Interface damage modeled by spring boundary conditions for in-plane elastic waves

In-plane elastic wave propagation in the presence of a damaged interface is investigated. The damage is modeled as a distribution of small cracks and this is transformed into a spring boundary condition. First the scattering by a single interface crack is determined explicitly in the low frequency limit for the case of a plane wave normally incident to the interface. The transmission at an interface with a random distribution of small cracks is then determined and is compared to periodically distributed cracks. The cracked interface is then described by a distributed spring boundary condition. As an illustration the dispersion relation of the first modes in a thick plate with a damaged interface in the middle is given.

Research Highlights
► Damage is modeled via spring boundary condition.
► Derivation of the spring stiffness is for normally incident plane wave.
► Methodology can be extended in several directions (3D case and anisotropy).
► Interface may be with only partial damage, damage in a layered plate, etc.