Dispersive waves in microstructure-informed peridynamic continua

We examine the dispersion behavior and spatial attenuation of generalized oriented peridynamic continua with non-central pair-potential interactions. The free-wave propagation problem is analyzed analytically through integral transform methods, enabling the closed-form derivation of dispersion relations for real-valued wavenumbers. A complementary perturbation approach is proposed to investigate the spatial attenuation behavior, derive the full band structure, and systematically explore the dispersive response of the model for complex wavenumbers, achieving progressively higher accuracy with increasing order of the truncated expansions. The integro-differential nature of the governing equations, together with the enhanced kinematic description and pairwise interaction formalism, provides a natural framework to represent the dynamic behavior of mechanical metamaterials - such as beam-and block-lattice systems - traditionally modeled through discrete Lagrangian formulations. A central result of this study shows that the oriented peridynamic continuum with pairwise potentials - also referred to as a continuum-molecular model, to emphasize its blend of continuous mass distribution and discrete-like kinematics - successfully reproduces both the acoustic and optical branches of the architected material when the horizon approaches the characteristic microstructural lengths, a capability unattainable in conventional peridynamic continua. Furthermore, the microstructure-informed oriented model typically attains higher accuracy than a micropolar continuum derived via standard continualisation of the lattice-like material equations. The theoretical framework is validated, and its physical implications are further illustrated through a case study of forced wave propagation in architected block-lattice materials featuring a hexagonal topology.