Transformation of body force generated by non-contact sources of ultrasound in an isotropic solid of complex shape into equivalent surface stresses

Non-contact techniques in ultrasonic nondestructive evaluation use external non-mechanical excitation (electromagnetic, heat) which interacts with the mechanical part to be tested. The part itself becomes the source of ultrasounds by transforming the non-mechanical energy into a mechanical one. This process involves the generation of dynamic body forces or of an eigenstrain that can be modeled as equivalent body forces, these forces being confined in the vicinity of the part surface. Many models developed for predicting ultrasonic field radiation in solids assume source terms given as surface distributions of stress. In order to predict ultrasonic fields radiated by non-contact sources by means of these radiation models, we developed a method to transform dynamic body forces into equivalent surface stress distributions, irrespective of the nature of the excitation. The approximate transformation relies on a second order expansion of Green's integral formulation of the elastic wave equation. To make this transformation applicable broadly, the geometry of the surface considered herein is of complex shape, implying thorough differential and tensorial analyses to achieve our aim. Some assumptions, notably isotropic elasticity, are made in deriving the transformation method, which are discussed in detail to clearly define its applicability. Numerical examples of radiated fields are given for illustration and validation.