Relevance to WCCM–ECCOMAS

Peridynamics represents a rapidly growing area in computational mechanics, with increasing relevance to fracture mechanics, multiscale modeling, and nonlocal methods. This course aligns strongly with the WCCM–ECCOMAS focus on advanced computational techniques and provides participants with both theoretical insight and practical skills for next-generation simulation technologies.

Course description

This short course introduces the fundamentals of peridynamic (PD) theory and its application to the modeling and simulation of damage and fracture in materials and structures. Peridynamics is a nonlocal formulation of continuum mechanics that overcomes key limitations of classical partial differential equation–based methods, particularly in problems involving discontinuities such as cracks and progressive failure.

The course begins with an overview of the theoretical foundations of peridynamics, including the derivation of its governing equations from the balance laws of classical continuum mechanics. Both bond-based and state-based formulations are discussed. Numerical discretization strategies, time integration schemes, and computational considerations for solving peridynamic models are then presented.

The second part of the course focuses on practical implementation and engineering applications. Participants will learn how peridynamic models can be coupled with traditional finite element methods within commercial simulation environments such as ANSYS and Abaqus. Through illustrative examples and case studies, the course demonstrates how PD–FE hybrid frameworks can be used for fracture and damage analysis in realistic engineering problems.

Objectives and target groups

By the end of this course, participants will be able to:

• Understand the theoretical principles and governing equations of peridynamic theory.
• Implement basic numerical schemes for peridynamic simulations.
• Apply peridynamic methods to model damage and fracture processes.
• Integrate peridynamic formulations with conventional finite element models in ANSYS and Abaqus.
• Assess the advantages and limitations of peridynamics relative to classical continuum and finite element approaches.

The course is intended for graduate students, researchers, and practicing engineers with a background in computational mechanics, finite element methods, or structural analysis. No prior knowledge of peridynamics is required.

Scientific and technical areas covered

• Peridynamic Theory: Concepts of PD, PD states, PD form of the deformation gradient, force density, PD form of strain energy density function, classification of PD equations of motion, surface effects, boundary conditions, and limitations.
• Peridynamic Differential Operator (PDDO): PD functions and their connection with PD theory.
• Unification of Local and PD Theory: PD equilibrium equations for homogeneous deformation, PD form of local equilibrium and traction equations, and imposition of boundary conditions.
• Failure Prediction: Bond breakage, local damage measures, and critical stretch criteria.
• Numerical Implementation: Spatial discretization, family search algorithms, and explicit and implicit solution schemes.
• PD–FE Coupling: Coupling with finite elements in commercial finite element frameworks, including ANSYS and Abaqus.