This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation.  PD is a bridge between differentiation and integration.  It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities.  PD also serves as a natural filter to smooth noisy data and to recover missing data.

This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error.  The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations.  It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions.  It also presents an alternative approach for the PD differential operator based on the least squares minimization.

Peridynamic  Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications.  Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.

This book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements. It details the implementation of the PD theory and its integration with traditional finite elements. The primary objective is to equip students, researchers, and practicing engineers with both theoretical and practical knowledge of the PD theory, along with the skills necessary for analyzing engineering problems using Ansys.

The book demonstrates that, unlike the conventional finite element method (FEM), the PD theory is highly suitable for progressive failure analysis, the multi-scale analysis of materials involving fracture and failure, and multi-physics analysis, including electromigration, corrosion, and electrodeposition. Additionally, it provides a step-by-step illustration of the specific procedures in the pre-processing, solution, and post-processing phases of the analysis through the Graphical User Interface (GUI) for various applications.

The book is designed to be introductory and self-contained, minimizing the need for additional reference material.

This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation.  PD is a bridge between differentiation and integration.  It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities.  PD also serves as a natural filter to smooth noisy data and to recover missing data.

This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error.  The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations.  It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions.  It also presents an alternative approach for the PD differential operator based on the least squares minimization.

Peridynamic  Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications.  Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.

This book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements. It details the implementation of the PD theory and its integration with traditional finite elements. The primary objective is to equip students, researchers, and practicing engineers with both theoretical and practical knowledge of the PD theory, along with the skills necessary for analyzing engineering problems using Ansys.

The book demonstrates that, unlike the conventional finite element method (FEM), the PD theory is highly suitable for progressive failure analysis, the multi-scale analysis of materials involving fracture and failure, and multi-physics analysis, including electromigration, corrosion, and electrodeposition. Additionally, it provides a step-by-step illustration of the specific procedures in the pre-processing, solution, and post-processing phases of the analysis through the Graphical User Interface (GUI) for various applications.

The book is designed to be introductory and self-contained, minimizing the need for additional reference material.