C.V. Massalas

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.

A Preisach model identification procedure and simulation of hysteresis in ferromagnets and shape-memory alloys

Abstract A Preisach model able to adjust to different systems with hysteresis is presented. The related identification scheme involved uses data from a major hysteresis curve and a least-squares error minimization procedure for the parameters of the characteristic density. The output sequence, f ( t ), is obtained by integrating the characteristic probability density function, ρ ( α , β ), of the elementary hysteresis operators, γ ab , operating on the input sequence u ( t ) over the Preisach plane. Once the appropriate operator is chosen and the Preisach plane adjusted accordingly, the parameters of the characteristic density are determined via a least-squares procedure minimizing the error between the experimental major curve and the calculated one. Results using two different scalar operators are discussed. Further, the reliability of the procedure is assessed by considering experimental data regarding two different magnetic samples and a shape-memory alloy sample.

A theoretical study of the hyperelasticity of electro‐gels

The continuum theory of electro‐elasticity is used in order to describe the large deformations observed in gels endowed with electric properties when they are placed in electric fields. The analytical solution of the properly constructed boundary‐value problem agrees quantitatively with available experimental data.

Tiersten's theory of thermoelectroelasticity: an extension

Abstract In the present work we present a generalized theory of thermoelastic dielectrics. The analysis is based on Tierstens theory, the entropy production inequality proposed by Green and Lindsay and the invariance of the first law of thermodynamics under rigid body translation and rotation.

Thermoelastic waves in a thin plate

SummaryIn the present work we deal with the propagation of thermoelastic waves in a thin plate occupying the Cartesian space (x1∈[−∞, +∞],x2∈[−α, +α],x3∈[−δ, +δ]). The analysis is based on the generalized theory of thermoelasticity proposed by Lord and Shulman modified for plane stress problems. A mathematical analysis is presented to study the wave motion characteristics of the plate and the proposed analysis is applied for the special cases of very short and very long waves.

A poroelastic bone model for internal remodeling

In this paper a theoretical analysis of the internal bone remodeling process induced by a medullary pin is presented. Bone is treated as a poroelastic material using Biots formulation. Based on the theory of small-strain adaptive elasticity, a new theoretical approach for internal remodeling is proposed. Our results show that the rate of internal remodeling decreases as the porosity of the bone increases.

Dynamic characteristics of the human skull-brain system

In this work, the dynamic characteristics of the human skull-brain system are studied. For the purpose of our analysis, we adopted a model consisted of a hollow sphere (skull), an inviscid and irrotational fluid (cerebrospinal fluid), and a concentrically located inner elastic sphere (brain). The mathematical analysis is based on the elasticity solution for the elastic spheres and the simplified description of the motion of the fluid by the wave equation. The roots of the characteristic equation were found numerically. The results are in agreement with other researchers analogous modelling work, however our three-dimensional analysis introduces a new pattern of frequencies to the natural frequencies spectra of the skull-brain system. The results are compared with experimental ones and the role of the various system parameters on the natural frequencies is investigated.

Frequency spectrum of the human head-neck system

A three-dimensional model of human skull-brain system has been extended to include neck support. The model is based on the assumption of having a hollow sphere (skull), the behaviour of which is described by the elasticity solution, filled with an inviscid, irrotational fluid (cerebrospinal fluid), whose motion is described by the wave equation. The neck is approximated by an elastic support which reacts in three dimensions. The problem is solved numerically for the eigenfrequency spectra and the results obtained are compared with the existing experimental ones showing good agreement. The role of the various system parameters is also investigated.

THERMOELASTIC WAVES IN A WAVEGUIDE

Abstract The propagation of thermoelastic waves in a waveguide occupying the Cartesian space x 1 ϵ [0, L ], x 2 ϵ [− H , + H ], x 3 ϵ [− ∞, + ∞] is discussed. The analysis is based on the generalized theory proposed by Lord and Shulman. The solution of the problem is expressed in terms of the Lames scalar and vector potentials and the frequency equations are derived. For the special case of very short waves numerical results for the wave motion characteristics are presented and the role of the various parameters entering into the problem is extensively discussed.

On the dynamic characteristics of the human skull

Abstract In this work an attempt is made to she dynamic characteristics of the human dry skull. The analysis is based on the three-dimensional theory of elasticity and the representation of the displacement field in terms of the Navier eigenvectors. The frequency equation was solved numerically and the results obtained are fairly good, in comparison to the experimental ones.