Gravitational frequency shifts in transformation acoustics

In metamaterial acoustics, it is conceivable that any type of fine-tuned acoustic properties far beyond those found in nature may be transferred to an appropriate medium. Effective design and engineering of these modern acoustic metadevices poses one of the forefront challenges in this field. As a practical example of a new covariant approach for modelling acoustics on spacetime manifolds, we choose to implement the acoustic analogue of the frequency shift due to gravitational time dilation. In accordance with Einstein's equivalence principle, two different spacetimes, corresponding to uniform acceleration or uniform gravity, are considered. For wave propagation in a uniformly accelerating rigid frame, an acoustic event horizon arises. The discussion includes a detailed numerical analysis for both spacetime geometries. Copyright (c) EPLA, 2013MMT wishes to thank MARKUS SCHOBINGER for an introduction to the SBVP MATLAB solver and acknowledges partial support by the Universidad Politecnica de Valencia (PAID-00-12) and the International Office of the Vienna University of Technology.Tung, MM.; Weinmüller, EB. (2013). Gravitational frequency shifts in transformation acoustics. EPL. 101(5):54006-54011. https://doi.org/10.1209/0295-5075/101/54006S5400654011101

An approximate, analytical approach to the 'HRR' solution for sharp V notches

The well-known so-called 'HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent 'n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than π/6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail