Work

Comparison Between Solutions to the Linear Peridynamics Model and Solutions to the Classical Wave Equation

Year: 2026

Type: article

Abstract: . In this paper, we consider an equation inspired by linear peridynamics and we establish its connection with the classical wave equation. In particular, given a horizon [Formula: see text] accounting for the region of influence around a material point, we prove existence and uniqueness of a solution [Formula: see text] and demonstrate the convergence of [Formula: see text] to solutions to the classical wave equation as [Formula: see text]. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1701861

Authors: G. M. Coclite, S. Dipierro, F. Maddalena, G. Orlando, E. Valdinoci

Institutions: Polytechnic University of Bari, The University of Western Australia

Language: English

Topic: Numerical methods in engineering

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: green