Speaker
Description
Brittle fracture of nanostructured solids cannot be described by the classical continuum approach. The related problem caused by the presence of singular strain field at the crack tip can be removed by its extension using the strain gradient elasticity theory (SGET) as proposed by Mindlin [1] and proved by Kotoul et al. [2]. This approach allows addressing deformation and fracture problems at micron and nano scales in an effective and computationally robust manner thus helping to bridge the gap between classical continuum theories and atomic-lattice theories.
There are many different forms of SGET. All of them employ one or more internal length scale parameters. The crucial point is to identify their values.
Numerical fitting procedure of the phonon dispersion relations of Si, Ge, Mo and W along high symmetry directions was employed to find out their length scale parameters from ab initio calculations of the acoustic phonon dispersions. These calculations were performed within the density functional perturbation theory implemented in Abinit code [3] and verified by the supercell method with the help of the Vienna Ab initio Simulation Package (VASP) software [4], [5].
The authors gratefully acknowledge a financial support of the Czech Science Foundation under the Project No.17-18566S. Computational resources were provided by the Ministry of Education, Youths and Sports of the Czech Republic under the Project IT4Innovations National Supercomputer Center (Project No.LM2015070) within the program Projects of Large Research, Development and Innovations Infrastructures.
References
[1] R.D. Mindlin and N.N. Eshel, Int. J.Solids Structures 4, 109 (1968).
[2] M. Kotoul et al., Mechanics of Materials, 136, 103074 (2019).
[3] X. Gonze et al., Comput. Phys. Commun. 180, 2582 (2009).
[4] G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).
[5] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
