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

• Published in: Advances in continuous and discrete models Vol. 2022; no. 1
• Main Authors: Dimola, Nunzio, Coclite, Alessandro, Fanizza, Giuseppe, Politi, Tiziano
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.10.2022; Springer Nature B.V
• Subjects: Analysis; Composite materials; Cracks; Difference and Functional Equations; Functional Analysis; Hypotheses; Kernels; Kinematics; Mathematical models; Mathematics; Mathematics and Statistics; Mechanics; Numerical analysis; Numerical models; Ordinary Differential Equations; Partial Differential Equations; Review; 74A70; Nonlocal fluids; Numerical methods; Peridynamics; 70G70; 74S20; 74B20; Nonlocal continuum mechanics; 35Q70
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-022-03732-6

Peridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity 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 this paper, we review and investigate several aspects of bond-based peridynamic models. We present a detailed description of peridynamics theory, applications, and numerical models. We display the employed BB-PD integral kernels together with their differences and commonalities; then we discuss some consequences of their mathematical structure. We critically analyze and comment on the kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in crack formation prediction. Finally, we propose and present the idea of extending BB-PD to fluids in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids.