Engineering mechanics includes all areas of theoretical and applied mechanics. Engineering mechanics focuses on the mechanics of solids and fluids: continuum mechanics; dynamics; stability; properties of materials; computational, probabilistic and experimental mechanics; biomechanics; and nano- and micro-mechanics.
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I do not think in Imechanica there has been an obituary for Paul Paris, whose work in fatigue crack propagation is extraordinary and one of the few important and lasting contributions ----- today our aircrafts, both civil and military, all rely on "damage tolerance", which is based on Paris' law. Paris' law, as every great innovations, was published in 1961 only after rejection by three of the leading journals in the fracture mechanics field. It bears the name of "law" although of course it is not like Newton's law. It is a power law, based perhaps on what Barenblatt calls "incomplete" some self-similarity considerations.
The problem was that people could not beleive that Irwin elastic stress intensity factor (the range of it), could predict fatigue crack propagation rate. In fact, previous laws had attempted to predict da/dN from plastic mechanisms, and in the end resulted, like Frost-Dugdale, in a law which is essentially Paris law, but with m=2. The australian Air Force and even USAF is returning to this assumption today (leading to exponential crack growth), but this is another story (see Jones, 2014).
An obituary can be found here.
Today Paris' law is so esthablished that it is difficult to get research funding on this fundamental problem. But each time I return to fatigue in my classes, I immediately tell students about a problem I encountered and identified in 2006 (Ciavarella and Monno, 2006), which still puzzles me. When we integrate Paris, we get also a finite life prediction. But the size effect predicted by Paris in the Kitagawa generalized diagram is very hard and funny to beleive. While the fatigue threshold DK_th gives a -1/2 classical size effect, and similarly does static failure KIc, Paris intergrated gives obviously 1/m-1/2, which for fixed life N smoothly converges to either limits ONLY for infinite m! And for m=2 the case is not much worse than, say, 3, but still unrealistic, and Paris integrated becomes (almost) horizontal, with the most striking difference.
I know that C in Paris tends to show size effects, and I have even written about it in JMPS (Ciavarella et al, 2008), which often are neglected, and normally are correlated with m (when you increase C, you tend to see decrease of m), but this is also found in a single size of initial cracks, by simply varying the specimen, like Virkler did in his famous work using 68 nominally identical specimen.
Has Paris' law been measured in a wide enough range of sizes? Nobody has explained this. The Paris law regime is simply inconsistent with the other size effects, and m=2 makes things even worse than any other m. Maybe if we do there is something new to say.
By the way, I also wrote a paper in the very first article of a new journal in 2011 (Ciavarella, 2011), where I show that if I had a generalized El Haddad law the way makes much more sense in the Kitagawa diagram, then the Paris law would show size effects, although it becomes less easy to write. Since most people find Paris with a single specimen, and do not start with different crack sizes (typically a CT specimen is used), probably this effect has been overlooked.
But this doesn't answer my question, and now that Paul Paris died, I feel so sad that I cannot ask him directly this challenging question.
Prof. Michele Ciavarella
Paris, P. and Erdogan, F. (1963), A critical analysis of crack propagation laws, Journal of Basic Engineering, Transactions of the American Society of Mechanical Engineers, December 1963, pp. 528–534.
Ciavarella, M., & Monno, F. (2006). On the possible generalizations of the Kitagawa–Takahashi diagram and of the El Haddad equation to finite life. International journal of fatigue, 28(12), 1826-1837.
Ciavarella, M., Paggi, M., & Carpinteri, A. (2008). One, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth. Journal of the Mechanics and Physics of Solids, 56(12), 3416-3432.
Ciavarella, M. (2011). Crack propagation laws corresponding to a generalized El Haddad equation. International Journal of Aerospace and Lightweight Structures (IJALS), 1(1).
D. A. Virkler, B. M. Hillberry and P. K. Gael, The statistical nature of fatigue crack propagation. J. Engng Mater.Technol. 101, 148-153 (1979).
Jones, R. (2014). Fatigue crack growth and damage tolerance. Fatigue & Fracture of Engineering Materials & Structures, 37(5), 463-483
The School of Mechanical and Mechatronic Engineering at the University of Technology Sydney is seeking PhD students to work on projects related to:
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Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins and core as a result of manufacturing defects or impact loads, degrading their mechanical properties. To improve both the safety and functionality of these systems, structural damage assessment methodologies can be implemented. This article presents a damage assessment algorithm to localize and quantify debonds in sandwich panels. The proposed algorithm uses damage indices derived from the modal strain energy method and a linear approximation with a maximum entropy algorithm. Full-field vibration measurements of the panels were acquired using a high-speed 3D digital image correlation (DIC) system. Since the number of damage indices per panel is too large to be used directly in a regression algorithm, reprocessing of the data using principal component analysis (PCA) and kernel PCA has been performed. The results demonstrate that the proposed methodology accurately identifies debonding in composite panels.
Keywords: sandwich panel; damage assessment; debonding; modal strain energy; linear approximation with maximum entropy.
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Can anyone please point me towards any open source Python-based Multiphysics Solver, preferably with GUI for simple CAD operations and mesh generation ?
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