English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Recently, the existence and properties of unbounded cavity modes, resultingin extensive plastic deformation failure of two-dimensional sheets of amorphousmedia, were discussed in the context of the athermal Shear-Transformation-Zones(STZ) theory. These modes pertain to perfect circular symmetry of the cavityand the stress conditions. In this paper we study the shape stability of theexpanding circular cavity against perturbations, in both the unbounded and thebounded growth regimes (for the latter the unperturbed theory predicts nocatastrophic failure). Since the unperturbed reference state is time dependent,the linear stability theory cannot be cast into standard time-independenteigenvalue analysis. The main results of our study are: (i) sufficiently smallperturbations are stable, (ii) larger perturbations within the formal lineardecomposition may lead to an instability; this dependence on the magnitude ofthe perturbations in the linear analysis is a result of the non-stationarity ofthe growth, (iii) the stability of the circular cavity is particularlysensitive to perturbations in the effective disorder temperature; in thiscontext we highlight the role of the rate sensitivity of the limiting value ofthis effective temperature. Finally we point to the importance of the form ofthe stress-dependence of the rate of STZ transitions. The present analysisindicates the importance of nonlinear effects that were not taken into accountyet. Even more importantly, the analysis suggests that details of theconstitutive relations appearing in the theory can be constrained by the modesof macroscopic failure in these amorphous systems.

The Stability of an Expanding Circular Cavity and the Failure of Amorphous Solids