144
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
when the requirement of coarse aggregates volumetric fraction is not very high, the
above criteria of invasion judgment for sphere can be used to save the modelling time.
If the volume fraction of the coarse aggregates is required to be high, the criteria of
invasion judgment based on the volume-index introduced in Liu and Gao (2003) can
be adopted. In order to improve the modelling efficiency, similarly, the methods of
block modelling and dropping the coarse aggregates in order of their particle sizes
are adopted at present. The 3D mesoscopic concrete model with random distributed
convex polyhedron coarse aggregates is shown in Fig. 5.36d, and the corresponding
modelling program is written by MATLAB and named as Polyhedron_Generation.
5.4.1.2 3D Mesoscopic Finite Element Model
The commonly meshing methods of finite element model include mapping, gridbased, Delaunay triangulation and advancing front methods, etc. (Guan et al. 2003).
Considering the element quality and meshing efficiency, the mapping method is
adopted at present, and the hexahedral element was adopted to guarantee the calculation accuracy (Landertshamer and Steffan 2010). In order to obtain the mesoscopic concrete model, the program named 3D_RanMesh for meshing is written
by MATLAB. When all the convex polyhedron coarse aggregates are completely
dropped, the meshing process is also finished simultaneously, and then the finite
element model is output.
Take the meshing of the 3D mesoscopic concrete model with random distributed
convex polyhedron coarse aggregates for example, there are two meshing types for
concrete with different components, one is the two-phase concrete composed of
coarse aggregates and mortar, and the other is the three-phase concrete with three
components: coarse aggregates, mortar and interfacial transition zone (ITZ).
(1) Meshing the two-phase concrete model
The elements generated by mapping method are all identical, and the coarse aggregates and mortar are not distinguished. Therefore, the generated elements must be
identified with material properties. Assuming that the element center is G, the outward
normal vector of any surface of coarse aggregates is
− →
i (1 < i < n, where n is the surface
number of polyhedral convex coarse aggregates), and one vertex on this surface is
P i . Then, the vector from the P i to G can be represented as
− − →
P i G. The boundary
conditions of the dropped coarse aggregates are identical with that in Sect. 5.4.4.1.
In order to improve the calculation efficiency, only identify the material properties of
elements which located around the coarse aggregates. The element sizes on the x, y
and z axes are denoted by E x , E y , E z , and n x , n y , n z are the number of elements which
needs to be identified in the corresponding direction. Then the element identification
range can be expressed as
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
when the requirement of coarse aggregates volumetric fraction is not very high, the
above criteria of invasion judgment for sphere can be used to save the modelling time.
If the volume fraction of the coarse aggregates is required to be high, the criteria of
invasion judgment based on the volume-index introduced in Liu and Gao (2003) can
be adopted. In order to improve the modelling efficiency, similarly, the methods of
block modelling and dropping the coarse aggregates in order of their particle sizes
are adopted at present. The 3D mesoscopic concrete model with random distributed
convex polyhedron coarse aggregates is shown in Fig. 5.36d, and the corresponding
modelling program is written by MATLAB and named as Polyhedron_Generation.
5.4.1.2 3D Mesoscopic Finite Element Model
The commonly meshing methods of finite element model include mapping, gridbased, Delaunay triangulation and advancing front methods, etc. (Guan et al. 2003).
Considering the element quality and meshing efficiency, the mapping method is
adopted at present, and the hexahedral element was adopted to guarantee the calculation accuracy (Landertshamer and Steffan 2010). In order to obtain the mesoscopic concrete model, the program named 3D_RanMesh for meshing is written
by MATLAB. When all the convex polyhedron coarse aggregates are completely
dropped, the meshing process is also finished simultaneously, and then the finite
element model is output.
Take the meshing of the 3D mesoscopic concrete model with random distributed
convex polyhedron coarse aggregates for example, there are two meshing types for
concrete with different components, one is the two-phase concrete composed of
coarse aggregates and mortar, and the other is the three-phase concrete with three
components: coarse aggregates, mortar and interfacial transition zone (ITZ).
(1) Meshing the two-phase concrete model
The elements generated by mapping method are all identical, and the coarse aggregates and mortar are not distinguished. Therefore, the generated elements must be
identified with material properties. Assuming that the element center is G, the outward
normal vector of any surface of coarse aggregates is
− →
i (1 < i < n, where n is the surface
number of polyhedral convex coarse aggregates), and one vertex on this surface is
P i . Then, the vector from the P i to G can be represented as
− − →
P i G. The boundary
conditions of the dropped coarse aggregates are identical with that in Sect. 5.4.4.1.
In order to improve the calculation efficiency, only identify the material properties of
elements which located around the coarse aggregates. The element sizes on the x, y
and z axes are denoted by E x , E y , E z , and n x , n y , n z are the number of elements which
needs to be identified in the corresponding direction. Then the element identification
range can be expressed as