Cancelling the effect of sharp notches or cracks with graded elastic modulus materials

Dear colleague

   I wonder if you could be interested in this idea of "Cancelling the effect of sharp notches or cracks with graded elastic modulus materials", particularly if you know who could help doing some experiments. Thanks for any comment, since this is a preprint it would be useful to discuss to make improvements.    RegardsMike    Cancelling the effect of sharp notches or cracks with graded elastic modulus materials

https://www.researchgate.net/publication/381316809

Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, σ ∼ r a , with a modulus varying as E ∼ r β. In the inhomogeneous case the order of singularity of the LEFM case decreases if β > 0, as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the "rounding" of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which involve, in the homogeneous material case, singular stress field, with potentially very wide applications.