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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access





Published: Sat, 16 Sep 2017 00:00:00 GMT

Last Build Date: Sat, 16 Sep 2017 03:49:35 GMT

 



Scaling in Cavity—Expansion Equations using the Isovector Method

2017-09-16

Summary
Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. We use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.



A Direct Method for Bloch Wave Excitation by Scattering at the Edge of a Lattice. Part I: Point Scatterer Problem

2017-09-02

Summary
A new method for determining the reflection and transmission properties of lattices is developed. The method uses multipole expansions, and certain transformations of the algebraic equation systems that appear when boundary conditions are applied. It is more direct, and much simpler, than earlier approaches based on integral transforms and the Wiener–Hopf technique. The method is demonstrated for the case of a semi-infinite lattice of sound soft acoustic point scatterers, but can easily be generalised to account for finite size effects, and more general boundary conditions.