Solving ultrasonic ray tracing in parts with multiple material layers through Root-Finding methods

•The work presents suitable iterative mathematical approaches for solving the ray-tracing problem in multi-layered structures;•A novel formulation improves the definition of the initial guess ray-path and provides a rationale for the choice of suitable criteria to stop the iterations;•The approach based on the Newton-Raphson root-finding method allow a threefold reduction of the computation time;•The work investigates also the combination of the Newton-Raphson methods with bisection-type iterations.