2021/02/12 by L. Lopez, Lopez, Luciano, Sabrina Francesca Pellegrino +1
Engineering · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Geotechnical Engineering and Underground Structures #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2102.06485
openalex publication_date 2021/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in\na second order in time partial integro-differential equation. In this paper, we\nconsider a nonlinear model of peridynamics in a two-dimensional spatial domain.\nWe implement a spectral method for the space discretization based on the\nFourier expansion of the solution while we consider the Newmark-\β method\nfor the time marching. This computational approach takes advantages from the\nconvolutional form of the peridynamic operator and from the use of the discrete\nFourier transform. We show a convergence result for the fully discrete\napproximation and study the stability of the method applied to the linear\nperidynamic model. Finally, we perform several numerical tests and comparisons\nto validate our results and provide simulations implementing a volume\npenalization technique to avoid the limitation of periodic boundary conditions\ndue to the spectral approach.\n