title: Modelling of multiscale nonlinear interaction of elastic waves with three-dimensional cracks.
abstract: This paper presents a nonlinear elastic material model able to simulate the nonlinear effects generated by the interaction of acoustic/ultrasonic waves with damage precursors and micro-cracks in a variety of materials. Such a constitutive model is implemented in an in-house finite element code and exhibits a multiscale nature where the macroscopic behavior of damaged structures can be represented through a contribution of a number of mesoscopic elements, which are composed by a statistical collection of microscopic units. By means of the semi-analytical Landau formulation and Preisach-Mayergoyz space representation, this multiscale model allows the description of the structural response under continuous harmonic excitation of micro-damaged materials showing both anharmonic and dissipative hysteretic effects. In this manner, nonlinear effects observed experimentally, such as the generation of both even and odd harmonics, can be reproduced. In addition, by using Kelvin eigentensors and eigenelastic constants, the wave propagation problem in both isotropic and orthotropic solids was extended to the three-dimensional Cartesian space. The developed model has been verified for a number of different geometrical and material configurations. Particularly, the influence of a small region with classical and non-classical elasticity and the variations of the input amplitudes on the harmonics generation were analyzed.
authors.affiliation: Material Research Centre, Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom.
authors.forename: Francesco
authors.initials: F
authors.lastname: Ciampa
authors.affiliation: The School of Engineering and Material Science, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
authors.forename: Ettore
authors.initials: E
authors.lastname: Barbieri
authors.affiliation: Material Research Centre, Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom.
authors.forename: Michele
authors.initials: M
authors.lastname: Meo