Modified wave dispersion properties in 1D and 2D state-based peridynamic media

Abstract

This study introduces a modification of wave propagation in state-based peridynamics (PD). Comprehensive investigations have been conducted to analyze wave dispersion in both 1-D and 2-D domains. We employ weighted residual techniques, specifically point collocation and the Galerkin method, to mitigate the wave dispersion phenomenon by introducing a set of scaling coefficients. The square-frequencies of the bond- and state-based PD models are correlated defining a new formulation. Utilizing these scaling coefficients, we demonstrate that the solution of the original PD converges towards that of the non-dispersive classical continuum method. It is shown that the proposed method alleviates wave dispersion in all PD models accurately.