All materials are anisotropic, that’s a fact. Like the fact that all materials have a nonlinear response. This we can’t deny. Still enormous progress has been made by assuming both isotropy and linear elasticity. The success, as we all know, is due to the fact that many construction materials are very close to being both isotropic and linear. By definition materials may be claimed to be isotropic and linear, provided that the deviations are held within specified limits. Very often or almost always in structural design nearly perfect linearity is expected. In contrast to that quite a few construction materials show considerable anisotropy. It may be natural or artificial, created by humans or evolved by biological selection, to obtain preferred mechanical properties or for other reasons. To be able to choose between an isotropic analysis or a more cumbersome anisotropic dito, we at least once have to make calculations of both models and define a measure of the grade of anisotropy. This is realised in the excellent paper
The study provides a thorough review of materials that might require consideration of the anisotropic material properties. As a great fan of sorted data, I very much appreciate the references the authors give listed in a table with specified goals and utilised analysis methods. There are around 30 different methods listed. Methods are mostly numerical but also a few using Lekhnitskiy and Stroh formalisms. If I should add something the only I could think of would be Thomas C.T. Ting’s book “Anisotropic Elasticity”. In the book Ting derives a solution for a large plate containing an elliptic hole, which provides cracks as a special case.
The present paper gives an excellent quick start for those who need exact solutions. Exact solutions are of course needed to legitimise numerical solutions and to understand geometric constraints and numerical circumstances that affect the result. The Lekhnitskiy and Stroh formalisms boil down to the “method of characteristics” for solving partial differential equations. The authors focus on the solution for the vicinity of a crack tip that is given as a truncated series in polar coordinates attached to a crack tip.
As far as I can see it is never mentioned in the paper, but I guess the series diverges at distances equal to or larger than the crack length 2a. Outside the circle r=2a the present series for r<2a should be possible to extend by analytic continuation. My question is: Could it be useful to have the alternative series for the region r>2a to relate the solution to the remote load?
Does anyone have any thoughts regarding this. Possibly the authors of the paper or anyone wishes to comment, ask a question or provide other thoughts regarding the paper, the method, or anything related.
Per Ståhle
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