ICAIIE–2023 Nano-Geo-Mechanics - Challenges to calculate friction for geomaterials

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International Conference on
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[Type here]International Conference on Academic & Industrial Innovations P P Savani University (PPSU),
Surat, India [August 12-13, 2023]
Nano-Geo-Mechanics: Challenges to calculate friction for
Geomaterials
Samirsinh P Parmara
, Atindra D Shuklab
a
Dharmsinh Desai University,Nadiad-387001, India.
b
Director, SSNT-Dharmsinh Desai University, Nadiad-387001, India.
Abstract
Geotechnical engineering has conventionally emphasized macro-scale phenomena in soil and rock mechanics. Nonetheless, the
latest progress in nanotechnology has unlocked fresh opportunities to investigate the behavior of geomaterials at the nanoscale.
This emerging field, known as nano-geo-mechanics, holds great promise for enhancing our understanding of fundamental
geotechnical processes and developing innovative solutions for geotechnical engineering challenges.
This paper provides an overview of the challenges associated with the application of nano-geo-mechanics in geotechnical
engineering. It discusses the scale dependence of friction in geomaterials, highlighting the complex interplay of surface
roughness, interfacial interactions, and atomic rearrangements. The computational complexity associated with atomistic
simulations, such as molecular dynamics, is also addressed, considering the large number of atoms present in geomaterials and
the need to simulate their behavior over relevant time and length scales. To address these challenges, a comprehensive
understanding of nano-geo-mechanics requires a multidisciplinary approach that combines experimental investigations, advanced
characterization techniques, theoretical models, and computational simulations. Continuous research endeavors seek to create
precise predictive models for nano friction in geomaterials, enhancing our comprehension of essential geotechnical processes and
laying the groundwork for groundbreaking applications in geotechnical engineering. This article underscores the significance of
nano-geomechanics in geotechnical engineering and serves as a valuable reference for researchers and practitioners keen on
exploring the opportunities and obstacles in this emerging domain. By addressing these challenges, nano-geo-mechanics has the
potential to revolutionize geotechnical engineering, leading to more sustainable and efficient geotechnical solutions.
Keywords: Nano mechanics, geo-materials, nano scale friction, governing equations, macro-nano
behavior of geomaterials.
Abbreviations:
RVE : Representative Volume Element
DPD : Dissipative Particle Dynamics
AFM : Atomic force microscopy
MD : Molecular Dynamics

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1. Introduction
Despite the advancements in modern geotechnical equipment, predicting soil behavior remains a challenging task
even in the present day. To achieve precision in prediction of soil behavior, it is necessary to establish exact
constitutive relationship of geometrical. However, the soil continuum behavior is extremely difficult considering the
factors such as fluid-soil interaction (e.g. water, contaminants and chemicals). The constitutive relationship derived
by mainly macro or micro-mechanics, but very rare indirect methods are available to predict soil continuum
constitutive behavior at micro to Nano-mechanics level. Moreover the parameters that affects the constitutive
relationship changes for the particle size of macro level to nano level. With the application of Nano materials into
the geometrical in various geotechnical experiments it is necessary to understand the effect of it at nano size (i.e.
molecular level). In further sections of the paper, the author delineates the implication of Nano-mechanics approach
into the modern geotechnical engineering to analyze soil behavior.
1.1. Review of literature
Nano- mechanics is the emerging branch of engineering to analyze soil behavior at Nano level particle size (i.e. 10-
9m), which signifies molecular or quantum molecular behavior. Hence, Nano-mechanics is mostly dominated by
forces exerted at atomic or molecular scale. In order to comprehend Nano-mechanics, it is essential to grasp the
influence of physical properties, including electrons, charges, electron permittivity, dihedral angle, and others. It is
advantages that, by understanding Nano-mechanics, the statistical average of material can be correlated with soil
behavior as continuum media. The macro or micro scale behavior is ultimately the integral behavior of nano-
mechanical behavior of continuum, which can be performed without much difficulty. (Voyiadjis et.al., 2003, Meng
and Voyiadjis, 2003; Srinivasan et. al., 2005). Soils and Nano materials may differ from each other, but they both
consist of fundamental particles like atoms and molecules, thus sharing similar operating mechanics.
1.2. Nano-geo-mechanics to study Nano scale geotechnical engineering
Nano-mechanics offers a highly intricate understanding of material behavior, thanks to its nano-level length scales
and pico to femto seconds time scales. Cui et al. 1996; Kaliakin et al. 2000; Ling et al. 2002, 2003; Manzari 2004;
Song and Voyiadjis 2005a; Voyiadjis and Song 2005b, Voyiadjis et al. 2000 studied modern continuum mechanics
and major contribution was made by Anandarajah, 2004, 1994; Peters, 2004 in discrete mechanics. Both continuum
and discrete mechanics approaches excel in offering macro-scale material behavior, yet their capacity to provide
detailed material behavior remains restricted. Fig. 1 illustrates the distinct contrasts of various scales. While some
advanced continuum mechanics methods can partially provide detailed material behavior, determining input
parameters remains a challenging task. Currently, Nano-mechanics is the preferred tool for analyzing intricate
behaviors in geo-materials, such as clay-fluid interaction. (Smith, 1998; Shroll and Smith, 1999).
Fig- 1 Comparison of dimensional scale to time scale of event for different problems of mechanics.

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Nano-mechanics boasts several advantages, including its highly established theories and straightforward input
parameters. One such theory is the potential energy equation depicted in (1), while some of the input parameters
consist of conventional physical and chemical constants, such as the permittivity of a vacuum and angle bend force
constant, which are already well-defined in Table-1.
ETotal = ECoul + EVDW + E Bond Stretch + E Angle Bend + E Torsion ___________(1)
In the given equation, the terms ECoul and EVDW represent the non-bonded energy components known as Coulombic
energy and van der Waals energy, respectively. The remaining three terms correspond to the explicit bonded energy
components associated with bond stretching, angle bending, and torsion dihedral. Table-1 provides a summary of
the significant characteristics of these energy components.
Table-1 Nano scale frictional forces contribution by different factors.
Sr.No. Forces Governing Equations Remark
1 Coulombic
In the given context, qi and qj denote
the charge of the two interacting
atoms (ions), e represents the electron
charge, and εo refers to the
permittivity (dielectric constant) of a
vacuum.
The Coulombic energy relies
on the classical depiction of
charged particle interactions
and exhibits an inverse
relationship with the distances
rij.
2 Van der
Waals
Lennard-Jones Potential Energy
Where, Do and Ro represent pragmatic
parameters.
The second term corresponds
to the van der Waals energy,
which represents the
attractive molecular
interactions.
3 Bond Stretch E Bond Stretch = k1(r − ro) 2
In this context, r denotes the
separation distance between the
bonded atoms, ro is the equilibrium
bond distance, and k1 represents an
empirical force constant.
The bond stretch term can be
expressed as a straightforward
quadratic (harmonic)
equation.
4 Angle Bend E Angle Bend = k2 (θ−θo) 2
In this case, θ represents the measured
bond angle for the configuration, θo is
the equilibrium bond angle, and k2 is
the angle bend force constant.
The angle bend energy
equation for a bonded system
is commonly formulated
using a harmonic potential.
5 Torsion ETorsion = k3 (1 + cos3ϕ)
Where, k3 is an experimental force
constant and ϕ is the dihedral angle.
The torsional dihedral
interactions, represented by
the dihedral angle ϕ, are
defined as the angle formed
by the terminal bonds of a
quartet of sequentially bonded
atoms when viewed along the
axis of the intermediate bond.
Notes Supplementary terms can be incorporated into the total potential energy
expression of (7.1), including an out-of-plane stretch term, particularly
for systems with a planar equilibrium structure.

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By utilizing equation (1) and the optimized energy or force field, it becomes feasible to calculate material properties
with ease. By comparing the potential energy along a specific direction to the strain energy in the same direction and
equating them, one can compute the spring constant or modulus. This forms the fundamental concept of the
Anderson-Parrinello-Rahmen theory. (Ray and Rahman, 1984; Ray, 1988; Parrinello and Rahmen, 1981). The
primary obstacles to this process lie in the complexities associated with molecular mechanics or quantum mechanics
theory and the substantial computational time required. Nevertheless, these challenges have significantly diminished
in recent times, thanks to the well-established concepts in molecular mechanics or quantum mechanics.
Since the introduction of the time-independent Schrödinger equation and the Born-Oppenheimer approximation,
which effectively separates nuclear and electronic motions, molecular interactions have become readily manageable
and computable. Additionally, the emergence of user-friendly molecular mechanics software like LAMMPS,
NAMD, BioCoRE, and Materials Studio has further alleviated this challenge. By utilizing these user-friendly
software programs and possessing basic knowledge of Physics and Chemistry, one can effectively conduct quantum-
level analyses. Dynamic conditions arise when there is an interaction between two distinct stable molecular systems.
As the two materials mix and interact, molecular interactions occur, leading to a new equilibrium state with a new
optimal (minimum) potential energy. The chemical procedure of obtaining this new equilibrium strictly adheres to
molecular dynamics principles (Katti et al., 2004). Consequently, the interaction between two different materials can
be conveniently analyzed using molecular dynamics. Once the chemical reaction is complete, molecular mechanics
can be employed to predict the physical properties.
Nevertheless, employing nano-mechanics in geo-materials poses certain challenges. While the equations and
minimization techniques for potential energies are considered correct, each equation or technique carries its own
inherent assumption(s) and approximation(s) that may not entirely suit geo-materials (see Belytschko, 2005). A
common misconception is that "Molecular mechanics does not assume anything and solves the problem very
accurately." However, in reality, extensive research is essential to assess and choose the appropriate optimization
technique(s) suitable for geo-materials.
1.3. Nano-mechanics as a tool to study macro-level material properties through continuumization
The preceding section showcased Nano-mechanics' capacity to assess intricate properties of geo-materials.
However, Nano-mechanics lags behind continuum mechanics in providing and predicting macroscale material
behavior due to its extensive computational time. Thus, a bridge is required to connect Nano-mechanics and
continuum mechanics, offering detailed Nano-scale material behavior as well as macro-scale material behavior at
the continuum level. This bridge allows the integration of Nano-mechanics with well-established modern continuum
mechanics, as illustrated in Table 2. Essentially, Nano-mechanics will furnish the fundamental properties required
by continuum mechanics (e.g., continuum mechanics parameters shown in Table 2), while continuum mechanics
will handle the micro and macro scale behavior of geo-materials.
Table-2 Equations governing micro-mechanical behavior of particles
Sr.
No.
Micromechani
cal
Behaviour
Form of Governing Equations Notations
References for
contribution
1
Rotation of
Particles
Where, Ws′′,ξ,ᾱ, and ds′′ are the
plastic rotation tensor, constant,
back stress, and distortion,
respectively.
Dafalias (1998), Cosserat
(1909), Song and
Voyiadjis (1999 to 2005),
Voyiadjis and Kattan
(1990, 1991)
2
Interaction of
Particles
Where, ῁ε vp ˙ἐvp v , and k are
the normalized strain rate, visco-
plastic volumetric strain rate and a
constant, correspondingly.
Di Prisco and Aifantis
(1999), Zbib (1994), Zbib
and Aifantis (1988),
Voyiadjis and Song
(2005), Song and
Voyiadjis (2005a)

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3
Damage of
particles
Where, λd, g and σ are the
damage strain, damage multiplier,
damage potential, and stress,
respectively.
Voyiadjis and Song
(2005a)
4
Viscosity of
pore fluid
where, f, fs,po, ηvp,˙¯p, Bii, and
m1 are the dynamic yield surface,
static yield surface, mean principal
stress, viscosity, time rate of the
mean stress, the differentiation of
fwith stress, and a constant,
respectively,
Perzyna (1963, 1966,
1988), Song and
Voyiadjis (2005a),
Voyiadjis and Song
(2005)
5
Flow
characteristics
of pore fluid
where, n, ρs, ρw aw, Kws, υs,
Pw and b are the porosity, mass
density of the soil, mass density of
the water, acceleration of water,
permeability tensor, solid velocity,
pore water pressure, and body force
vector.
Coupled theory of
mixtures Biot (1955,
1978), Prevost (1980,
1982), Muraleetharan et
al. (1994), Schrefler et al.
(1990), Wei and
Muraleetharan (2002)
Song and Voyiadjis (1999
to 2005) Voyiadjis and
Song (2000 to 2005)
By adopting this approach, one can fully utilize the capabilities of modern continuum mechanics without the need
for exhaustive efforts in evaluating input parameters. A promising technique within continuum mechanics known as
RVE (Representative Volume Element) offers a promising solution for combining nano-mechanics and continuum
mechanics. This integration allows for obtaining detailed material behavior at the Nano-scale as well as macro-scale
material behavior, all while minimizing computational costs. The fundamental concept of the RVE (table 3) lies in
the notion that macro-scale behavior is essentially an averaged representation of lower-scale behavior. By
incorporating nano mechanics within the lowest RVE of continuum mechanics, one can attain detailed material
properties with minimal input parameters.
An additional valuable technique, known as the "Equivalent Beam or Truss Element Method" (Table 3), proves to
be beneficial. These approaches represent the lattice structure of molecules as joints and beams in conventional
numerical analyses. Elongation stiffness and torsional stiffness are derived from equating the bond stretch potential
and twisting potential in molecular mechanics to the elongation strain energy and torsional strain energy in
traditional mechanics. This enables the effective execution of molecular-level simulations using widely-used
commercial software like ANSYS. Notably, this method has proven to be highly effective for continua. (Srinivasan
et al., 2005).
Table- 3 Distinguished averaging methods
Sr.
No.
Method Equations Notation Remark Reference
1 RVE Where, A′ is
the property
at upper
scale, V is
the volume
of RVE, A is
Just like the homogenization
technique in continuum mechanics,
this method fully encompasses the
incorporation of molecular
interactions.
Belytschko and
Xiao (2003)
Huang and Jiang
(2005)
Liu et al. (2005)
Belytschko (2005)

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the property
at lower
Scale.
Song and Al-
Ostaz (2005)
2 Equivalent
beam or
truss
element
This represents the continuum
formulation of molecular mechanics.
The stiffness input parameters, like
Young's modulus, were determined
by comparing the potential energy
for stretching to the corresponding
strain energy, as follows:
This method proves to be less
effective in simulating dynamic
processes, such as the interaction
between minerals and pore fluids.
Li and Chou
(2003)
Odegard et al.
(2001)
Ostoja-
Starzewski,
(2002)
Srinivasan et al.
(2005)
Wang et al.
(2005)
Nano mechanics offers the fundamental characteristics of discrete elements, whereas the process of
continuumization bridges the gap between discrete elements and continuum, resulting in macro-level behavior.
(Cosserat brothers 1909; Anandarajah 2004; Tordesillas et al. 2004; Peters, 2004). The Nano-mechanics technique
for soils presents unique challenges and must be distinct from that used for other continuous materials. The
following outlines the rational procedure:
1) Use Nano-mechanics to study grain and grain-liquid interactions.
2) Determine the material properties of discrete particles and their surroundings.
3) Convert the discrete attributes to continuous properties using a continuumization approach.
(Maiti et al., 2004) introduced a novel averaging method known as "DPD (Dissipative Particle Dynamics)," This
method, widely utilized in Chemistry, is employed to analyze the interaction between two different fluids. The DPD
method makes use of
Fig-2 Fluid droplets in DPD (Maiti et al., 2004)
In dynamic analysis, the positions and momenta of the "fluid droplets" depicted in Fig. 2 are utilized instead of
individual atoms. Consequently, the DPD approach resolves molecular dynamics in terms of RVE (Representative
Volume Element), allowing computation of the equilibrium condition across extended time and length scales Maiti
et al. (2004) improved the DPD theory by incorporating interactions between carbon nanotubes and fluid, leading to
the derivation of an equilibrium morphology that can serve as an input for standard finite element algorithms. This
approach shares similarities with the RVE concept in continuum mechanics, but it stands apart by operating at the
molecular level, often referred to as "coarse-grained" molecular dynamics. The enhanced DPD method (Maiti et al.,
2004) can be likened to a molecular-level RVE, eliminating the need for additional averaging schemes.
Consequently, the DPD technique proves to be a highly cost-effective approach for investigating interactions
between clay particles and pore fluid. Through RVE and the related integration technique, material properties from
Nano mechanics can be seamlessly transferred to continuum properties. This strategy also has significant

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drawbacks. Traditional continuumization approaches work well for continuous material but not for particulate
media. The DPD approach appears to be promising for clayey soils; nevertheless, more comprehensive investigation
is required before it can be considered entirely viable.
1.4. Factors affecting nanoscale friction
Understanding the factors that influence nano scale friction is significant for developing effective approaches to
control and reduce friction at the nanoscale. By manipulating these factors, it may be possible to design surfaces and
materials with reduced friction forces, which could have important applications in a wide range of fields, including
nanotechnology, biotechnology, and materials science.
The behaviour of Nano scale friction is influenced by several variables, such as:
i. Surface roughness: The roughness of the contacting surfaces can have a significant effect on nano scale
friction. Rough surfaces tend to have higher friction forces than smoother surfaces.
ii. Adhesion: Adhesion between the contacting surfaces can affect the friction force at the Nano scale.
Strong adhesion between surfaces can increase the frictional force, while weak adhesion can decrease it.
iii. Surface chemistry: The chemical properties of the surfaces in contact can influence Nano scale friction.
The presence of surface contaminants or changes in the surface chemistry can affect the frictional force.
iv. Applied load: The magnitude of the applied load can influence Nano scale friction. Higher loads can
result in greater friction forces.
v. Sliding velocity: The velocity at which the surfaces slide past each other can affect Nano scale friction.
Generally, higher sliding velocities can result in higher friction forces.
vi. Temperature: Temperature can have a significant effect on Nano scale friction. Changes in temperature
can cause changes in the chemical and physical properties of the contacting surfaces, which can affect the
frictional force.
vii. Lubrication: The presence or absence of a lubricant can also affect Nano scale friction. Lubricants can
reduce friction by reducing adhesion between surfaces and providing a barrier between them.
viii. Understanding the factors that influence Nano scale friction is important for developing effective
strategies to control and reduce friction at the nanoscale. By manipulating these factors, it may be
possible to design surfaces and materials with reduced friction forces, which could have important
applications in a wide range of fields, including nanotechnology, biotechnology, and materials science.

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1.5. Methods to calculate nano scale friction
Calculating nano scale friction between surface coatings can be challenging due to the complex interplay of
various factors involved. However, several approaches can be used to estimate Nano scale friction between surface
coatings. One common method is to use atomic force microscopy (AFM), which can directly measure the frictional
forces between two surfaces. AFM can provide information on the surface topography, adhesion, and frictional
forces at the Nano scale. This technique can be used to compare the frictional forces of different surface coatings
under different conditions, such as varying applied loads, sliding velocities, and temperatures.
Another approach is to use computer simulations, such as molecular dynamics (MD) simulations, to predict the
frictional forces between surface coatings at the Nano scale. MD simulations can provide atomistic-level details of
the interaction between surfaces, which can be used to estimate frictional forces. The simulations provide an
opportunity to explore the impact of various factors on Nano scale friction, including surface roughness, adhesion,
and lubrication. Calculating Nano scale friction between surface coatings is a complex task that requires careful
consideration of several factors. Experimental techniques like AFM and computer simulations like MD simulations
can be used to provide estimates of frictional forces and understand the underlying mechanisms.
1.6. Equations governing calculation of Nano friction between surfaces
There is no single equation to calculate nano friction between surfaces, as the phenomenon of friction at the
nanoscale is complex and influenced by many factors. However, there are several theoretical models and empirical
equations that can be used to estimate nano friction between surfaces.
 Amontons-Coulomb friction law: This is a classical model that describes the friction force as proportional to
the applied load, with a proportionality constant known as the coefficient of friction. At the nanoscale, this
model may need to be modified to account for the effects of surface roughness and adhesion.
 Prandtl-Tomlinson model: This is a theoretical model that describes the frictional interaction between a tip and
a surface as a series of "stick-slip" events, where the tip moves smoothly until it encounters a barrier and then
jumps forward in discrete steps. This model can provide insight into the relationship between surface
topography and friction.
 Johnson-Kendall-Roberts (JKR) theory: This model describes the interaction between two elastic spheres in
contact, taking into account the deformation of the spheres and the adhesion between them. This model can be
used to estimate the adhesive and elastic components of the friction force.
 Molecular dynamics simulations: These are computational simulations that can provide a detailed, atomistic-
level view of the frictional interaction between two surfaces. By simulating the motion of individual atoms,
these simulations can provide insight into the effects of factors like surface roughness, adhesion, and
lubrication on Nano friction.
Overall, the calculation of Nano friction between surfaces is a complex problem that requires consideration of
many factors and the use of various models and methods.
1.7. equations governing Nano Surface coating frictional forces
The frictional forces of Nano surface coatings are governed by equations that rely on diverse factors, including the
type of coating, surface roughness, material properties, and environmental conditions in which the coating is
applied. Presented below are some general equations that can be utilized to describe the frictional behaviour of Nano
surface coatings:
1. Amontons' law: This law states that the frictional force between two surfaces is proportional to the normal
force pressing the surfaces together. Mathematically, it can be expressed as:
F_friction = μ*F_normal
Where, μ is the coefficient of friction. Jianping G (2004), further classified the friction as Adhesion-
controlled and Load-controlled friction.

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2. Archard's equation: The Archard wear equation serves as a fundamental model for characterizing sliding
wear, founded on the principles of asperity contact theory. It is given by
V = kFN/(H*ρ)
Where, V is the wear volume, k is the wear coefficient, F is the applied load, N is the number of sliding
cycles, H is the hardness of the material, and ρ is its density.
2. Coulomb's law of friction: The law stipulates that the frictional force between two surfaces is directly
proportional to the normal force and remains unaffected by the contact area between the surfaces.
Mathematically, it can be expressed as follows:
F_friction = μ*N,
Where, N is the normal force.
4. Johnson-Kendall-Roberts (JKR) model: This model is used to describe the contact mechanics of elastic
spheres in contact with a flat surface. It is given by
F_adhesion = (3/2)E(R_1*R_2)/(R_1+R_2)*δ^(3/2),
Where, F_adhesion is the adhesive force, E is the elastic modulus, R_1 and R_2 are the radii of the two
contact surfaces, and δ is the distance between them.
5. Derjaguin-Muller-Toporov (DMT) model: This model is similar to the JKR model but assumes that the
contact is dominated by van der Waals forces. It is given by
F_adhesion = πR^2W,
Where, R is the radius of the contact area and W is the surface energy.
Note that these equations are general and may need to be modified or adapted to account for specific factors
affecting the frictional behaviour of nano surface coatings.
1.8. Coupled behavior of Nano-micro and Micro- Macro mechanism
The macro-behavior of geomaterials emerges from the intricate interplay of multiple constituent elements,
encompassing coupled micro-behaviors. Micromechanical behavior involves grain rotation, grain interactions like
grain interlocking, pore fluid viscosity, and grain integrity. (Voyiadjis and Song, 2003). Fig-3 depicts the particle
size distribution for geomaterials and the factors which influence its behavior under various fraction of particle size.
The rotation of grains has an effect on the equilibrium equations since it uses some of the input energy. There are
numerous approaches to grain rotation; this study addresses this aspect by incorporating the concept of plastic spin.
Grain contact significantly influences stress-strain redistribution and the numerical techniques' well-posedness.
Under shear applied to soils with a lower than critical void ratio, dilation (volume expansion) mainly occurs along
the shear band. The soil particles within the shear band experience higher stress compared to those in the
surrounding region, leading to stress transfer to the adjacent area and subsequent volume expansion. This method
minimizes tension in the shear band, which in turn reduces strain. This phenomenon is also known as the
homogeneity mechanism (nearly formally).
The rate dependency of materials is influenced by the soil's viscous nature. In localized shearing zones, such as
the shear band region, the strain rate is significantly higher than outside the shear band. Consequently, the material
within the shear band exhibits a stronger response compared to the material outside the shear band, resulting in the
spread of the shear band to the surrounding area. This rate dependence gives rise to another form of localization or
homogenization mechanism. During the loading and unloading processes, grain integrity may be compromised due
to particle crushing, micro-cracks, or wear-out of sharp edges. Researchers like De Boer (1996), Lee (1965), and
Lee and Finn (1967) have explicitly demonstrated how particle crushing leads to a deterioration of the friction angle.

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Fig-3 ASTM Soil classification according to grain size along with the forces affecting soil behaviour.
As a result of this occurrence, the modulus will experience a reduction. Desai and Zhang (1998) as well as Desai
et al. (1997) have explored modulus reduction due to the "disturbed state." Eventually, all damaged pathways
contribute to the reduction in the macroscopic stiffness of the soils. This decrease in material stiffness leads to
softening and localized high strains within the localized shearing zone, such as the shear band, thus enhancing strain
localization. The above discussion demonstrates the intricate interconnection of micromechanical behavior, where
certain mechanisms promote localization while others foster homogenization.
2. Challenges in calculation of Nano friction applicable to geomaterials. (i.e. geo-mechanics)
The calculation of Nano friction in geomaterials poses several challenges due to the complex nature of these
materials and the scale at which the calculations are performed. Some of the key challenges include:
Scale dependence: Friction at the nanoscale is influenced by various factors such as surface roughness, interfacial
interactions, and atomic rearrangements. These phenomena are strongly scale-dependent, and their effects become
more pronounced as the system size decreases. Accounting for these scale-dependent effects is a challenge in
accurately calculating nano friction in geomaterials.
Surface characterization: Accurate characterization of surface roughness and topography is crucial for
understanding and predicting Nano friction. Geomaterials often exhibit complex and heterogeneous surface
structures, making their characterization challenging. High-resolution techniques, such as atomic force microscopy
(AFM) and scanning electron microscopy (SEM), are commonly employed. However, the process of extracting
meaningful information from the obtained data and integrating it into friction models is a challenging task that
requires careful consideration.
Interfacial interactions: Friction at the nanoscale is governed by interfacial interactions between atoms or
molecules. In the case of geomaterials, these interactions can be highly complex due to the presence of various
chemical and physical forces, such as van der Waals forces, adhesion, electrostatic interactions, and surface
hydration. Capturing the full range of interfacial interactions and their impact on friction is a significant challenge in
the calculation of Nano friction in geomaterials.
Multiscale modeling: Geomaterials exhibit a hierarchical structure, spanning multiple length scales from
nanometers to meters. To accurately capture the friction behavior, it is often necessary to employ multiscale
modeling approaches. However, bridging the gap between different scales and integrating the information across the
scales poses a significant challenge. Developing effective multiscale models that can capture the essential frictional
behavior at the nanoscale and upscale it to larger scales is an ongoing research area.
Computational complexity: The calculation of Nano friction involves atomistic simulations, such as molecular
dynamics (MD), which can be computationally intensive. Geomaterials typically consist of a large number of atoms,
and simulating their behavior over relevant time and length scales requires significant computational resources.
Efficient algorithms and parallel computing techniques are necessary to overcome the computational complexity
associated with Nano friction calculations in geomaterials.
Addressing these challenges requires a combination of experimental investigations, advanced characterization
techniques, theoretical models, and computational simulations. Ongoing research efforts aim to improve our
understanding of Nano friction in geomaterials and develop more accurate predictive models for practical
applications.

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3. Conclusion:
The field of Nano-geo-mechanics presents exciting opportunities for advancing our understanding of
geotechnical processes and improving the design and performance of geotechnical systems. In this paper, we have
discussed the challenges associated with the application of Nano-geo-mechanics in geotechnical engineering.
The scale dependence of friction in geomaterials has been highlighted as a crucial factor, with surface roughness,
interfacial interactions, and atomic rearrangements playing significant roles. The characterization of complex and
heterogeneous surface structures poses challenges in accurately capturing the Nano-scale properties of geomaterials.
Additionally, the intricate nature of interfacial interactions, encompassing various forces, further complicates the
calculation of Nano friction.
Multiscale modeling approaches have been acknowledged as a valuable means of bridging the gap between
various length scales and capturing crucial frictional behavior. Nevertheless, the integration of information across
these scales continues to pose a challenge, necessitating further research and development efforts.
The computational complexity associated with atomistic simulations presents another obstacle, necessitating the
use of effective algorithms and parallel computation techniques to overcome the resource demands of Nano friction
calculations.
Addressing these challenges requires a multidisciplinary approach that combines experimental investigations,
advanced characterization techniques, theoretical models, and computational simulations. By working towards a
comprehensive understanding of Nano-geo-mechanics, we can improve our predictive capabilities and develop
innovative solutions for geotechnical engineering applications.
In conclusion, Nano-geo-mechanics holds great potential for transforming the field of geotechnical engineering.
By overcoming the challenges discussed in this paper, we can unlock new insights into the behavior of geomaterials
at the nanoscale and pave the way for more sustainable, efficient, and reliable geotechnical systems. Continued
research and collaboration across disciplines will be essential in realizing the full potential of Nano-geo-mechanics
and its applications in geotechnical engineering.
Acknowledgements
I acknowledge Prof. Atindra D Shukla, Director, Shah and Schulman center of excellence, Surface science and
nanotechnology, Dharmsinh Desai University, Nadiad for his valuable guidance to research in this direction.
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