15 Homogenization-Based Mechanical Behavior Modeling of Composites …
255
Fig. 15.1 Examples of elementary axial or planar alignments of inclusions and fibers
deformation once embedded in a matrix. In the 3D network case, fiber layer interconnections were mathematically accounted for, inspired from the behavior of 2D
pantographic structures (Alibert et al. 2003; Barchiesi and Placidi 2017; Eremeyev
et al. 2018, 2019; Eremeyev and Turco 2020). At last, some new examples of structures built from elementary alignments are commented. Since the spheroids coincide
with laminate layers when infinitely flat, the new examined case of “spheroid skewers” is shown to bring at hand approximate descriptions for other structure types as
the case of laminate structures with pillars in between layers.
15.3 Elementary Axial and Planar Alignments of Axially
Symmetric or Fiber-like Elements
The brief equation recalls in Sect. 15.2 amount to pointing that in estimating effective properties of composite structures, the essential need, aside of phase properties
and relative volume fractions is, as it is now quite well known, the description of
their morphology, in the sense of shapes and spatial organization of the constitutive
elements. In that respect, determining a mGO for representing the substructure in
the matrix is essential, equivalently to determining a mean Eshelby tensor for it but
more easily thanks to more helpful specific properties.
Figure 15.1 presents different regular
2 “elementary” alignments that have been
working on, in the recent years, either in terms of axial patterns (left) or planar ones
2 These regular cases of quite simple extension to infinite alignments are taken from general less
regular ones.
255
Fig. 15.1 Examples of elementary axial or planar alignments of inclusions and fibers
deformation once embedded in a matrix. In the 3D network case, fiber layer interconnections were mathematically accounted for, inspired from the behavior of 2D
pantographic structures (Alibert et al. 2003; Barchiesi and Placidi 2017; Eremeyev
et al. 2018, 2019; Eremeyev and Turco 2020). At last, some new examples of structures built from elementary alignments are commented. Since the spheroids coincide
with laminate layers when infinitely flat, the new examined case of “spheroid skewers” is shown to bring at hand approximate descriptions for other structure types as
the case of laminate structures with pillars in between layers.
15.3 Elementary Axial and Planar Alignments of Axially
Symmetric or Fiber-like Elements
The brief equation recalls in Sect. 15.2 amount to pointing that in estimating effective properties of composite structures, the essential need, aside of phase properties
and relative volume fractions is, as it is now quite well known, the description of
their morphology, in the sense of shapes and spatial organization of the constitutive
elements. In that respect, determining a mGO for representing the substructure in
the matrix is essential, equivalently to determining a mean Eshelby tensor for it but
more easily thanks to more helpful specific properties.
Figure 15.1 presents different regular
2 “elementary” alignments that have been
working on, in the recent years, either in terms of axial patterns (left) or planar ones
2 These regular cases of quite simple extension to infinite alignments are taken from general less
regular ones.