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Related Experiment Video

Updated: Jun 29, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

Finite-time singularities in surface-diffusion instabilities are cured by plasticity.

Ting-Shek Lo¹, Anna Pomyalov, Itamar Procaccia

¹Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

External stress causes material surfaces to become unstable, leading to shape changes. Plasticity in materials prevents a singularity, transforming it into a regular crack, a key finding for material science.

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The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Area of Science:

Materials Science
Solid Mechanics
Surface Physics

Background:

Free material surfaces supporting surface diffusion are susceptible to instability under nonhydrostatic stress.
Stress concentration within indentations increases chemical potential, driving material diffusion.
Elastic materials under stress may exhibit instabilities leading to finite-time cusp singularities.

Purpose of the Study:

To investigate the effect of plastic deformation on surface instabilities driven by stress.
To determine if plastic effects can alter the predicted cusp singularity in stressed surfaces.
To analyze the transition from singular instability to crack formation in materials.

Main Methods:

Theoretical analysis of surface diffusion under nonhydrostatic stress.
Modeling of material behavior incorporating both elastic and plastic deformation.
Mathematical investigation of instability evolution and singularity formation.

Main Results:

Surface instabilities are initiated by stress concentrations in indentations, causing material to diffuse outwards.
Plastic effects in the bulk material modify the instability dynamics.
The predicted finite-time cusp singularity is resolved by plasticity, leading to a regular crack formation.

Conclusions:

Plasticity plays a crucial role in stabilizing stressed material surfaces against singular instabilities.
The transition from cusp singularity to a regular crack is a direct consequence of incorporating plastic deformation.
This finding has implications for understanding material failure and surface evolution under mechanical load.