Biomedical Engineering Reference
In-Depth Information
5.7 Dynamic fracture simulation setup with FEM discretization for
performing the CFEM simulations.
homogeneous material longitudinal wave velocity) (14.3 MPa and 57.3 MPa
at V
0
=0.5 m/sec and 2 m/sec, respectively) and a linear ramp from zero to
that value in the initial phase of loading. The specimen is stress free and at
rest initially. Conditions of plain strain are assumed to prevail.
For the CFEM mesh and the bilinear cohesive law used, convergence
analyses of the dependence of mesh element size on simulation results have
been performed [40]. Based on those analyses, we require the characteristic
finite element size, h, to satisfy: 750 nm
30 nm. The upper limit is
based on the minimum cohesive zone size estimate based on the properties
listed in Table 5.1 [40]. The lower limit is based on the elimination of
material softening because of the use of bilinear law with finite initial
stiffness [40]. The characteristic element size of 75 nm satisfies the
convergence criterion. The characteristic size corresponds to four finite
elements (Fig. 5.7). Accordingly, there are 542 000 elements in each analyzed
finite element mesh.
>
h
≥
5.5 Molecular dynamics (MD) modeling
The MD simulations described here were carried out under 3D conditions
(using periodic boundary conditions (PBCs)). The focus of the analyses is on
understanding the deformation mechanisms in the composites and on
delineating the factors affecting their strength. The microstructures analyzed
are shown in Fig. 5.8. Six different atomistic morphologies were analyzed:
M1 is a 10 nm sized cubic single crystal Si
3
N
4
block; M2 a 10 nm sized cubic
bi-crystalline Si
3
N
4
block; M3 is a microstructure based on M1 with a 3 nm
