A model for the fragmentation kinetics of crumpled thin sheets

Area of Science:

• Physics of materials science
• Complex systems dynamics
• Geometric frustration phenomena

Background:

• Confined thin sheets spontaneously segment into facets bounded by ridges during crumpling.
• Statistical properties of crumpled sheets display remarkable reproducibility despite apparent disorder.
• Experiments show total crease length increases logarithmically with repeated compaction and unfolding.

Purpose of the Study:

• To provide physical insight into the reproducible statistical properties of crumpled sheets.
• To explore the connection between crumpling and fragmentation processes.
• To explain the logarithmic scaling of crease length in crumpled paper.

Main Methods:

• Developed a physical model for the evolution of facet area and ridge length distributions.
• Proposed a re-fragmentation mechanism driven by geometric frustration.
• Investigated a feedback loop where facet size distribution influences fragmentation rate.

Main Results:

• The model successfully describes the evolution of facet and ridge distributions.
• Identified a re-fragmentation mechanism driven by geometric frustration.
• Demonstrated the model's ability to reproduce the logarithmic crease length scaling.

Conclusions:

• The proposed fragmentation mechanism provides a physical basis for the observed logarithmic crease length accumulation.
• The study offers a new understanding of the statistical mechanics of crumpling.
• Geometric frustration plays a key role in the self-organizing properties of crumpled sheets.