The objective of the study was to evaluate the ability of a nonlinear ultrasound technique, the so-called nonlinear resonant ultrasound spectroscopy (NRUS) technique, for detecting early microdamage accumulation in cortical bone induced by four-point bending fatigue. Small parallelepiped beam-shaped human cortical bone specimens were subjected to cyclic four-point bending fatigue in several ste...

Two coupled nonlinear Klein-Gordon equations modeling the three-dimensional dynamics of a twisted elastic rod near its first bifurcation threshold are analyzed. First, it is shown that these equations are Hamiltonian and that they admit a 2-parameter family of traveling wave solutions. Second, special solutions corresponding to simple deformations of the elastic rod are considered. The stabilit...

In this paper, we report theoretical and numerical solutions of linear and nonlinear elastic waves in a thin rod. First, the classical solution of linear elastic wave in a thin rod is adapted such that it is ready to be compared with the numerical solution of a nonlinear formulation. Based on mass and momentum conservation, we then derive several forms of modeling equations for nonlinear elasti...

2014 A tripod field is used as model for a general anisotropic fluid. The elastic energy density is expanded as invariant polynomial in the components of the contortion tensor. Surface energy terms are derived from compatibility conditions for the tripod field. The model is applied to cholesteric liquid crystals of large and small pitch, to 3He-A, and to biaxial nematic liquid crystals. J. Phys...

This paper describes a new bidirectional image registration algorithm that estimates a consistent set of nonlinear forward and reverse transformations between two Ndimensional images. The registration problem is formulated in a N+1-dimensional space where the additional dimension is referred to as the temporal or time dimension. A periodic-in-time, nonlinear, N+1-dimensional transformation is e...

Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting sonic-vacuum-type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. ...

We present PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation. PetClaw unifies two well-known scientific computing packages, Clawpack and PETSc, using Python interfaces into both. We rely on Clawpack to provide the infrastructure and kernels for time-dependent nonlinear wave propagation. Similarly, we rely on PETSc to manage distributed data arrays and t...

Propagation of elastic waves is studied in a 1D medium containing N cracks modeled by nonlinear jump conditions. The case N = 1 is fully understood. When N > 1, the evolution equations are written as a system of nonlinear neutral delay differential equations, leading to a well-posed Cauchy problem. In the case N = 2, some mathematical results about the existence, uniqueness and attractivity of ...

In this work, we consider the problem of reconstructing a small anomaly in a viscoelastic medium from waveeld measurements. We choose Szabo's model to describe the viscoelastic properties of the medium. Expressing the ideal elastic eld without any viscous e ect in terms of the measured eld in a viscous medium, we generalize the imaging procedures, such as time reversal, Kirchho Imaging and Back...