Evaluating the effects of nonlocality and numerical discretization in peridynamic solutions for quasi-static elasticity and fracture

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Peridynamics (74A70)

Cites Work

Studies of dynamic crack propagation and crack branching with peridynamics
Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations
Reformulation of elasticity theory for discontinuities and long-range forces
Numerical methods for the nonlocal wave equation of the peridynamics
Surface corrections for peridynamic models in elasticity and fracture
Convergence studies in meshfree peridynamic simulations
Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics
A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture
A discussion on nonlocality: from fractional derivative model to peridynamic model
Onto resolving spurious wave reflection problem with changing nonlocality among various length scales
Overall equilibrium in the coupling of peridynamics and classical continuum mechanics
A constructive peridynamic kernel for elasticity
Wellposedness of a nonlinear peridynamic model
Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics
New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics
The peridynamics-based finite element method (PeriFEM) with adaptive continuous/discrete element implementation for fracture simulation
Dispersive effects in two- and three-dimensional peridynamics
A peridynamic model for advection-reaction-diffusion problems
On the one-point quadrature discretization in peridynamics: a novel perspective from Monte Carlo integration
A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) Schemes
Analytical solutions of peridynamic equations. II: Elastic wave propagation

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