Handbook of Peridynamic Modeling

Florin Bobaru, John T. Foster, Philippe H Geubelle, Stewart A. Silling, Florin Bobaru, John T. Foster, Philippe H Geubelle, Stewart A. Silling

• Publisher: Chapman and Hall/CRC
• Year: 2016
• Print ISBN: 9780367424916
• eBook ISBN: 9781315355948
• Edition: 1
• Topic: Mathematics
• Subtopic: Mechanical Engineering
• Index: Mathematics

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.

Part III

Material Models and Links to Atomistic Models

Chapter 6

Constitutive Modeling in Peridynamics

John T. Foster

The University of Texas at Austin

CONTENTS

6.1 Introduction

6.2 Kinematics, momentum conservation, and terminology

6.3 Linear peridynamic isotropic solid

6.3.1 Plane elasticity

6.3.1.1 Plane stress

6.3.1.2 Plane strain

6.3.2 “Bond-based” theories as a special case

6.3.3 On the role of the influence function

6.3.4 Other elasticity theories

6.4 Finite Deformations

6.4.1 Invariants of peridynamic scalar-states

6.5 Correspondence models

6.5.1 Non-ordinary correspondence models for solid mechanics

6.5.2 Ordinary correspondence models for solid mechanics

6.6 Plasticity

6.6.1 Yield surface and flow rule

6.6.2 Loading/unloading and consistency

6.6.3 Discussion

6.7 Non-ordinary models

6.7.1 A non-ordinary beam model

6.7.2 A non-ordinary plate/shell model

6.7.3 Other non-ordinary models

6.8 Final Comments

References

6.1 Introduction

The peridynamic theory of solid mechanics was originated by Silling [53, 60] as a reformulation of classical elasticity * primarily motivated by the desire to replace the spatial derivatives in the governing equations with an integral functional that provides mathematical consistency with the nature of displacement discontinuities (e.g., cracks) in an otherwise continuously deforming body. Numerical simulations conducted with discrete peridynamic equations have demonstrated a unique capability to easily capture many interesting and challenging problems related to crack propagation, e.g., crack branching [19, 8], oscillatory crack path instabilities in membranes [57], pervasive failure of brittle materials [55], and complex...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Foreword
• Preface
• List of Figures
• List of Tables
• Contributors
• I The Need for Nonlocal Modeling and Introduction to Peridynamics
• II Mathematics, Numerics, and Software Tools of Peridynamics
• III Material Models and Links to Atomistic Models
• IV Modeling Material Failure and Damage
• V Multiphysics and Multiscale Modeling
• Index