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Matched asymptotic solution for crease nucleation in soft solids
P Ciarletta1,2
1MOX Laboratory, Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133, Milano, Italy. pasquale.ciarletta@polimi.it.
Nature Communications
|February 7, 2018
Summary
Soft solids develop creases under compression, a nonlinear instability distinct from buckling. This study analytically predicts crease nucleation thresholds, matching experimental and numerical results.
Area of Science:
- Solid mechanics
- Material science
- Nonlinear elasticity
Background:
- Soft solids exhibit creases (self-contacting folds) under large compression.
- Creasing is a nonlinear material instability, distinct from elastic instabilities like buckling or wrinkling.
Purpose of the Study:
- To provide theoretical insights into the physics of crease nucleation in soft solids.
- To analytically predict the nucleation threshold for creasing.
Main Methods:
- Theoretical analysis of nonlinear material instability.
- Global bifurcation analysis to identify co-existing deformation states.
- Matched asymptotic solution in the intermediate region.
Main Results:
- Creasing occurs via a global bifurcation, allowing co-existing outer and inner solutions.
- Analytic prediction of the crease nucleation threshold shows excellent agreement with experiments and simulations.
- Derived analytic expressions for the matched asymptotic solution and its validity range.
Conclusions:
- Crease nucleation in soft solids is a fully nonlinear phenomenon akin to phase transformation.
- The study provides a fundamental analytic prediction for crease nucleation thresholds.
- Self-contact plays a crucial role, analogous to disturbances in fluid dynamics solutions.
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