Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

TL;DR

This survey reviews bond-based peridynamics, highlighting its applications, mathematical structure, and potential extension to fluid dynamics within a fading memory framework, aiming to deepen understanding of nonlocal theories.

Contribution

It provides a comprehensive review of bond-based peridynamics, discusses its mathematical and physical aspects, and proposes extending it to fluid dynamics using fading memory concepts.

Findings

Analysis of different integral kernels and their properties

Discussion on nonlocality and crack formation mechanisms

Proposal for extending peridynamics to fluid dynamics

Abstract

Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling limitations, is widely employed in numerical simulations, due to its easy implementation combined with physical intuitiveness and stability. In the present paper, several aspects of bond-based peridynamic models have been reviewed and investigated. A detailed description of peridynamics theory, applications and numerical models has been presented. Employed BB-PD integral kernels have been displayed, together with their differences and commonalities; then, some consequences of their mathematical structure have been discussed. The kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in cracks formation prediction have been critically analyzed and commented. Finally the idea of extending BB-PD to fluids is proposed and presented in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids.