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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the nonlocal formulation of continuum mechanics described byperidynamics. We provide a link between peridynamic evolution and brittlefracture evolution for a broad class of peridynamic potentials associated withunstable peridynamic constitutive laws. Distinguished limits of peridynamicevolutions are identified that correspond to vanishing peridynamic horizon. Thelimit evolution is associated with dynamic brittle fracture and satisfies adynamic energy inequality expressed in terms of the kinetic energy of themotion together with a bulk elastic energy and a Griffith surface energy. Itcorresponds to the simultaneous evolution of elastic displacement and brittlefracture with displacement fields satisfying the wave equation inside thecracking domain. The wave equation provides the dynamic coupling betweenelastic waves and the evolving fracture path inside the media. The elasticmoduli, wave speed and energy release rate for the evolution are explicitlydetermined by moments of the peridynamic influence function and the peridynamicpotential energy.

Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics