The Effects of Anisotropic Insulations with Different Spatial Distributions on Material Properties of Mortar Specimens
International Journal of Concrete Structures and Materials
The Effects of Anisotropic Insulations with Different Spatial Distributions on Material Properties of Mortar Specimens
Mohamed Abd Elrahman
Insulating concrete is a material designed to reduce heat conduction with pores/insulations, and these pores strongly affect the material characteristics. In general, the insulation effect is directly proportion to the pore volume, while the material strength decreases as the porosity increases. To overcome this contrary, anisotropic insulations with different spatial distributions are proposed and investigated in this study. A set of mortar specimens with different arrangements of coin-shaped insulations are produced to examine the anisotropic insulation effect on the material characteristics. In addition, different types of insulation materials and their effect on the materials are also investigated here. X-ray computed tomography images and probabilistic description methods are used to confirm the arrangement of the insulations. The thermal and mechanical responses for different directions are investigated using both experimental and numerical methods. From the results, it is demonstrated that the use of anisotropic insulations for a specific direction can enhance the insulation efficiently as well as minimizing the loss of compressive strength.
insulating concrete; anisotropic insulation; X-ray CT; probability function; thermal conductivity; compressive strength
In recent years, energy consumption is considered as a
serious problem in many engineering fields, and many efforts
have been conducted to improve energy efficiency. Many new
buildings and construction materials have been suggested and
used over the last decades
(Roma-Jr and Martello 2008; Sales
et al. 2010; Benmansour et al. 2014)
. In particular, insulating
concrete has been widely used to reduce energy consumption.
Insulating concrete is a material designed to enhance insulation
effect by using insulating components, such as lightweight
aggregates, and entrained pores. The type of insulation
contained in the specimen and its characteristics play a significant
role in reducing heat transfer and material properties of
(Narayanan and Ramamurthy 2000; Baetens
et al. 2011; Chabannes et al. 2014; Binici et al. 2016)
Insulating concrete contains numerous pores inside the
material, and the volume ratio and the spatial distribution of
these insulations strongly affect the characteristics of
concrete. Thus, it is important to correctly investigate the
spatial distribution of insulation materials, and many
researchers have studied the insulation/pore distribution and
its effect on the material properties.
Dorey et al. (2002)
investigated the pore clustering effect on the material
properties of ceramic.
Won and Chau (2005)
concrete specimens with different constituent distributions.
Chung et al. (2013)
examined the correlation between the
pore characteristics and the directional modulus of
lightweight aggregates and evaluated the effect of the pore
distribution on thermal properties of insulating specimens using
Chung et al. (2016)
. Hao et al. (2016)
investigated the effect of optimized porosity distribution of
insulation materials by the variational method.
In general, the thermal conductivity decreases as the
volume ratio of insulations increases, while the mechanical
properties, such as strength and directional modulus, have a
direct proportion to the insulation volume. In order to
overcome the contrary behavior between these physical
properties, several studies have been reported on related
Cabrillac and Malou (2000)
modeling of anisotropic pores using a homogenization method,
Zake-Tiluga et al. (2014)
behavior of compressive strength in porous ceramics. In
Cabrillac et al. (2006)
suggested and examined
concretes with anisotropic pores and their effect on the
Chung et al. (2016)
the effect of ellipsoidal (anisotropic) pores on the thermal
properties of materials using 3D printed samples. From these
studies, it is demonstrated that a proper use of anisotropic
pores can effectively overcome the contrary responses
between thermal and mechanical properties without causing
However, pores with anisotropic geometries are difficult to
produce in a real specimen due to heterogeneity of concrete.
Thus, rigid insulation materials with very low thermal
conductivity can be used as artificial pores to examine the effect
of anisotropic pores on the characteristics of insulating
concrete. Several materials have been used as insulation
used pumice aggregates as an
insulation materials to investigate the effect on thermal
properties and showed its effect in reducing the thermal
Ng and Low (2010)
thermal properties of specimens with newspaper sandwiched
lightweight panels, which is much lower than that of
Jiang et al. (2013)
natural leaves to improve the insulation of concrete by reducing
energy consumption and environmental damage.
In this study, three different materials are utilized as
insulation materials for the specimens: low-density
expanded polystyrene (EPS), Af/Armaflex (Armacell, UK) made
of elastomeric nitrile rubber, and corrugated paper used for
packing box; these materials have very low thermal
conductivity and can be utilized as alternative pores. To secure
anisotropic pores (or insulations) in the sample, these three
insulation materials were cut into a coin-shape, and a set of
insulating mortar specimens with the coin-shaped insulations
were generated to evaluate the effect of anisotropic pores on
the material characteristics and properties. Using these
artificial anisotropic insulations, the real samples with
anisotropic pores can be produced, and their arrangements can be
easily controlled. For characterization of the insulation
distributions, probability functions, such as two-point
(Tewari et al. 2004; Gokhale et al. 2005)
(Lu and Torquato 1992; Chung and Han
, were used. These probability functions were utilized
to describe the degree of pore clustering and connectivity for
a specific direction
(Ke et al. 2009; Neithalath et al. 2010)
Effects of anisotropic insulations on the material properties
were examined experimentally and numerically.
The main objective of this study is to examine the effect of
the spatial distribution of different anisotropic insulations on
the physical properties of mortar specimens. For the purpose,
different insulation materials were used to secure anisotropic
artificial pores in the specimens. In addition, the effects of the
insulation volumes and the spatial distribution of insulations
on the insulating specimens were also investigated. For
effective modeling of the specimens with anisotropic
insulations, virtual insulating specimens with different distributions
of insulations were generated, and their characteristics and
properties were numerically computed. Then, a set of concrete
(mortar) specimens with different insulations and
arrangements were produced based on the numerical results. The
insulation arrangements within the concrete specimens were
confirmed using X-ray computed tomography (CT) without
damaging the specimen. The material properties, such as the
thermal conductivity, compressive strength, and Young’s
modulus, were also evaluated from experimental methods.
The thermal properties of the insulating specimens are
examined using a Hot Disk, a device which satisfies ISO
. The compressive
strength values of the specimens were measured using a Toni
Technik loading tool
. The obtained
properties were compared with those from simulations. The
relationship between the probabilistic descriptions and the
physical properties is investigated to evaluate the effect of
anisotropic insulations on the material characteristics of
insulating mortar specimens.
2. Concrete Specimens with Different
A set of virtual samples with different insulation
distributions are designed to identify the effect of anisotropic
insulations on the characteristics and properties of materials.
Then, real mortar specimens with different insulation types
and distributions are manufactured, and their properties as
well as the spatial distribution of insulations are also
2.1 Modeling of Virtual Samples with Different
Here, a set of virtual samples with different number of
anisotropic insulations are generated. For a geometry of
Cabrillac et al. (2006)
et al. (2016)
reported that an ellipsoid is an optimal shape for
the anisotropic insulation; however, ellipsoidal insulations
are difficult to produce for a real specimen. Therefore, all the
insulation materials here are alternatively designed as
Figure 1 shows target virtual specimens with different
numbers of anisotropic insulation layers. Each side of the
virtual samples in Fig. 1 is discretized into 150 voxels for
the x, y, and z directions, and each sample is composed of
total of 3,375,000 voxels. All the coin-shape insulations
have the same dimension with diameter of 0.16 and
thickness of 0.032 in a unit cube with edge length 1, and each
insulation layer in the x–y plane is composed of 25
anisotropic insulations (5 5 in x y direction). The virtual
specimens in Fig. 1 are denoted as L3 (Fig. 1a), L6
(Fig. 1b), and L9 (Fig. 1c) samples. Each specimen contains
3 (L3), 6 (L6), and 9 (L9) insulation layers with total of 75,
150, and 225 coin-shaped insulations, respectively. The
volume ratios of anisotropic insulations in each specimen are
5.97% (L3), 9.29% (L6), and 13.27% (L9). Using these
samples, the effect of the anisotropic insulations with
different spatial distributions can be examined numerically.
2.2 Preparation of the Mortar Specimens with Different Anisotropic Insulations
The designed specimens in Fig. 1 are produced as real
mortar specimens with different types of insulations. For the
purpose, three different materials are used for insulations:
expanded polystyrene (EPS), Af/armaflex (Armacell, UK),
and corrugated paper; these insulation materials are denoted
Fig. 1 Virtual specimens with different arrangements of anisotropic insulations: a L3 sample with 3 insulation layers (total of 75
insulations), b L6 sample with 6 layers (150 insulations), c L9 samples with 9 layers (225 insulations) [In the figure, the dark
gray voxels represent anisotropic insulations. Each coin-shaped insulation has the same dimension, and each insulation
layer is composed of 25 insulations (5 5 in y plane)].
here as EPS, Rubber, and Paper, respectively. These
insulations are selected because of their low thermal conductivity
and formability, and the physical characteristics of each
insulation material are shown in Table 1; these properties are
obtained from experimental devices and other investigators
including the manufacturers
(Yucel et al. 2003; Russ et al.
Figure 2 shows the preparation of the mortar specimens
with different anisotropic insulations. All the insulations are
cut into coin-shaped pieces with diameter of 16.0 ± 1.0 mm
and thickness of 3.0 ± 1.0 mm. The mortar specimens are
prepared in a mold with dimensions of 100 100 100
mm. To produce regular arrangement of the insulations, a
layer with a specific thickness is spread in the mold. Then,
the coin-shaped insulations are uniformly distributed as
shown in Fig. 2, and repeat the same procedure by
considering the target number of insulation layers. The thickness
between each insulation layer depends on the total number
of layers in the specimen; the layer thicknesses of the
specimens with 3, 6, and 9 insulation layers are 24.0, 12.8,
and 8.3 mm, respectively. The whole process is repeated
until the entire specimen is filled with mortar along the
height direction. The mix designs are given in Table 2, and
CEM I 42.5N is used for all specimens. The used aggregates
in this study are normal sand with size fraction of 0–2 mm.
Using these specimens, the effects of the insulation
distributions as well as the type of insulations on the material
properties are investigated.
3. Characterization and Property
Measurements of Anisotropic Insulations
3.1 Probabilistic Characterization of
The insulation distributions in the specimens significantly
affect the material properties of insulating concrete. For
more detailed investigation of the spatial distribution of
insulations, appropriate quantitative and qualitative methods
are required. Here, low-order probability functions, such as
two-point correlation and lineal-path functions, are used to
examine the anisotropic insulation distribution, and their
integrations are also utilized for the quantitative description.
3.1.1 Two-Point Correlation Function
Among the several probability functions, the two-point
correlation function, denoted as Piiðr; h; /Þ, is adopted.
Piiðr; h; /Þ is the probability that any two points are located
in the insulation phase
Tewari et al. (2004)
and utilized to
describe the degree of phase clustering for a specific
direction. Here, i denotes the insulation phase, r is the distance
between two points, h is the angle between a test line and the
z-axis, and / is the angle between the projection of a test line
on the xy-plane and the x-axis. For two-phase materials that
are classified into insulations and solids, the general limits of
the two-point correlation function for the insulation phase
are given as follows
(Gokhale et al. 2005; Kumar et al.
Thermal conductivity (W/ m/K)
Specific heat (J/g/K)
Elastic modulus (GPa)
Yield strength (MPa)
Rubber specimen Paper specimen 750 1500
rli!m0 Piiðr; h; /Þ ¼ fi; lim Piiðr; h; /Þ ¼ ½fi 2
where fi is the volume fraction of the insulation phase. In
Eq. (1), the probability of finding the insulation phase at
both points converges to fi as the distance between two
points approaches zero, while the function converges to the
product of fi as r increases. Pii, can be calculated using a
simple form of the function suggested by
Gokhale et al.
Piiðr; h; /Þ ¼ fið1
expf ð½PLðh; /Þ is=ð2fifsÞÞrg Þ
where the subscript s denotes the solid phase, fs is the solid
volume fraction, and ½PLðh; /Þis is the number of
intersections between a test line and the i-s phase interface per unit
test line length.
The two-point correlation function can be utilized to
describe the spatial distribution of insulations in materials;
however, it is difficult to be used for quantitative analysis
because the function is a form of the probability distribution
(Chung et al. 2013, 2016)
. To describe the
probabilistic function as a representative value, Pii for a particular
direction is integrated from 0 to 1, and normalized by
dividing the insulation volume fraction of the specimen.
Here, the integration of the function is expressed as Pii and
calculated as follows:
Pii ¼ fi 0
1 Z 1
where r denotes r / D, and D is the specimen length. For the
quantitative description of the insulation distributions, Pii
values for different directions are calculated and assigned to
each point of a grid represented on a sphere, which is
composed of 1538 nodal points. Here, the 3D space is
discretized into 1538 grids for effective visualization of
anisotropy, and the calculation of r is repeated for the whole
discrete directions. The Pii values between the nodal points
are calculated from the standard finite element interpolation,
and detailed description of this method is shown in
et al. 2013; Han and Dawson 2005)
3.1.2 Lineal-Path Function
The lineal-path function, Liðr; h; /Þ, is also used here to
describe the continuity of insulations. Liðr; h; /Þ is the
probability that a randomly placed line with length r is
located in the insulation phase
Chung et al. (2016)
Piiðr; h; /Þ, Liðr; h; /Þ can be utilized to examine the
continuous connectivity of the insulation phase for a specific
direction because the function only includes the case that a
whole line is positioned in the insulation phase Lu and
Torquato (1992); therefore, Liðr; h; /Þ can be utilized as a
complementary function of Piiðr; h; /Þ. The general limits of
Liðr; h; /Þ are given as:
rli!m0 Liðr; h; /Þ ¼ fi; lim Liðr; h; /Þ ¼ 0
In this study, the Coker and Torquato’s method is adopted to
obtain Liðr; h; /Þ for the insulating specimens, and detailed
procedure is presented in
Coker and Torquato (1995)
Likewise the case of Piiðr; h; /Þ, Liðr; h; /Þ for different
directions are also integrated and normalized for quantitative
description of the insulation distribution, as follows:
1 Z 1
Li ¼ fi 0 Lidr
To quantify the anisotropy of the insulation distribution, Li
values for different directions are calculated.
3.2 Investigation of the Physical Properties of the Specimens
The thermal and mechanical properties of the specimens
with different insulations and distributions are examined
using numerical as well as experimental methods. The
material responses of the virtual samples are evaluated to
investigate the anisotropy of the properties using finite
element (FE) analysis. In addition, the thermal conductivity and
compressive strength values of the specimens with different
types of insulations are examined using experimental tools.
3.2.1 Numerical Simulation for Thermal and
To investigate the anisotropic effect on the material
properties, the thermal and mechanical responses of the
virtual samples in Fig. 1 are evaluated using FE simulations.
The ABAQUS package
is used for the
numerical simulations, and detailed descriptions on the FE
formulations for thermal and mechanical analysis are
(Chung et al. 2016; Incropera et al. 2006)
; only a brief
description is presented here.
For heat transfer analysis, the governing equation for 3D
heat flow by considering heat loss can be described as:
ot ¼ qC
o2T o2T o2T
ox2 þ oy2 þ oz2
where, q is the mass density (kg/m3), C is the specific heat
(J/g/K), and k is the thermal conductivity (W/m/K). T is the
temperature (K), T is the surrounding temperature (K), k is
the heat loss coefficient (1/s), and t is the time (s).
For the FE simulation, a weak form is obtained by
integrating the governing equation in Eq. (6), and the heat flux
can be calculated by averaging the specimen heat flux. Then,
the effective thermal conductivity is calculated by the
Fourier law as:
where 4TðnÞ is the temperature difference in the direction of
thermal conduction, n is the directional component, and L is
the characteristic length.
The required input parameters for the heat analysis, such
as the bulk thermal conductivity and specific heat of
hydrated mortar and insulation materials, are obtained from
experiments using a Hot Disk device that satisfies ISO
; the parameters
used here are presented in Table 1. For the boundary
condition, a constant temperature (60 C) is imposed on the top
side of the specimen, while heat loss is allowed only in the
opposite side along in each direction. The remaining
surfaces are considered to have no heat loss, and the
surrounding temperature is set as 22 C. Heat loss coefficient, k,
is obtained from the Hot Disk device and selected as 1.6 (1/
s). In this study, the thermal conductivities for all the
specimens are measured in the x and z directions to examine
anisotropic thermal properties.
The compressive strengths of the virtual samples are also
evaluated using the FE analysis. For the simulations, the
ABAQUS software including the concrete damage plasticity
(CDP) model is used to describe the behavior of the virtual
insulating specimens with different insulation distributions.
Detailed descriptions of the FE formulations are presented
Kmiecik and Kaminski (2011)
, and only a brief
description of the constitutive model is shown in this paper. The
stress-strain relation of the CDP model is governed by a
scalar damaged elasticity as:
r ¼ ð1
dÞDe0l : ð
plÞ ¼ D0 : ð
where, r is the stress tensor, d is the scalar stiffness
degradation variable between 0 (undamaged material) to 1 (fully
damaged material), De0l is the initial elastic modulus, D0 is
the degraded elastic stiffness, is the total strain tensor, and
pl is the plastic strain tensor.
Each elemental stress is calculated at the center of each
element, and the effective stress is obtained from the element
stresses by integrating over the whole volume. For the
boundary condition, a displacement boundary condition is
imposed on the top surface in each x and z direction, while a
fixed boundary condition is applied to the bottom plane.
Other remaining lateral surfaces are set to be traction free.
The parameters for the CDP model, such as dilation angle
and eccentricity, are selected and adjusted from the data
(Kmiecik and Kaminski 2011; Jankowiak and
. The input parameters for the mechanical
simulations of the specimens with different insulations are
listed in Table 1. The simulation results are compared with
experiments for validation purpose. The effect of different
insulations and the correlation between the insulation
distribution and the directional compressive strength are also
confirmed from the results
3.2.2 Experiments for the Evaluation of Material
Using the Hot Disk machine (Hot Disk AB, Sweden),
thermal properties, such as thermal conductivity, thermal
diffusivity, and specific heat capacity can be effectively
measured, and the obtained results are utilized for the
numerical simulations as the input parameters. This device is
based on the use of a transiently heated plane sensor, and the
sensor is sandwiched between two sheets of an insulating
material to be measured. Detailed description of the
measurement process is shown in Fig. 3a. The compressive
strength of the specimens are also evaluated using the Toni
Technik (Zwick Roell, Germany) machine in Fig. 3b, a
device which meets German standard 12390-4
with loading rate of 0.50 MPa/s and with
loading capacity of 3000 kN. Likewise the thermal property,
the strengths of the specimens are evaluated for the different
(x and z) directions to confirm the effect of anisotropic
insulations on the mechanical properties of the specimens.
All tests have been carried out on three specimens and the
mean value is considered in each case. Here, at least three
specimens of each case are tested to enhance the accuracy,
and only the mean values are presented.
4. Characteristics and Properties
of the Insulating Specimens with Different
The characteristics of the insulation distributions are
described using the methods in Sect. 3.1 In particular, the
anisotropic characteristics of the specimens with different
insulation distributions are identified, and their effects on the
material properties are examined using the numerical and
4.1 Anisotropic Characteristics of the Virtual
The virtual specimens in Fig. 1 contain anisotropic
insulations inside the specimens. The characteristics of the
insulation distributions are investigated using the
probabilistic and quantitative methods. Fig. 4 shows the
probability functions of the virtual samples with anisotropic
insulations in the x, y, and z directions; Fig. 4a–c are the
twopoint correlation function (PiiðrÞ), and Fig. 4d–f are the
lineal-path function (LiðrÞ). In each function, r represents the
distance between two random points, and D is the specimen
edge length. In these figures, the porosities and the directional
characteristics of the insulation distributions are clearly
described; the porosities in each function are 0.0597, 0.0929,
and 0.1327 for L3, L6, and L9 samples, respectively. PiiðrÞ
and LiðrÞ in Fig. 4 show almost the same functions in the x
and y directions, while the function values in the z direction
are smaller than other directions; this represents that the size
of the insulations in the z-direction is smaller than that of
other directions, and the insulation distributions in the
specimens are anisotropic. In Fig. 4a–c, the relative degree of
clustering of insulations can be estimated using PiiðrÞ. In
particular, LiðrÞ can be used to demonstrate the anisotropy of
the coin-shaped insulation used in this study. The ratio
between the diameter and the thickness of each coin-shaped
insulation is designed as approximately 5:1. In Fig. 4d–f, the
function values in the x and y directions are zero when r /
D reaches 0.16, while the function for the z-direction is zero
when r / D is about 0.3; this ratio is almost identical with that
of the coin-shaped insulation, and it is examined that the
probability functions used here can be effectively used to
describe the directional characteristics of insulation materials.
For the quantitative description of the insulation
distribution, Pii of the specimens in Fig. 1 is also investigated. To
describe the relative anisotropy of the insulation distribution,
Pii for every direction is divided by the minimum value of
Pii for each specimen, and the Pii values are visualized on a
sphere mesh, as shown in Fig. 5. In these figures, the
indexed values (Pii/minPii) for the x–y plane is distinctly
larger than that of the z-direction. The maximum anisotropy
ratio of Pii between different directions decreases as the
number of insulation layers for the z-direction increases:
2.11 (L3), 1.81 (L6), and 1.62 (L9). In addition, the
anisotropy ratio of the integration of LiðrÞ, Li, bears the same
characteristics, as 4.5 (L3), 4.2 (L6), and 3.3 (L9), although
they are not visualized here. The maximum anisotropy ratio
decreases as the total volume of the insulations increases
because the insulation layers are stacked only in the
z-direction. These results demonstrate that Pii as well as Li can
be efficiently utilized to describe the characteristics of the
insulation distributions, and the insulation distributions in
each specimen are anisotropic.
4.2 Material Responses of the Virtual Insulating
The thermal and mechanical properties of the virtual
specimens with different insulation types and distributions
are investigated using FE simulations. Fig. 6 shows the
contours of heat flux and temperature isosurfaces for the
virtual insulating specimens with Rubber insulations. In the
heat flux contours (Fig. 6a, c, and e), it can be confirmed that
heat flows through a solid (mortar) part, while heat transfers
rarely through insulation parts. In particular, the heat
transfers well through the x-direction, the direction parallel to the
flat surface of the coin-shaped insulation; however, the less
heat flows through the z-direction than other (x and y)
directions because the flat surfaces of the coin-shaped
insulations disrupt the heat flow. In all directions, the solid region
where heat transfers mostly, decreases as the volume of
insulations increases; therefore, the total amount of heat
which flows through the solids decreases as more
coinshaped insulations are contained in the specimen. The effect
of the coin-shaped insulations can be also identified from the
temperature isosurfaces in Fig. 6b, d, and f. In the
isosurfaces for the x-direction, the isosurfaces are almost flat
because the insulations parallel to the heat flow direction
rarely affect the heat transfer. However, in the right figures of
Fig. 6b, d, and f, the fluctuations of the temperature
isosurfaces can be found near the insulations; this result
demonstrates that the coin-shaped insulation strongly affects
the hear flow for the perpendicular direction to its flat
surface. The same trends are also examined for the use of
different insulations, such as EPS and Paper.
Fig. 6 The view cut of heat flux contour and temperature isosurface of the specimens with Rubber insulations for the x and
z directions: a Heat flux of L3 sample, b Temperature isosurface of L3 sample, c Heat flux of L6 sample, d Temperature
isosurface of L6 sample, e Heat flux of L9 sample, f Temperature isosurface of L9 sample (Note In all figures, left figure is for
the x-direction heat flow, and right figure is for the z-direction heat flow.).
The mechanical responses of the virtual specimens with
Rubber insulations are also investigated using FE analysis.
Fig. 7 shows the stress contours of the specimens with
anisotropic insulations. In the contour figures, the effect of
coin-shaped insulations can be identified. In the left
figures of Fig. 7, the stress distributions are relatively uniform
over the whole specimen when the loading is applied to the
direction that parallel to the flat surfaces of the coin-shaped
insulations (x-direction), although the vicinity of the
insulations shows less stress values than other parts. In contrast,
when the loading is applied to the z-direction, perpendicular
to the flat surface of the anisotropic insulation, the stress
concentrations can be found near the edge and vertex of the
coin-shaped insulations, and these stress concentrations can
be critical for early specimen failure from that location; it
denotes that the direction of coin-shaped (anisotropic)
insulations affects the mechanical responses of the specimen
significantly. Likewise the thermal responses, the same
tendencies of the stress distribution are confirmed for the
different insulation materials.
For the quantitative investigation of the material
responses, thermal conductivity and compressive strength are
calculated from the simulation results in Figs. 6 and 7, as
shown in Fig. 8. In Fig. 8a, the thermal conductivities of the
virtual specimens with different insulation distributions are
presented. For all insulation materials, the thermal
conductivity as well as compressive strength decrease as the number
of insulation layers increases. In particular, both material
properties in the z-direction significantly decrease more than
those of the x-direction as the layer number increases. From
these results, as shown in Figs. 6 and 8, it is confirmed that
the material properties are more affected by the coin-shaped
insulations in the perpendicular direction to the flat surface
of the insulation. The effect of the different insulations can
also be examined from the graphs; the use of different
insulations rarely affects the thermal and mechanical
properties for the x-direction, as shown in Fig. 8. Otherwise, the
material properties for the z-direction are affected by the type
of insulation, especially the compressive strength of the
specimen. In these results, it is shown that the EPS is the
most effective to reduce the thermal conductivity because of
its higher specific heat
Owrak et al. (2015)
, while corrugated
paper is the most beneficial insulation material for larger
strength of the specimen because of its larger elasticity and
strength. Fig. 8 is the theoretical result to investigate the
effect of different insulations and distributions on material
characteristics and properties.
4.3 Physical Properties of the Insulating
Specimens with Different Anisotropic Insulations
Here, experimental study is also performed to investigate
the effect of anisotropic insulations on the real specimens.
Fig. 9 shows the thermal conductivity and compressive
Fig. 7 The view cut of von-Mises stress contour of the specimens with Rubber insulations for the x and z directions: a L3 sample,
b L6 sample, c L9 sample (Note: In the figures, left figure is for the x-direction of loading, and right figure is for the z-direction
1 2 3 4 5 6 7 8
Number of anisotropic insulation layers (z-dir.)
1 2 3 4 5 6 7 8
Number of anisotropic insulation layers (z-dir.)
Fig. 8 Comparison of numerical material properties of the virtual insulating specimens with different insulations for the x and
z directions: a Thermal conductivity, b Compressive strength.
strength of the real mortar specimens with anisotropic
insulations measured from experimental tools. For the
property evaluation, the Hot Disk (thermal) and the Toni
Technik (mechanical) devices are used here. For each case,
measurements are repeated at least 6 times in order to
improve accuracy. The mean values are calculated by
excluding the extreme values, and the difference between the
used values are within 3%. In Figs. 8 and 9, the differences
between the numerical and experimental results of the
material properties can be identified; the differences are
generally within 7%, and this error level can be considered
as a reasonable tolerance. In Fig. 9, it is confirmed that both
thermal conductivity and compressive strength decrease as
the insulation volume increases, like the simulation results.
In general, compressive strength and directional modulus of
materials decrease as the weight of the specimen decreases,
while the insulation effect increases; the results in Fig. 9
demonstrate the effect of the weight loss of the specimen on
the material properties, and the anisotropic insulation can be
utilized to optimize this phenomenon. In the experimental
results, the anisotropic trends of material properties are
similar to those of the simulations, while the differences
between the different types of insulations are more distinct
than the simulations; these differences are mainly due to the
coarse structure of the insulations which can be filled by
mortar in the real specimens and are not considered in the
simulation model. In addition, the location movements of the
insulations can also affect the difference between the
simulation and the experiment. Fig. 10 shows the partial sections
of X-ray CT images for each specimen. In this figure, it is
examined that the coin-shaped insulations are positioned
well as originally designed, but some position shifts and
irregular shapes of the insulations which occurs during the
sample preparation can be found. In addition, it can be seen
in Fig. 10c that mortar is infiltrated into the corrugated paper
in some layers; these migrated and infiltrated insulations can
cause the differences between the results. Even though the
differences, the general trend of the thermal and mechanical
characteristics of the mortar specimens with anisotropic
insulations is almost the same with that of the simulations.
Likewise the numerical results, EPS is the most effective
material to have the lower thermal conductivity, and Paper
can be considered as a material to obtain larger strength than
other materials used here. The results suggest that the use of
anisotropic insulations can improve the material’s insulation
effect, especially when heat flows through the perpendicular
direction to the flat surface of the anisotropic insulation, and
arrangements and types of insulation materials should be
The anisotropic insulation and its effect on the material
characteristics are examined. To secure anisotropic
insulations in the specimen, a set of coin-shaped insulations with
different materials, such as expanded polystyrene (EPS),
elastomeric nitrile rubber (Rubber), and corrugated paper
(Paper), are prepared, and these insulations are used to
produce mortar specimens with different arrangements. The
virtual specimens are designed to evaluated the effect of
anisotropic insulations on the material using numerical
methods, and the results are adopted to produce real
insulating specimens. Low-order probabilistic functions and their
modified indexes are utilized for the characterization of the
insulation distribution. The physical properties, such as
thermal conductivity and compressive strength, are
examined using both FE simulations and experimental tools.
Then, the correlation between the material characteristics
and properties is investigated.
The anisotropy of the insulation distribution is effectively
examined using the characterization methods utilized here.
Comparing the directional material properties, it is
demonstrated that the thermal conductivity is smaller when heat
flows in the direction perpendicular to the flat surface of the
coin-shaped insulation, while the strength is larger when the
loading direction is parallel to the flat surface. Among the
three insulation materials used here, EPS is the most
effective material to improve the insulation effect, although
strength loss should be carefully considered. The results
confirm that appropriately arranged anisotropic insulations
can be effectively used to obtain a material with low thermal
conductivity by minimizing strength loss, and anisotropic
insulations/pores can be a promising method for better
insulating material without increasing the insulation/pore
The project is supported by the German Federal Ministry of
Education and Research (BMBF, Project Number:
13XP5010B and 01DR16007) and the German Academic
Exchange Service (DAAD, Ref. No.: 91563255). The
authors also want to thank Mr. Paul H. Kamm (Helmholtz
Centre Berlin) for his assistance in CT imaging.
This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unre
stricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original
author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
ABAQUS. ( 2013 ). Version 6 .13, Dassault Systemes , Pawtucket, Rhode Island.
Baetens , R. , Jelle , B. P. , & Gustavsen , A. ( 2011 ). Aerogel insulation for building applications: A state-of-the-art review . Energy and Buildings , 43 , 761 - 769 .
Benmansour , N. , Agoudjil , B. , Gherabli , A. , Kareche , A. , & Boudenne , A. ( 2014 ). Thermal and mechanical performance of natural mortar reinforced with date palm fibers for use as insulating materials in building . Energy and Buildings , 58 , 98 - 104 .
Binici , H. , Aksogan , O. , & Demirhan , C. ( 2016 ). Mechanical, thermal and acoustical characterizations of an insulation composite made of bio-based materials . Sustainable Cities and Society , 20 , 17 - 26 .
Cabrillac , R. , Fiorio , B. , Beaucour , A. , Dumontet , H. , & Ortola , S. ( 2006 ). Experimental study of the mechanical anisotropy of aerated concretes and of the adjustment parameters of the introduced porosity . Construction and Building Materials , 20 , 286 - 295 .
Cabrillac , R. , & Malou , Z. ( 2000 ). Mechanical modelization of anisotropic porous materials with a homogenization method. Application to aerated concretes . Construction and Building Materials , 14 , 25 - 33 .
Chabannes , M. , Benezet , J.-C. , Clerc , L. , & Garcia-Diaz , E. ( 2014 ). Use of raw rice husk as natural aggregate in a lightweight insulating concrete: An innovative application . Construction and Building Materials , 70 , 428 - 438 .
Chung , S.-Y., & Han, T .-S. ( 2010 ). Reconstruction of random two-phase polycrystalline solids using low-order probability functions and evaluation of mechanical behavior . Computational Materials Science , 49 , 705 - 719 .
Chung , S.-Y., Han, T.-S., Kim , S.-Y., Kim , J.-H. J. , Youm , K. S. , & Lim , J.-H. ( 2016 ). Evaluation of effect of glass beads on thermal conductivity of insulating concrete using micro CT images and probability functions . Cement and Concrete Composites , 65 , 150 - 162 .
Chung , S.-Y., Han, T.-S., Yun , T. S. , & Yeom , K. S. ( 2013 ). Evaluation of the anisotropy of the void distribution and the stiffness of lightweight aggregates using CT imaging . Construction and Building Materials , 48 , 998 - 1008 .
Chung , S.-Y., Stephan , D. , Elrahman , M. A. , & Han, T .-S. ( 2016 ). Effects of anisotropic voids on thermal properties of insulating media investigated using 3D printed samples . Construction and Building Materials , 111 , 529 - 542 .
Coker , D. A. , & Torquato , S. ( 1995 ). Extraction of morphological quantities from a digitized medium . Journal of Applied Physics , 77 , 6087 - 6099 .
DeutscheNorm , Plastics-Determination of thermal conductivity and thermal diffusivity-Part 2: Transient plane heat source (Hot Disc) method , German version EN ISO 22007-2 , Berlin, Germany, 2012 .
DeutscheNorm. ( 2010 ). Testing hardened concrete-Part 4: Compressive strength; Specification for testing machines , German version EN 12390-4:2000 , Berlin, Germany.
Dorey , R. , Yeomans , J. , & Smith , P. ( 2002 ). Effect of pore clustering on the mechanical properties of ceramics . Journal of the European Ceramic Society , 22 , 403 - 409 .
Gokhale , A. , Tewari , A. , & Garmestani , H. ( 2005 ). Constraints on microstructural two-point correlation functions . Scripta Materialia , 53 , 989 - 993 .
Gunduz , L. ( 2008 ). The effects of pumice aggregate/cement ratios on the low-strength concrete properties . Construction and Building Materials , 22 , 721 - 728 .
Han , T .-S., & Dawson , P. R. ( 2005 ). Representation of anisotropic phase morphology . Modelling and Simulation in Materials Science and Engineering , 13 , 203 - 223 .
Hao , J.-H. , Chen , Q. , & Hu , K. ( 2016 ). Porosity distribution optimization of insulation materials by the variational method . International Journal of Heat and Mass Transfer , 92 , 1 - 7 .
Incropera , F. P. , Dewitt , D. P. , Bergman , T. L. , & Lavine , A. S. ( 2006 ). Fundamentals of heat and mass transfer . New York: Wiley.
Jankowiak , T. , & Lodygowski , T. ( 2008 ). Identification of parameters of concrete damage plasticity constitutive model . Foundations of Civil and Environmental Engineering , 6 , 53 - 69 .
Jiang , D. , Cui , S. , Song , X. , & Zhang , J. ( 2013 ). Analysis of micromorphology and heat-insulating property of leaf concrete . Construction and Building Materials , 49 , 663 - 671 .
Ke , Y. , Beaucour , A. L. , Ortola , S. , Dumontet , H. , & Cabrillac , R. ( 2009 ). Influence of volume fraction and characteristics of lightweight aggregates on the mechanical properties of concrete . Construction and Building Materials , 23 , 2821 - 2828 .
Kmiecik , P. , & Kaminski , M. ( 2011 ). Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration . Archives of Civil and Mechanical Engineering , 11 , 623 - 636 .
Kumar , H. , Briant , C. L. , & Curtin , W. A. ( 2006 ). Using microstructure reconstruction to model mechanical behavior in complex microstructures . Mechanics of Materials , 38 , 818 - 832 .
Lu , B. , & Torquato , S. ( 1992 ). Lineal-path function for random heterogeneous materials . Physical Review A , 45 , 922 - 929 .
Narayanan , N. , & Ramamurthy , K. ( 2000 ). Structure and properties of aerated concrete: A review . Cement and Concrete Composites , 22 , 321 - 329 .
Neithalath , N. , Sumanasooriya , M. S. , & Deo , O. ( 2010 ). Characterizing pore volume, size, and connectivity in pervious concretes for permeability prediction . Materials Characterization , 61 , 802 - 813 .
Ng , S.-C. , & Low , K.-S. ( 2010 ). Thermal conductivity of newspaper sandwiched aerated lightweight concrete panel . Energy and Buildings , 42 , 2452 - 2456 .
Owrak , M. , Aminy , M. , Jamal-Abad , M. T. , & Dehghan , M. ( 2015 ). Experiments and simulations on the thermal performance of a sunspace attached to a room including heatstoring porous bed and water tanks . Building and Environment , 92 , 142 - 151 .
Roma Jr. , L. C. , Martello , L. S. , & Savastano , H. ( 2008 ). Evaluation of mechanical, physical and thermal performance of cement-based tiles reinforced with vegetable fibers . Construction and Building Materials , 22 ( 4 ), 668 - 674 .
Russ , A. , Schwartz , J. , Bohacek , S. , Lubke , H. , Ihnat , B. , & Pazitny , A. ( 2013 ). Reuse of old corrugated cardboard in constructional and thermal insulating boards . Wood Research , 58 , 505 - 510 .
Sales , A. , Souza , F. R. , Santos , W. N. , Zimer , A. M. , & Almeida , F. C. R. ( 2010 ). Lightweight composite concrete produced with water treatment sludge and sawdust: Thermal properties and potential application . Construction and Building Materials , 24 , 2446 - 2453 .
Tewari , A. , Gokhale , A. M. , Spowart , J. E. , & Miracle , D. B. ( 2004 ). Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions . Acta Materialia , 52 , 307 - 319 .
Wong , R. C. K. , & Chau , K. T. ( 2005 ). Estimation of air void and aggregate spatial distributions in concrete under uniaxial compression using computer tomography scanning . Cement and Concrete Research , 35 , 1566 - 1576 .
Yucel , K. , Basyigit , C. , Ozel , C. ( 2003 ). Thermal insulation properties of expanded polystyrene as construction and insulating materials . In 15th symposium on thermophysical properties (pp. 54 - 66 ).
Zake-Tiluga , I. , Svinka , R. , & Svinka , V. ( 2014 ). Anisotropy of compressive strength in porous alumina ceramics . Key Engineering Materials , 604 , 153 - 156 .
584 | International Journal of Concrete Structures and Materials (Vol. 11 , No. 4 , December 2017 )