Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Peridynamics via finite element analysis
Finite Elements in Analysis and Design
Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
SIAM Journal on Numerical Analysis
A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
Journal of Computational Physics
Discretized peridynamics for linear elastic solids
Computational Mechanics
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An alternative theory of solid mechanics, known as the peridynamic theory, formulates problems in terms of integral equations rather than partial differential equations. This theory assumes that particles in a continuum interact with each other across a finite distance, as in molecular dynamics. Damage is incorporated in the theory at the level of these two-particle interactions, so localization and fracture occur as a natural outgrowth of the equation of motion and constitutive models. A numerical method for solving dynamic problems within the peridynamic theory is described. Accuracy and numerical stability are discussed. Examples illustrate the properties of the method for modeling brittle dynamic crack growth.