Analysis of three-dimensional hexagonal and cubic polycrystals using the boundary element method

BESLE: Boundary element software for 3D linear elasticity

“…Program Title: BESLE CPC Library link to program files: (to be added by Technical Editor) Developer's repository link: https://github.com/Afgr1087/BESLE_v1.0.git Licensing provisions: GPL-v3.0 Programming language: Fortran 90, C++/C External libraries: LAPACK [1], BLAS [2], SCOTCH [3], ScaLAPACK [4], MUMPS [5], Voro++ [6], Triangle [7] Nature of problem: The solution of 3D elasticity models of heterogeneous materials is often arduous owing to the complexity of the underlying system of partial differential equations.…”

“…[1] LAPACK: http://www.netlib.org/lapack/ [2] BLAS: http://www.netlib.org/blas/ [3] SCOTCH: https://gforge.inria.fr/projects/scotch/ [4] ScaLAPACK: http://www.netlib.org/scalapack/ [5] MUMPS: http://mumps.enseeiht.fr/…”

“…At the microscale, each grain is usually modeled as a linear elastic anisotropic material as presented in the majority of metallic and ceramic crystalline materials. This Polycrystal mesh generator is a C++/C| multi-compiler code based on the procedure presented in [5,15,42] for generating artificial polycrystalline structures. This sub-package requires as input parameters the number of grains in each direction, it means the number of grains is given by ngrains_x*ngrains_y*ngrains_z.…”

“…Some additional desirable features include the possibility to assess high-gradient mechanical fields and accurate solutions at material points within the domain. The BEM has been successfully implemented in homogenization, failure and multiscale analyses in polycrystal aggregates [4][5][6][7][8][9], composites [10][11][12] and bone tissue [13,14] and has been shown to be a versatile and adaptable method for realistic continuum modelling.…”

“…Classical limitations of the BEM stem from the high numbers of degrees of freedom (DOF) and that the incidence matrices are fully populated non-symmetrical. To deal with this issue an MPI parallel algorithm described in [5,15] was incorporated allowing for an efficient solution. For this purpose, it is also possible to use adaptive cross approximation, also known as hierarchical matrices [16][17][18] and other high-performance BEM implementations, such as those in [19,20].…”