Shock calculations for axially symmetric shear wave propagation in a hyperelastic incompressible solid

The shock pattern for axially symmetric shear wave propagation in a hyperelastic incompressible solid

“…The family of outgoing characteristics are given by aðr; tÞ ¼ const. It was shown by Barclay (2004) that the above approximate solution is the leading term in a uniform expansion valid for small values of the parameter kck. Regarding kck as a small parameter is a reasonable assumption, since as we noted earlier, jc k j ( 1 for many real materials.…”

“…An approximate solution to (2.19) with (2.21) for axial shear waves was obtained by Barclay (2004) using Whitham's nonlinearization technique. A similar solution can be obtained for torsional shear waves propagating alone, but a solution cannot be constructed in an analogous way for combined axial and torsional shear wave propagation.…”

“…In Barclay (2004), we obtained and used an approximate solution to estimate the breaking time of a nonlinear axial shear wave. The approximate solution was constructed using the nonlinearization technique described in Chapter 9 of Whitham (1974).…”

Wave motion in relaxation-testing of nonlinear elastic media

“…This work studies these issues through a solution for wave motion in a nonlinear elastic, model relaxation specimen, and describes how the results can be applied to characterization of some viscoelastic materials. Although linear elastic and linear viscoelastic material models applied to the same specimens result in linear equations that can be solved with well-established methods (Achenbach 1973;Eringen & Suhubi 1975;Suf & Farris 1994;Ginsberg 2001;Barclay 2004), the nonlinear material model used in this paper results in a hyperbolic wave equation (Jeffrey & Taniuti 1964;Nayfeh & Mook 1979;Bukiet et al 1996;Thoo & Hunter 2003). Nonlinear wave equations can be solved using numerical techniques (Armen & Garnet 1976;Shamardan 1990;Bukiet et al 1996) and several analytical schemes including the perturbation method (Giacaglia 1972;Skorokhod et al 2002), the method of multiple scales (Kakutani et al 1968;Achenbach 1973;Whitham 1974;Nayfeh & Mook 1979) and the method of characteristics (Fox 1955;Jeffrey & Taniuti 1964).…”