Civil Engineering Reference
In-Depth Information
tools of nanoscale synthesis and manipulation became available, there was
a pressing need for concurrent development of the predictive modeling
techniques. Continuum micromechanics represent the systematic approach
for upscaling properties (mechanical, physical, etc.) of composite materials
based on the constituents' properties that compose the heterogeneous
microstructure. Typical models incorporate the fundamental mechanical
properties of C-S-H together with estimates of the volumetric proportions
( f i ) of all constituent phases ( i ) in a multi-scale homogenization scheme
that can predict the composite macroscopic elastic ( E hom , v hom
F( E i , v i , f i ))
(Constantinides and Ulm, 2004; Ulm et al. , 2004; Sanahuja et al. , 2007) and
strength ( c hom ,
=
i , f i )) behavior (Pichler et al. , 2009; Pichler and
Hellmich, 2011), where the only input requirements are the elastic ( E i , v i )
and plastic ( c i ,
ϕ
hom
=
F( c i ,
ϕ
i ) properties of the individual constituents and their volu-
metric proportions ( f i ). The morphological arrangement of the phases in
space is taken into consideration in the choice of the continuum microme-
chanical models. It has been found that for cementitious materials, a com-
bination of Mori-Tanaka and self-consistent schemes appears to deliver
robust results (Constantinides, 2006). Figure 2.5 demonstrates the predic-
tive capabilities of continuum-based micromechanical models, suggesting
ϕ
Structure
(m)
1:1
Cement paste
Mortar/concrete
Chemically/
thermally affected
Undrained
60
50
Mortar/concrete
(cm)
40
30
￿ ￿ ￿ ￿ ￿ ￿
20
Cement paste
(
clinker
10
µ
m)
2 = 0.98
R
CSH
0
0
20
40
60
Measurements (GPa)
(b)
C-S-H
(nm)
(a)
2.5 (a) Multi-scale think model for cement-based materials.
(b) Micromechanical predictions vs. macroscopic experimental data
for the elastic properties of cementitious materials.
Search WWH ::




Custom Search