Nonlinear and Hysteretic Constitutive Models for Wave Propagation in Solid Media with Cracks and Contacts
Résumé
This chapter is devoted to theoretical concepts and models for wave propagation, vibrations, or other elastic deformations in solids containing internal contacts (cracks, delaminations, etc.). A direct problem of solid mechanics is solved by building up a solution for elastic fields in materials with known geometry and properties. This study is oriented to nondestructive testing and therefore focuses on the case where the material contains few cracks of known configuration, in contrast to microcracked solids in which a statistical ensemble of a large number of internal contacts is present. Our approach is based on finite element simulations and a frictional contact model assuming generic semi-analytical solutions. These solutions account for surface roughness, friction, and the evolution of stick and slip zones in the contact area. Finally, load–displacement relationships valid for arbitrary loading histories are produced which are used as boundary conditions imposed at internal boundaries (cracks) in the material. As a result, we have developed a numerical toolbox capable of modeling elastic waves and vibrations in damaged samples or structures. The access to all elastic fields together with their nonlinear components makes nondestructive testing fully transparent and offers an opportunity of purposeful optimization of the experimental techniques.
Mots clés
Waves in heterogeneous materials
Waves in materials with cracks
Vibrations of solids with internal contacts
Contact acoustical nonlinearity
Mechanics of materials with damage
Nonlinear nondestructive testing
Nonlinear ultrasound
Damage detection in solids
Nonlinear acoustic imaging
Cracks and delaminations
Contact mechanics
Method of memory diagrams
Frictional cracks
Frictional shift contact problem
Hertz-Mindlin problem
Cattaneo-Mindlin problem
Contact load–displacement relationships
Problem of frictional shift
Hysteresis and friction
Contact of rough surfaces
Reduced elastic friction principle
Ciavarella-Jäger theorem
Axisymmetric contact problem
Hysteretic nonlinearity
Hysteresis in elasticity