Six Stress Intensity Factors: How Hydraulic Fracture Pays Back to Fracture Mechanics?

主講人 : Gennady Mishuris 院士

This talk aims to provide an overview of key results in the mathematical and numerical modelling of hydraulic fracture that I and my group have been privileged to work with over the last decade. Revisiting the approach to a basic (BEM) algorithm for the classic HF models (PKN, KGD, Radial), has eventually allowed us to construct an extremely accurate and effective time-space adaptive algorithm for the models. Utilizing this algorithm, and adjusting where necessary, we have been continuing our endeavour to analyse some of the more delicate pieces of this extremely rich theory. In particular, we considered an effect of the shear traction induced by the fluid on the crack surface and discover another, fourth, stress intensity factor, which to our best knowledge was not previously known in the classical Fracture Mechanics. This required us to compute Rice’s Energy Release Rate taking the effect into account. Furthermore, discussing the results, we have extended the classic Irwin’s crack closure integral representation to the ERR computation. Interestingly, this leads to a complete LEFM theory with six SIFs with applications to, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. It also resolves an ambiguity in using the same SIF’s terminology in the cases of open cracks and rigid inclusions.

主講人簡介：

Gennady Mishuris 院士，阿伯里斯特威斯大學數學系教授。2014年當選英國威爾士學術院院士，德國洪堡學者、歐盟瑪麗居里學者，利華休姆研究員，波蘭最高學術稱號—貝爾維德爾教授，英國皇家學會沃爾夫森研究卓越獎。