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 …

Publisher Summary The classical theory of solid mechanics is based on the assumption of a
continuous distribution of mass within a body and all internal forces are contact forces that …

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a
reformulation of continuum mechanics based on integration of interactions rather than …

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 …

A recently developed nonlocal vector calculus is exploited to provide a variational analysis
for a general class of nonlocal diffusion problems described by a linear integral equation on …

A vector calculus for nonlocal operators is developed, including the definition of nonlocal
divergence, gradient, and curl operators and the derivation of the corresponding adjoint …

In this paper we survey some results on the Dirichlet problem \left{_u=g^Lu=f_inR^n\Ω^inΩ\
right. for nonlocal operators of the form Lu\left(x\right)=PVR^n\left{u\left(x\right) …

Fractional differential equations are becoming increasingly used as a powerful modelling
approach for understanding the many aspects of nonlocality and spatial heterogeneity …

In contrast to classical partial differential equation models, the recently developed
peridynamic nonlocal continuum model for solid mechanics is an integro-differential …