Dynamics of singularities in a constrained elastic plate.

Area of Science:

• Mechanics of Materials
• Solid Mechanics
• Elasticity Theory

Background:

• Large deformations in thin elastic plates commonly result in singular structures, such as linear ridges or point-like developable cones.
• These singularities are considered generic in crumpled plates but have been studied mainly in simplified geometries.
• Previous research indicates that sequential instabilities can generate a significant number of these singularities.

Purpose of the Study:

• To experimentally and numerically investigate the generation and behavior of singularities in a generic large deformation scenario of thin elastic plates.
• To analyze the position and dynamics of singularity pairs induced by a specific deformation process.
• To understand the relationship between singularity formation and the plate's resistance to deformation.

Main Methods:

• Experimental deformation of thin elastic plates.
• Numerical simulation of large plate deformations using governing equations.
• Geometrical analysis to predict observed singularity patterns.

Main Results:

• The study observed the generation of singularity pairs when a plate, initially bent into a cylindrical arch, was deformed by a central load.
• Numerical simulations accurately predicted the formation of developable cones, showing quantitative agreement with experimental results.
• Geometrical arguments, based on the assumption that plate energy is dominated by singularity energy, successfully predicted the observed patterns.

Conclusions:

• The research provides a quantitative understanding of singularity generation in a generic large deformation scenario for thin elastic plates.
• The findings confirm the formation of developable cones and their agreement with experimental observations.
• The study highlights the importance of singularity energy in predicting the behavior of deformed elastic plates.