Coupling of Local and Non-Local Model for Wave Propagation in 1D Higher Order Structure

Abstract Detecting the presence of small-sized cracks in a structure is essential for assessing the health of structures with small length scales, such as carbon nanotubes and nanobots. Due to the absence of a length scale parameter in the local continuum model, non-local theories serve as alternatives for modeling structures to capture physics at different length and time scales. Eringen’s second-order stress gradient non-local continuum model eliminates stress singularity at the crack tip and captures the dispersive nature of the continuum body at higher frequencies, aligning with experimental observations. Coupling classical continuum models with non-local theories allows for leveraging the computational efficiency of the former while utilizing the latter’s ability to capture behavior at small length scales at high frequencies. In this paper, we introduce a coupling zone at the interface of domains modeled with different constitutive equations. This coupling zone effectively eliminates spurious reflections caused by differences in constitutive laws.