A unified bond-based peridynamic model with insights into high-frequency elastodynamic problems in geotechnical and structural engineering

Abstract

The nonlocal effects in high-frequency dynamic problems cannot be captured by classical continuum mechanics (CM), thereby introducing several compelling topics that warrant further exploration. Peridynamics (PD) offers a novel perspective for investigating these issues. This study proposes a unified bond-based peridynamic (UBB-PD) model, with an emphasis on high-frequency dynamics that account for nonlocal properties. The UBB-PD model incorporates a general criterion for constructing the micromodulus function. Then, the eigenfunction method is introduced to solve the UBB-PD governing equations. The proposed model can naturally reduce into three different versions: CM, local PD model, and nonlocal PD model. The equivalence between PD and CM can be achieved by selecting an appropriate length-scale parameter (Formula presented.), with the wave frequency serving as a bridge connecting the two theories. Simulation results reveal that the local PD model perfectly reproduces the elastodynamic behavior found in CM across all frequencies. However, the nonlocal PD model inherently exhibits wave dispersion, arising from its nonlocal nature, which cannot be eliminated at high frequencies. PD stresses are affected by wave dispersion at high frequencies, with dissipative forces arising from inappropriate (Formula presented.) potentially inducing non-conservation of mechanical energy. These results reveal findings not previously reported in relevant literature.