文档A new method to solve crack problems based on G2 theory.ppt

In the sequel we seek that value of the length scale that gives the exact agreement of the mid-point displacement of the uniformly pressurized CDD with the analytical solution for the uniformly pressurized crack,assuming that the latter is discretized with only one element. The above value of DD should be equal to the mid-point opening of the Mode-I crack as it given from Eq. (2) Solution!.. Construction of the new G2CDD element (G2 stands for grade-2 or 2nd gradient theory) Creation of new Influence Functions !!!.... New G2-term Comparison of G2CDD with CDD LDD: 1st case of Mode III crack problem under uniform shear The case of three co-linear straight cracks Analytical solution: Generalization for multiple cracks of any shape Validation of G2CDD against known results Interaction of multiple cracks with a free surface This solution is constructed by superposition from the infinite body results presented in Part I by using the classical method of images (Hirth and Lothe, 1982). Validation of G2CDD against known results Conclusions A brief account of existing analytical methods for attacking LEFM problems has been made. A new CDD element was presented for the numerical solution of Mode I, II and III crack problems, based on the strain gradient elasticity theory in its simplest possible Grade-2 (second gradient of strain or G2 theory) variant. It has the advantage of simplicity, yet it has rather good accuracy appropriate for the fast solution of multiple crack problems. 21st ALERT Doctoral School Friday 8th October 2010 George Exadaktylos Slide * of 43 Sixth framework program of the European union A new method to solve crack problems based on G2 theory Elementary Fracture Mechanics George Exadaktylos Technical University of Crete Greece exadakty@mred.tuc.gr http://minelab.mred.tuc.g Dedicated to the memory of Prof. Ioannis Vardoulakis The presence of crack-like voids is known to have a profound effect on the strength