Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing
The effect of particle rolling and crushing on the evolutions of the two types of anisotropy, i.e., anisotropy of particle packing (microstructure) and anisotropy of force chains, is investigated numerically using the discrete element method. To this end, the classical fabric tensor is adopted...
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| Опубліковано в: : | Проблемы прочности |
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| Дата: | 2014 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/112716 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing / L.L. Zhou, X.H. Chu, Y.J. Xu // Проблемы прочности. — 2014. — № 2. — С. 73-80. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859908081651023872 |
|---|---|
| author | Zhou, L.L. Chu, X.H. Xu, Y.J. |
| author_facet | Zhou, L.L. Chu, X.H. Xu, Y.J. |
| citation_txt | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing / L.L. Zhou, X.H. Chu, Y.J. Xu // Проблемы прочности. — 2014. — № 2. — С. 73-80. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | The effect of particle rolling and crushing on the
evolutions of the two types of anisotropy, i.e.,
anisotropy of particle packing (microstructure)
and anisotropy of force chains, is investigated
numerically using the discrete element method.
To this end, the classical fabric tensor is adopted
to describe the anisotropy of microstructure,
while two similar orientation tensors defined by
the directions of contact forces are used to characterize
the anisotropy of force chains. Numerical
results show that the evolutions of
anisotropy follows the same tendency as the
stress–strain curve, and the anisotropy of force
chains is more intense than that of the
microstructure. In addition, particle rolling exerts
different effect on anisotropy before and after
the peak stress state, and particle crushing
decreases the anisotropy of granular materials.
Представлено чисельне дослідження за допомогою методу дискретних елементів
впливу скочування і дроблення частинок на еволюцію анізотропій скочування частинок (мікроструктура) і силового ланцюжка. Для опису анізотропії мікроструктури
використовується структурний класичний тензор, а два аналогічних тензора орієнтації, що характеризуються напрямком контактних зусиль, – для визначення анізотропії силового ланцюжка. Результати чисельного дослідження показали, що еволюція анізотропій має той же характер, що і залежність деформації від напруження,
однак анізотропія силового ланцюжка є більш інтенсивною порівняно з анізотропією
мікроструктури. Більш того, скочування частинок по-різному впливає на анізотропію
до і після досягнення максимального значення напруження, в той час як дроблення
частинок зменшує анізотропію гранульованих матеріалів.
Представлено численное исследование с помощью метода дискретных элементов влияния
скатывания и дробления частиц на эволюцию анизотропий скатывания частиц (микроструктура) и силовой цепочки. Для описания анизотропии микроструктуры используется структурный классический тензор, а два аналогичных тензора ориентации, характеризующихся
направлением контактных усилий, – для определения анизотропии силовой цепочки. Результаты численного исследования показали, что эволюция анизотропий имеет тот же характер, что и зависимость деформации от напряжения, однако анизотропия силовой цепочки
является более интенсивной по сравнению с анизотропией микроструктуры. Более того,
скатывание частиц по-разному влияет на анизотропию до и после достижения максимального значения напряжения, тогда как дробление частиц уменьшает анизотропию гранулированных материалов.
|
| first_indexed | 2025-12-07T16:01:07Z |
| format | Article |
| fulltext |
UDC 539.4
Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and
Particle Crushing
L. L. Zhou, X. H. Chu,
1
and Y. J. Xu
Department of Engineering Mechanics, Wuhan University, Wuhan, China
1 chuxh@whu.edu.cn
ÓÄÊ 539.4
Âëèÿíèå ñêàòûâàíèÿ è äðîáëåíèÿ ÷àñòèö íà ýâîëþöèþ àíèçîòðîïèè
ãðàíóëèðîâàííûõ ìàòåðèàëîâ
Ë. Ë. Æîó, Ê. Õ. ×ó
1
, ß. Æ. Êñó
Ôàêóëüòåò ìàøèíîñòðîåíèÿ, Óõàíüñêèé óíèâåðñèòåò, Óõàíü, Êèòàé
Ïðåäñòàâëåíî ÷èñëåííîå èññëåäîâàíèå ñ ïîìîùüþ ìåòîäà äèñêðåòíûõ ýëåìåíòîâ âëèÿíèÿ
ñêàòûâàíèÿ è äðîáëåíèÿ ÷àñòèö íà ýâîëþöèþ àíèçîòðîïèé ñêàòûâàíèÿ ÷àñòèö (ìèêðîñòðóê-
òóðà) è ñèëîâîé öåïî÷êè. Äëÿ îïèñàíèÿ àíèçîòðîïèè ìèêðîñòðóêòóðû èñïîëüçóåòñÿ ñòðóê-
òóðíûé êëàññè÷åñêèé òåíçîð, à äâà àíàëîãè÷íûõ òåíçîðà îðèåíòàöèè, õàðàêòåðèçóþùèõñÿ
íàïðàâëåíèåì êîíòàêòíûõ óñèëèé, – äëÿ îïðåäåëåíèÿ àíèçîòðîïèè ñèëîâîé öåïî÷êè. Ðåçóëü-
òàòû ÷èñëåííîãî èññëåäîâàíèÿ ïîêàçàëè, ÷òî ýâîëþöèÿ àíèçîòðîïèé èìååò òîò æå õàðàê-
òåð, ÷òî è çàâèñèìîñòü äåôîðìàöèè îò íàïðÿæåíèÿ, îäíàêî àíèçîòðîïèÿ ñèëîâîé öåïî÷êè
ÿâëÿåòñÿ áîëåå èíòåíñèâíîé ïî ñðàâíåíèþ ñ àíèçîòðîïèåé ìèêðîñòðóêòóðû. Áîëåå òîãî,
ñêàòûâàíèå ÷àñòèö ïî-ðàçíîìó âëèÿåò íà àíèçîòðîïèþ äî è ïîñëå äîñòèæåíèÿ ìàêñèìàëü-
íîãî çíà÷åíèÿ íàïðÿæåíèÿ, òîãäà êàê äðîáëåíèå ÷àñòèö óìåíüøàåò àíèçîòðîïèþ ãðàíóëèðî-
âàííûõ ìàòåðèàëîâ.
Êëþ÷åâûå ñëîâà: ãðàíóëèðîâàííûå ìàòåðèàëû, àíèçîòðîïèÿ, ìåòîä äèñêðåòíûõ ýëå-
ìåíòîâ, ñêàòûâàíèå ÷àñòèö, äðîáëåíèå ÷àñòèö.
Introduction. Granular materials consist of particles in contact at the microlevel and
transfer the loads through the contact points. The micromechanical characteristics of the
particle assembly, such as the orientation distributions of contacts, contact forces, etc., are
of great importance for the macro- mechanical behaviors of granular materials. The average
orientation of contacts can be described by an anisotropic fabric tensor [1], which has been
widely used to characterize the anisotropic behaviors of granular materials based on the
continuum approach [2, 3]. However, the evolution of fabric tensor cannot be directly
obtained based on the continuum approach.
The discrete element method has been widely used to investigate the evolution of
fabric tensor in granular materials due to its advantage in capturing the detailed information
on the microlevel. Kruyt [1] investigated the physical mechanisms of fabric evolution by
decomposing the change of fabric tensor into contributions due to three mechanisms:
contact creation, contact disruption and contact reorientation. Guo and Zhao [4] investigated
the characteristics of shear-induced anisotropy in granular materials based on the three-
dimensional discrete element method (DEM) simulations. Despite the importance of
particle rolling on the micro-macro behavior of granular materials [5, 6], there are few
investigations on the effect of particle rolling on the evolution of anisotropy in granular
© L. L. ZHOU, X. H. CHU, Y. J. XU, 2014
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 73
materials. One aim of this study is to investigate the evolution of anisotropy based on the
discrete element method incorporating rolling resistance. The classical fabric tensor is
adopted to describe the anisotropy of microstructure, and another two orientation tensors
are defined to represent the orientation distribution of contact forces in granular materials.
The reasons why these two orientation tensors need to be defined are as follows. The fabric
tensor cannot quantify the orientation distribution of contact forces when tangential forces
exist at contact points. Moreover, the anisotropy of contact forces is more effective to
reflect the anisotropy of the macroscopic behavior of granular materials since the contact
forces are directly related to the external loads.
Another aim of this study is to investigate the evolution of anisotropy in crushable
granular materials. Particle crushing and its influence has been focused previously [7–11].
In general, there are two approaches to simulate particle crushing in the discrete element
method. The first one is that the crushable particle is considered as an agglomerate of
bonded smaller particles that can disaggregate when the interaction force between bonded
particles is above the bond strength [7, 8]. The second one assumes that particles will crush
when the failure criterion is satisfied and will be replaced with a group of smaller
sub-particles according to the particle crushing model [9–11]. The failure criterion and
crushing model describing the distribution of sub-particles should be predetermined. In this
paper, the second approach is utilized to investigate the effect of particle crushing on the
fabric tensor and the orientation distribution of contact forces.
Orientation Tensors. To quantify the overall orientation of the particle contact
normal in granular materials, the second order fabric tensor can be defined as follows [1]:
�ij
c
i
k
j
k
k
N
N
n n
c
�
�
�
1
1
, (1)
where N c is the total number of contacts and ni
k is the component in direction i of the
unit contact normal vector. In two-dimensional cases, i and j take values 1, 2 and the
fabric tensor �ij has two principal values �1 and �2. The sum of the two principal
values is the unity (� �1 2 1� � ) which implies that there is only one independent variable.
The anisotropy of the material is then taken as the difference between the major and the
minor principal components of fabric tensor: A � �� �1 2. For an isotropic material, there
will be � �1 2 0 5� � . .
To characterize the orientation of contact forces, another orientation tensor is defined
as follows:
�ij i
k
j
k
k
N
N
m m�
�
�
1
1
, (2)
m
F
| F|
� , F n t� �f fn t , (3)
where m is the unit direction vector of contact forces. Similar to those in Eq. (1), mi
k is
the component in direction i of the unit contact force vector, F is the contact force vector,
fn and ft are the normal and tangential contact forces, respectively, while n and t are
the contact normal and tangential direction vectors, respectively.
In general, the strong contact forces greater than the average force play an important
role in mechanical behavior of granular materials. Therefore, the following tensor to
characterize the orientation of strong contact forces is defined:
L. L. Zhou, X. H. Chu, and Y. J. Xu
74 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
�ij i
k
j
k
k
N
N
m m�
�
�
1
1
, (4)
where N is the total number of contact points bearing strong contact forces.
Implementation of Particle Rolling and Crushing. Particle Rolling. Recognizing
the significant role of particle rolling in the mechanical behaviors of granular materials,
many researchers have proposed various contact models incorporating particle rolling
[7–11]. In this study, the normal and tangential contact forces are calculated by the linear
model in the DEM code PFC2d, in which the increments of normal and tangential contact
forces are proportional to the increments of normal and tangential displacements,
respectively, while the tangential contact force needs to satisfy Coulomb criterion. The
rolling moment is computed by a model which can be easily implemented by PFC2d code:
M kr r r�� � , (5)
where kr is the constant rolling stiffness and � r is the relative rotation between two
particles in contact [6].
Particle Crushing. Particle crushing inevitably disturbs the stability of force chains at
the microscopic level, which results in the change of the macromechanical behavior.
Similarly to particle motions, such as sliding, rotating, and rolling at the microscopic level,
particle crushing also plays an important role in the macroscopic deformation of a
crushable particle assembly. In this study, particle crushing is implemented using PFC2d.
The approach used in the simulations is that a crushable particle will crush if the failure
criterion is satisfied, and the particle is replaced with sub-particles according to the particle
crushing model. The failure criterion adopted to determine particle crushing is based on the
Weibull statistics of fracture, which was also used by Chu and Li [11]. The crushing model
referred to as model A, which was used in our simulations, has been proposed by
Lobo-Guerrero and Vallejo [10]: a particle is replaced by a set of eight sub-particles of
three different sizes as shown in Fig. 1a.
It is observed that the distribution of contact orientation within the sub-particles in
model A is anisotropic, and the probability of contacts oriented along the vertical direction
is higher than in the horizontal one. This anisotropy within the sub-particles of crushing
model may affect the overall anisotropy of the assembly. In order to verify the effect of
particle crushing model, another crushing model, model B, is also applied in the
simulations. According to model B, the crushed particle will break into a set of six
sub-particles of two different sizes as shown in Fig. 1b. The contacts within model B are
mostly oriented along the horizontal direction.
Numerical Test. Two-dimensional numerical biaxial compression tests are carried out
using the discrete element code PFC2d. The biaxial box has originally a width of 90 mm
and a height of 180 mm, which is contained within four frictionless walls. A specimen
generation method called “radius expansion method” is used to generate the granular
Evolution of Anisotropy in Granular Materials ...
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a b
Fig. 1. Crushing models used in the numerical simulations: (a) model A; (b) model B.
assembly in the biaxial box. This assembly consists of 5792 particles with a radius
distribution in the range of 0.75–1.0 mm. After the desired number of particles is generated,
the assembly is isotropically consolidated with a hydrostatic pressure of 1 MPa. Then the
shear loading of the assembly is performed by increasing the vertical strain. The top and
bottom walls move in the vertical direction toward each other with a constant velocity,
while the velocity of the lateral walls is controlled by a servo-control algorithm to maintain
a constant confining stress.
The parameters used in the study are summarized in Table 1. The normal stiffness of
the top and bottom walls is the same as that of the particle, while the normal stiffness of the
left and right walls treated as semi-rigid walls is 1/10th of the respective value of the
particle. To investigate the influence of rolling friction, the biaxial tests are run with the
rolling friction coefficient � varying from 0 to 0.3, the values of other model parameters
are kept the same as is shown in Table 1. For � � 0, there is no rolling resistance at the
contact points. The value of � � 0 3. indicates a high rolling friction.
In this study, a contact model incorporating particle rolling is introduced in PFC2d.
This approach has been used by many researchers, referring to work of Mohamed at al. [6].
The stress of each particle will be computed to determine particle crushing according to the
failure criterion at the beginning of each step. The particle that satisfies the failure criterion
is replaced by a group of small sub-particles according to the crushing model. The
properties of the sub-particles are same as that of the crushed particle. However, the density
needs to be recalculated to ensure mass conservation since the total solid volume of the
sub-particles in Fig. 1 is less than that of the crushed particle.
Effect of Rolling Friction. To investigate the effect of rolling friction on the
stress-strain and the evolution of anisotropy of granular materials, the rolling friction
coefficient attains values 0, 0.1, 0.2, and 0.3, respectively. Other model parameters
confining stress and initial void ratio are the same for all � values.
76 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
L. L. Zhou, X. H. Chu, and Y. J. Xu
T a b l e 1
Model Parameters Used in the DEM Simulations
Model parameter Value
Biaxial box dimensions (mm): height/width 180/90
Number of particles 5792
Particle size (mm) 0.75–1.0
Particle density (kg/m3) 1000
Initial void ratio 0.14
Particle normal stiffness (N/m) 5 0 108.
Particle tangential stiffness (N/m) 2 5 108.
Inter-particle sliding friction coefficient 0.5
Particle rolling stiffness (N
m) 5000
Inter-particle rolling friction coefficient 0, 0.1, 0.2, 0.3
Top and bottom walls' normal stiffness (N/m) 5 0 108.
Left and right walls' normal stiffness (N/m) 5 0 107.
Confining stress (MPa) 1.0
The deviator stress–strain curves of assemblies are shown in Fig. 2a. It can be seen
that the deviator stress q (i.e., � �1 2� ) increases quickly to its peak at about axial strain
2% for all rolling frictional coefficients, and then decreases to some extent and remains
constant during further loading. This indicates that the critical state stage appears. It is also
easy to observe that the peak deviator stress increases significantly with the increasing
rolling friction coefficient � . The increase in the peak deviator stress with the increasing
� indicates that the rolling resistance enhances the overall friction resistance of granular
materials. In addition, the post-peak strain softening is more obvious for high � values.
The fabric anisotropy can be measured by the difference between the principal values
of fabric tensor [2, 5]. The three orientation tensors, including fabric tensor �, orientation
tensor � of contact forces, and orientation tensor � of strong contact forces, are
investigated for various rolling friction coefficients. The differences between the principal
values of these three tensors are denoted as A� , A� , and A
�
, respectively. Figure 2b–d
shows the evolutions of anisotropies of these three tensors with axial strain for different
rolling friction coefficients. It is observed that the values of A� , A� , and A�
for all �
values increase with axial strain increasing, atttain their peak values at strain level of about
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Evolution of Anisotropy in Granular Materials ...
a b
c d
Fig. 2. Effect of the rolling friction on the stress-strain behavior and the evolution of anisotropies
of the assemblies: (a) deviator stress–strain curves; (b) evolution of anisotropy of fabric tensor;
(c) evolution of anisotropy of force chains; (d) the evolution of anisotropy of strong force chains.
2%, and then drop down. Comparison of Fig. 2b, 2c, and 2d shows that the evolution trends
of the anisotropies of these three tensors are similar. The only difference between them is
the intensity of anisotropy. The anisotropy of strong force chains is the most intense, and
the anisotropy of fabric tensor is the weakest. In addition, it is seen from Fig. 2b that the
values of A� for low � values are higher than those for high � values before axial
strain reaches about 2%, but the former has a more significant reduction than the latter with
further loading. At large strains exceeding 2% the values of A� for low � values are
lower than those for high � values. In Fig. 2c and 2d, the rolling friction coefficient �
has a strongly manifested effect on the values of A� and A�
before the peak values at
the axial strain of about 2%, except for � � 0. However, the peak values of anisotropies
of forces chains and strong forces chains increase with the increasing � value, and the
values of anisotropies of these two tensors for high � values are still higher than those
for low � values with further loading.
Effect of Particle Crushing. In order to investigate the influence of particle crushing
on the mechanical behaviors of granular materials, a series of numerical biaxial tests with
particle crushing are conducted providing rolling frictional coefficient � � 0.3. All values
L. L. Zhou, X. H. Chu, and Y. J. Xu
78 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
a b
c d
Fig. 3. Effect of particle crushing on the stress-strain behavior and the evolution of anisotropies
of the assemblies: (a) deviator stress–strain curves; (b) evolution of anisotropy of fabric tensor;
(c) evolution of anisotropy of force chains; (d) evolution of anisotropy of strong force chains.
of other model parameters, confining stress and the initial void ratio are kept the same as in
Table 1. The symbol “Un” in the legend in Fig. 3 represents the uncrushable case. The
symbol “A” and “B” mean the crushable case using the crushing model A and model B,
respectively.
The deviator stress–strain curves of assemblies are shown in Fig. 3a. The peak
deviator stresses of two crushable cases decrease significantly, as compared to the
uncrushable case. The post-peak strain softening also exhibits a significant reduction in the
crushable cases. However, the difference between the deviator stress–strains curves of two
crushable cases is small. This means that these two crushing models have a minor effect on
the stress-strain behavior of the crushable assembly.
The evolution curves of anisotropies of fabric and contact force chains with axial
strain under the biaxial compression with particle crushing are shown in Fig. 3b–d. It can
be observed that the tendencies of evolutions of the anisotropies of these three tensors for
crushable granular assemblies are similar to the curves without particle crushing, and the
peaks of curves also occur at the same axial strains. However, particle crushing results in
lower peak values of the anisotropies. Microscopically, the contact force chains and the
contact normal vectors align more in the direction of major principal stress (i.e., the vertical
direction) when the peaks at the axial strain 2%, which results in the intense anisotropies at
the peak stress state. For crushable cases, the large particle-to-particle contact forces cause
crushing of many particles. As a result, the contact force chains may collapse, therefore the
contact force chains and the contact normal vectors deviate from the major principal stress
direction. Particle crushing disturbs the stability of force chains at the microscopic level
and weakens the anisotropies of assemblies. The effects of particle crushing on the
anisotropies are in agreement with the results obtained by Wang and Yan [8]. In their
simulation, the crushable particles were simulated by the agglomerates of bonded smaller
particles. In addition, it can be can also be noted that the effect of using crushing model B
has the same tendency as that of using crushing model A, but with larger reductions of the
values of anisotropies. This indicates that the two crushing models in the study affect only
the degree of the reductions of the anisotropies.
Conclusions. The main objectives of this study are to analyze the effects of particle
rolling and particle crushing on the anisotropy in granular materials. The microstructure
anisotropy is described by the fabric tensor defined by contact normal directions. Another
two tensors, defined by the orientation of contact forces, are used to characterize the
anisotropy of force chains in granular materials. The numerical results show that the
evolutions of anisotropies of the three tensors follow the same tendency as the deviator
stress–strain curve. As compared to the microstructure anisotropy described by the fabric
tensor, the anisotropy of the force chains is more intense.
Numerical examples focus on the effects of particle rolling and particle crushing on
the evolutions of anisotropies of the three tensors. The simulations are based on the
user-defined model for particle rolling and apply the failure criterion based on the Weibull
statistical theory and simplified crushing models, in order to achieve particle crushing in
PFC2D code. According to the results of performed simulations, before the peak stress
state, the increasing rolling friction reduces the microstructure anisotropy and has no
obvious effect on the anisotropy of force chains. After the peak stress state, the anisotropies
of the three tensors increase with the increasing rolling friction. Particle crushing has a
minor effect on the tendencies of evolutions of the anisotropies, but significantly weakens
the anisotropies of the three tensors. The two crushing models in the study only affect the
degree of the reductions of particle crushing of the anisotropies.
Acknowledgments. The authors are pleased to acknowledge the support of this work
by the National Natural Science Foundation of China through Contract/Grant Nos.
10802060 and 11172216 and the Natural Key Basic Research and Development Program of
China (973 Program) through Contract/Grant No. 2010CB731502.
Evolution of Anisotropy in Granular Materials ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 79
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âïëèâó ñêî÷óâàííÿ ³ äðîáëåííÿ ÷àñòèíîê íà åâîëþö³þ àí³çîòðîï³é ñêî÷óâàííÿ ÷àñòè-
íîê (ì³êðîñòðóêòóðà) ³ ñèëîâîãî ëàíöþæêà. Äëÿ îïèñó àí³çîòðîﳿ ì³êðîñòðóêòóðè
âèêîðèñòîâóºòüñÿ ñòðóêòóðíèé êëàñè÷íèé òåíçîð, à äâà àíàëîã³÷íèõ òåíçîðà îð³ºí-
òàö³¿, ùî õàðàêòåðèçóþòüñÿ íàïðÿìêîì êîíòàêòíèõ çóñèëü, – äëÿ âèçíà÷åííÿ àí³çî-
òðîﳿ ñèëîâîãî ëàíöþæêà. Ðåçóëüòàòè ÷èñåëüíîãî äîñë³äæåííÿ ïîêàçàëè, ùî åâîëþ-
ö³ÿ àí³çîòðîï³é ìຠòîé æå õàðàêòåð, ùî ³ çàëåæí³ñòü äåôîðìàö³¿ â³ä íàïðóæåííÿ,
îäíàê àí³çîòðîï³ÿ ñèëîâîãî ëàíöþæêà º á³ëüø ³íòåíñèâíîþ ïîð³âíÿíî ç àí³çîòðîﳺþ
ì³êðîñòðóêòóðè. Á³ëüø òîãî, ñêî÷óâàííÿ ÷àñòèíîê ïî-ð³çíîìó âïëèâຠíà àí³çîòðîï³þ
äî ³ ï³ñëÿ äîñÿãíåííÿ ìàêñèìàëüíîãî çíà÷åííÿ íàïðóæåííÿ, â òîé ÷àñ ÿê äðîáëåííÿ
÷àñòèíîê çìåíøóº àí³çîòðîï³þ ãðàíóëüîâàíèõ ìàòåð³àë³â.
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Received 22. 11. 2013
80 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
L. L. Zhou, X. H. Chu, and Y. J. Xu
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| id | nasplib_isofts_kiev_ua-123456789-112716 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T16:01:07Z |
| publishDate | 2014 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Zhou, L.L. Chu, X.H. Xu, Y.J. 2017-01-26T19:04:30Z 2017-01-26T19:04:30Z 2014 Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing / L.L. Zhou, X.H. Chu, Y.J. Xu // Проблемы прочности. — 2014. — № 2. — С. 73-80. — Бібліогр.: 11 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112716 539.4 The effect of particle rolling and crushing on the evolutions of the two types of anisotropy, i.e., anisotropy of particle packing (microstructure) and anisotropy of force chains, is investigated numerically using the discrete element method. To this end, the classical fabric tensor is adopted to describe the anisotropy of microstructure, while two similar orientation tensors defined by the directions of contact forces are used to characterize the anisotropy of force chains. Numerical results show that the evolutions of anisotropy follows the same tendency as the stress–strain curve, and the anisotropy of force chains is more intense than that of the microstructure. In addition, particle rolling exerts different effect on anisotropy before and after the peak stress state, and particle crushing decreases the anisotropy of granular materials. Представлено чисельне дослідження за допомогою методу дискретних елементів впливу скочування і дроблення частинок на еволюцію анізотропій скочування частинок (мікроструктура) і силового ланцюжка. Для опису анізотропії мікроструктури використовується структурний класичний тензор, а два аналогічних тензора орієнтації, що характеризуються напрямком контактних зусиль, – для визначення анізотропії силового ланцюжка. Результати чисельного дослідження показали, що еволюція анізотропій має той же характер, що і залежність деформації від напруження, однак анізотропія силового ланцюжка є більш інтенсивною порівняно з анізотропією мікроструктури. Більш того, скочування частинок по-різному впливає на анізотропію до і після досягнення максимального значення напруження, в той час як дроблення частинок зменшує анізотропію гранульованих матеріалів. Представлено численное исследование с помощью метода дискретных элементов влияния скатывания и дробления частиц на эволюцию анизотропий скатывания частиц (микроструктура) и силовой цепочки. Для описания анизотропии микроструктуры используется структурный классический тензор, а два аналогичных тензора ориентации, характеризующихся направлением контактных усилий, – для определения анизотропии силовой цепочки. Результаты численного исследования показали, что эволюция анизотропий имеет тот же характер, что и зависимость деформации от напряжения, однако анизотропия силовой цепочки является более интенсивной по сравнению с анизотропией микроструктуры. Более того, скатывание частиц по-разному влияет на анизотропию до и после достижения максимального значения напряжения, тогда как дробление частиц уменьшает анизотропию гранулированных материалов. The authors are pleased to acknowledge the support of this work by the National Natural Science Foundation of China through Contract/Grant Nos. 10802060 and 11172216 and the Natural Key Basic Research and Development Program of China (973 Program) through Contract/Grant No. 2010CB731502. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing Влияние скатывания и дробления частиц на эволюцию анизотропии гранулированных материалов Article published earlier |
| spellingShingle | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing Zhou, L.L. Chu, X.H. Xu, Y.J. Научно-технический раздел |
| title | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing |
| title_alt | Влияние скатывания и дробления частиц на эволюцию анизотропии гранулированных материалов |
| title_full | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing |
| title_fullStr | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing |
| title_full_unstemmed | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing |
| title_short | Evolution of Anisotropy in Granular Materials: Effect of Particle Rolling and Particle Crushing |
| title_sort | evolution of anisotropy in granular materials: effect of particle rolling and particle crushing |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112716 |
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