Estimation of Intrinsic Damage State in Materials using Non-local Perturbation: Application to Active Health Monitoring

Abstract

Quantifying damage parameters from macroscale wave signals has gained enormous popularity in recent years in the field of structural health monitoring (SHM). However, suitable parametric variation which manifests such lower scale effect to predict incubation of damage is an intricate subject. Hence, a relatively simpler way of quantifying the damage state is discussed in this article. An effort has been made to preset the dispersive solution of Cristoffel equation using non-local formulation. The solution of non-local Cristoffel equation is presented for isotropic (iron crystal—metal) and anisotropic material (cubic crystal—gallium arsenide—semiconductor). Conventional solution of Cristoffel equation is non-dispersive, but this study shows that the wave modes such as quasi-longitudinal, quasi-shear wave speeds are dispersive when non-local theory is employed. However, velocity directions are not perturbed from the non-local Cristoffel equation. Non-local parameters can be used as a migratory parameter for elastodynamic analysis at the macroscale considering the intrinsic length scale effect. The variations of wave velocities (phase velocities) in frequency domain are also presented under the influence of non-local parameter. This study has two implications in the SHM field. The dispersive nature of waves in a periodic crystal structure can be obtained from a MD study of the undamaged condition. Hence, a suitable value of the non-local parameter can be found and can be used as an input parameter in the derived equation in this article. On the other hand, the experimental study on wave velocity can be used to estimate the suitable non-local parameter as a damage parameter which carries the property of damaged crystals. In this article, the later approach has been adopted to study using COMSOL multiphysics software. Three different types of damages are considered inside the materials mentioned above. The effect on wave velocity is found and from the reverse analysis, non-local parameter is determined.