Dirichlet-type absorbing boundary conditions for ordinary state-based peridynamics

We present time-domain Dirichlet-type absorbing boundary conditions (ABCs) for 2D ordinary state-based peridynamics using the Linear Peridynamic Solid (LPS) model, aimed at efficiently truncating unbounded elastodynamic domains while retaining the flexibility of arbitrary Poisson ratios. The proposed ABCs are built from a semi-analytical far-field representation expressed as a finite superposition of plane-wave modes satisfying the discrete LPS dispersion relation, so that outgoing waves are absorbed consistently with the numerical P- and S-wave branches and their Poisson-ratio-dependent polarizations. A cloud-based collocation and least-squares procedure eliminates the unknown modal amplitudes locally and yields precomputable updating operators that prescribe boundary displacement and velocity directly within explicit time stepping, avoiding spatial derivatives, transform techniques, auxiliary evolution equations, and surface-correction procedures at truncated horizons. Unlike our earlier bond-based ABC formulations, the present work requires a new state based far-field theory, a new discrete dispersion operator with coupled P- and S-wave branches for general Poisson ratios, and an additional treatment of the nonlocal dilatation field. Numerical benchmarks show that the resulting ABCs strongly suppress nonphysical reflections over a broad range of material parameters, providing a simple and robust alternative to absorbing layers.