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A 3D notched specimen has been analyzed in three-point-bending using
the direct explicit integration. The specimen
geometry is shown in Fig. 12. Initially, the employed constitutive model is a
nonlocal variant of rotating crack model. Once cracking
process reaches a certain critical state (identified by principal
stress to tensile strength ratio and by current shear stiffness to
shear modulus ratio), the procedure switches to a damage
type formulation. The final stage is then described by the damage
model, that uses the anisotropic stiffness multiplied by a
scalar factor, that decays to zero value as the cracking continues.
The constitutive
properties are summarized in Table 1. In order to simulate
static test, the specimen loading has been controlled by the
prescribed displacement of a transverse edge in the middle of
the top specimen surface, which has been determined from the
requirement of minimal inertia forces [12]. The mesh contains 1964
nodes and 9324 linear tetrahedral elements. The total number of time
steps analyzed is 7500. The modified node-cut strategy (allowing for
nonlocal material model) has been used.
The mesh partitioning implementation is based on METIS
partitioning library. A general front-end application to METIS
serving simultaneously as a data converter between the (sequential)
mesh generator [16]
and the object oriented computational code [14] has been written. This
application firstly transforms the general mesh into an appropriate
graph structure, according to the selected cut strategy.
A METIS graph partitioning
routine is then used to obtain the mesh partitioning which is further
modified to account for zones involved in averaging algorithms.
The partitions have been generated prior the analysis and
have been kept constant throughout the whole analysis
(static load balancing). An example of domain decomposition for
4-processor analysis is depicted in Fig. 13.
The results achieved on Dell PC cluster and SP2 machine are presented
in Figs 14 and 15, respectively. Note
that the heterogeneity of the computing platforms has been taken into
account neither in the mesh partitioning (all partitions
are equally load balanced) nor in the speedup or efficiency
evaluation. Since the single processor computation has been
always performed on the most powerful processor, the speedup is
slightly underestimated whenever a slower processor has
participated in the calculation. The degradation of the speedup
profile is also caused by the adopted static load balancing.
Since the computational complexity at some regions is increasing
considerably during the analysis (strain-softening), the
load balance is disturbed, resulting in the less loaded processors to
be idle. This effect is becoming more significant as the
number of processors increases. Despite these facts, the achieved
speedup and efficiency are significant, leading to considerable
reduction of the computational time.
The same problem was solved using the microplane material model M4. The
model geometry (see Fig. 16) was slightly modified in order to enable the use of
uniform structured mesh. This is necessary to ensure the material properties
(summarized in Table 1) to be the same for each element, otherwise
separate fitting procedure would be required for each element to
specify appropriate material properties. Note that the dependence of material
properties can be eliminated by introduction of nonlocal version of
microplane model. Again, the static loading was simulated by prescribed
displacement of transverse edges on top of specimen surface.
The structured mesh contains 2772 nodes and 2030 linear brick elements
(each with 8 integration points). The analysis has been performed
using 7500 time increments. The achieved computation times and speedups on PC cluster
are presented in Fig. 17. Note that superlinear speedup has been
achieved, which can be explained by enlarged amount of available
cache and by preserving computation to communication ratio at high values.

** Next:** Parallel Implicit Analysis of Composite Plates
**Up:** Examples
** Previous:** Parallel Mesh Generation
*Daniel Rypl *

2005-12-03