods:

• Deeper analysis of stress-erosion feedback in natural formations.
• Application of shape and topology optimization principles.
• Numerical simulations of erosion using a topological-shape optimization model.

Main Results:

• Natural erosion processes can be framed as local optimization for minimum elastic strain energy.
• The Mohr-Coulomb law of dry friction governs stochastic surface forces.
• Simulations validated the hypothesis of optimized erosion patterns.

Conclusions:

• Stochastic erosion, driven by friction and stress, naturally creates optimized shapes.
• This research provides a framework for understanding exotic landscape formations.
• The findings have implications for identifying similar formations on other planets.