Computational Methods Based On Peridynamics And Nonlocal Operators Theory And Applications Timon Rabczuk by Timon Rabczuk, Huilong Ren, Xiaoying Zhuang 9783031209055, 3031209052 instant download after payment.

Among the nonlocal models, Peridynamics (PD) attracts much attention in
the field of fracture mechanics. One key feature of PD is the
nonlocality, which is quite different from the ideas in conventional
methods such as FEM and meshless methods. However, conventional PD
suffers from problems such as constant horizon, explicit algorithm,
hourglass mode. In this book, by examining the nonlocality with
scrutiny, we proposed several newconcepts such as Dual-Horizon (DH) in
PD, Dual-Support (DS) in smoothed particle hydrodynamics (SPH), nonlocal
operators and operator energy functional. The conventional PD (SPH) is
incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous
discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can
be viewed as some fundamental improvement on the conventional PD (SPH).
Dual formulation of PD
and SPH allows h-adaptivity while satisfying the conservation of linear momentum, angular momentum and energy.
By
developing the concept of nonlocality further,we introduced the
nonlocal operator method as a  generalization of DH-PD (DS-SPH).
Combined with energy functional of various physical models, the nonlocal
forms based on dual-support concepts are derived. In addition, the
variation of the energy functional allows implicit formulation of the
nonlocal theory. The introduction of dual-support is a mathematical
innovation. Traditional integral equation is formulated in an integral
domain. Dual-support is actually the dual-integral domain in
mathematics. It is as well a natural consequence of the nonlocal model
under the variationally derivation. Meanwhile, we developed the higher
order nonlocal operator method which is capable of solving
higher order partial differential equations on arbitrary domains in higher dimensional space.