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 …

Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

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

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 …

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 nonlocal operator method is proposed which is generally applicable for solving partial
differential equations (PDEs) of mechanical problems. The nonlocal operator can be …

A higher order nonlocal operator method for the solution of boundary value problems is
developed. The proposed higher order nonlocal operator brings several advantages as …

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