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Register a new userOn relationship between trigonal and cubic symmetry classes of an elasticity tensor
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Authors
Filip P. Adamus
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In the literature, there is an ambiguity in defining the relationship between trigonal and cubic symmetry classes of an elasticity tensor. We discuss the issue by examining the eigensystems and symmetry groups of trigonal and cubic tensors. Additionally, we present numerical examples indicating that the sole verification of the eigenvalues can lead to confusion in the identification of the elastic symmetry.
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The classical models of Hertz, Sneddon and Boussinesq provide solutions for problems of indentation of a semi-infinite elastic massif by a sphere, a sphere or a cone and a flat punch. Although these models have been widely tested, it appears that at small scales and for flexible materials, surface tension can contribute to considerably to the mechanical response to indentation. The scales are typically those of the less than one micron for an elastomer and less than one millimetre for a gel. The exploitation of certain experimental results of microscopy or nanoindentation remain approximate due to the absence of models incorporating the effect of surface tension.
We discuss several physical constraints imposed on elasticity parameters of a transversely isotropic (TI) tensor. There are three types of restrictions we investigate; a fundamental one of stability conditions, and two additional ones, commonly considered in seismology. The first commonly considered restriction comes from an assumption of a wave with a greater speed in the horizontal than vertical direction. The second constitute the assumption that quasi-P wave is faster than quasi-S waves. We show several numerical examples to examine how these restrictions affect a TI tensor with known values of certain elasticity constants that could be acquired from the vertical or horizontal measurements.
[Background] Refactoring has matured over the past twenty years to become part of a developers toolkit. However, many fundamental research questions still remain largely unexplored. [Aim] The goal of this paper is to investigate the highest and lowest quartile of refactoring-based data using two coupling metrics - the Coupling between Objects metric and the more recent Conceptual Coupling between Classes metric to answer this question. Can refactoring trends and patterns be identified based on the level of class coupling? [Method] In this paper, we analyze over six thousand refactoring operations drawn from releases of three open-source systems to address one such question. [Results] Results showed no meaningful difference in the types of refactoring applied across either lower or upper quartile of coupling for both metrics; refactorings usually associated with coupling removal were actually more numerous in the lower quartile in some cases. A lack of inheritance-related refactorings across all systems was also noted. [Conclusions] The emerging message (and a perplexing one) is that developers seem to be largely indifferent to classes with high coupling when it comes to refactoring types - they treat classes with relatively low coupling in almost the same way.
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