Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of the Acoustical Society of America 2009-05, Vol.125 (5), p.3414-3427
Main Authors: Vavva, Maria G., Protopappas, Vasilios C., Gergidis, Leonidas N., Charalambopoulos, Antonios, Fotiadis, Dimitrios I., Polyzos, Demosthenes
Format: Article
Language:English
Subjects:
Algorithms
Biological and medical sciences
Bone and Bones - physiology
Elasticity
Fundamental and applied biological sciences. Psychology
Humans
Kinetics
Models, Biological
Skeleton and joints
Ultrasonics
Vertebrates: osteoarticular system, musculoskeletal system
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g , introduced in the strain energy, and (b) the micro-inertia term h , in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h = 10 − 4   m and h = 10 − 5   m . For each case, three subcases for g were assumed, namely, g > h , g < h , and g = h . The values of g and h were of the order of the osteons size. The velocity dispersion curves of guided waves were numerically obtained and compared with the Lamb modes. The results indicate that when g was not equal to h (i.e., g ≠ h ), microstructure affects mode dispersion by inducing both material and geometrical dispersion. In conclusion, gradient elasticity can provide supplementary information to better understand guided waves in bones.
ISSN:0001-4966
1520-8524
DOI:10.1121/1.3110203