Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in
2000. The roots of PD can be traced back to the early works of Gabrio Piola according to …

Computational modeling of the initiation and propagation of complex fracture is central to the
discipline of engineering fracture mechanics. This review focuses on two promising …

Peridynamic models are derived by assuming that a material point is located in the bulk.
Near a surface or boundary, material points do not have a full non-local neighborhood. This …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

The nonlocal Allen--Cahn equation, a generalization of the classic Allen--Cahn equation by
replacing the Laplacian with a parameterized nonlocal diffusion operator, satisfies the …

In this paper, crack propagation and coalescence behaviors in rock specimens containing
pre-existing open flaws under uniaxial compression are investigated using the novel …

The fractional Laplacian (-Δ)^α/2 is a nonlocal operator which depends on the parameter α
and recovers the usual Laplacian as α→2. A numerical method for the fractional Laplacian is …

Many problems in nature, being characterized by a parameter, are of interest both with a
fixed parameter value and with the parameter approaching an asymptotic limit. Numerical …

Efficient and accurate calculation of spatial integrals is of major interest in the numerical
implementation of peridynamics (PD). The standard way to perform this calculation is a …