Finite elements & human civilization

Prepared by
Md. Saniul Haque Mahi
The cutting-edge applications that the engineers are bringing with using finite element
procedure for the human civilization and the emergence of new techniques in solving real life
scenarios in finite element procedures.

References,
Cutting-edge Applications Using Finite Element
Procedure for the Human Civilization
New Techniques in Solving Real Life
Scenarios in Finite Element Procedures
Introduction,
OUTLINE

INTRODUCTION
The finite element method is a numerical method use effectively in resolving the complex engineering problems. This method was developed for stress analysis of
the aircrafts bodies in 1956 at the first time [1]. Also, it is understood that, it can be used with success in the solution of applied science and engineering problems in
the next decade. In years later, the finite element method and solution techniques are swiftly developed and today it has become one of the best method for solving
complex problems.
Traces of modern finite element method can be found since the beginning of the 1900s. During these years, some researchers have modeled with discrete elastic in
elastic constant state of equal sized. However, Richard Courant has been called the first person for develop of the finite element method [2]. Courant, published an
article in the 1940s, about the triangular piece polynomial interpolation sub-regions for to investigate the torsional problems (elements) used on [3].
The basic idea in the finite element method is reducing complex problem into a simple problem and get way of solution. Main problem is obtained approximate
result rather than the final results due to the reducing a complex problem to a simply problem, but the result could be improve and getting much closer to the final
results by spending more effort. Even it is possible to reach definitive conclusions. If the conventional mathematical tools are insufficient to find an approximate
results, FEA would be the only method that can be used for the solving problems.
The finite element method is using for structural and mechanical problems as well as heat conductions, fluid mechanics, electricity and also is using for the solution
of engineering problems associated with magnetic fields [4]. The cause of so many fields of this application is there are lots of similarities between the various
engineering problems. With the help of finite element procedure engineers bring a new era in human civilization. Few applications of FEA in different sectors of
engineering are listed in the next slide.

Civil Engineering AircraftEngineering Thermal Conduction Geomechanics
 Structure of the frames,
sheets, roofs, walls,
buildings, bridges, beams,
shear and static analysis of
pre stressed concrete
elements.
 determination of natural
frequency and flexural
modulus
 stability analysis
 Analyzing of the stress
waves
 response of the structure to
the non-periodic loadings
 Static analysis of body, wings
and airfoils of the aircraft.
 Static analysis of rockets and
missiles.
frequency and flexural modulus.
 response of the structure to the
non-periodic loadings
 response of the structure to the
random loadings
 Temperature distribution in
solids and fluids for the
steady-state condition.
 Heat flow in the exhaust
outlet of the rockets, in
internal combustion engines,
turbine blades, vanes and
buildings
 Stress analysis in
excavation, retaining walls,
underground spaces, the
analysis of the interaction
of rock and soil, the hills
and base of the dam body.
 Interaction between dam
and the structure of the
soil. Finding the same
natural frequency.
 Soil interaction problem
due to the time.
 Stress analysis for hillsides
and sets. Loading handling
and settlement analysis of
building foundations.
01 02 03 04

Hydraulics and waterresources
engineering
Nuclear Engineering Biomedical Engineering Mechanic Design
 Analysis of hydraulic structures
and dams. Potential free surface
boundary layer and solving
transonic aerodynamics problems
with viscous flow.
 Shallow ponds, lakes, the
availability of natural period of the
harbor. Rigid and flexible
movement of liquids in containers
 Unsteady flow and wave
propagation analysis. Gas leak in
porous structure dynamics
magneto hydrodynamics flows.
 Analysis of the permeable layer
with groundwater. Thermal
analysis of water circulation in the
lake. In the estuary, spread
resulting in rivers and sea tides
and scattering analysis. Analysis of
flow in the channel.
 Nuclear pressure vessels and
structures analysis. The
temperature range for reactor
steady disintegration.
frequency and flexural modulus.
 Response to dynamic loads of
the structure. Analysis of reactor
during unstable temperature
 Thermal distribution analysis of
the reactor viscoelastic structure
 Analysis of concrete reactor
body. The solution of multi-
group neutron diffusion
problems.
 Stress analysis of the bones,
teeth, eyes, and so on. The
load carrying capacity
analysis for natural
structures and dentures.
Heart valves mechanics.
 Impact analysis of the skull.
 The dynamics of anatomical
structures.
 Stress analysis of pressure
vessels, pistons, composite
materials, gear.
 Stress concentration
problems
 Finding natural frequency
and making stability
analysis of machine
elements, machine tools of
gear.
 Under dynamic loads crack
and fracture mechanics
problems.
05 06 07 08

Introduction Analytical Study Results Discussions Conclusion
Scope for Future
Work
A Finite Element Analysis of a Lightweight Blast Proof Sandwich Structure
Cutting-edge Applications Using Finite Element Procedure for the Human Civilization
OUTLINE

A Finite Element Analysis of a Lightweight Blast Proof Sandwich Structure
Introduction
Over the last few decades, considerable attention has been raised on the behavior of structures subjected to blast or impact loading. Due to the recent increase in
various terrorist activities all over the world, for the safety of civilians structures should be designed to resist blast loads.
Explosive devices have become smaller in size but more powerful than before, Leading to increased mobility of the explosive material and large damage effects.
Usually, the casualties from such a detonation are not only limited to instant casualties which are a consequence of the direct release of energy, but also to structural
failures that could result in extensive life loss. Keeping this in mind a better solution for such situations is required to protect the lives of people. Blast loads are dynamic
loads that need to be calculated and the structures should be designed by considering these loads to make it blast resistant. One of the objectives of this investigation is
to review the works on the effects of blast loading on structures. A composite material was chosen for the design so that the weight of the structure will be reduced
almost by half when compared with steel and have better damage tolerance properties. No structure can be designed to resist the explosive loads completely. But the
designer could take certain steps to better understand the behaviour of a material under blast load and design to protect the lives of people.
Figure 1. Blast wave pressure-time history.
Table 1. Design conditions.
An explosion is a quick and stable compound reaction which advances through the explosive at supersonic speed. This detonation velocity ranges from 6700 m s−1 to
8500 m s−1 for most high explosives. This explosion wave quickly converts the explosives into a hot, thick, and high-pressure gas which is the source of a strong shock
wave in air. The pressure close to an explosion front ranges from 18.6 GPa to 33.7 GPa. A time history graph of the blast wave has been provided in figure 1. Just
around 33% of the complete explosive vitality is discharged in an explosion. The remaining 67% are all the more gradually discharged into the air as the objects of the
explosion combine with air and burn.
Cutting-edge Applications Using Finite Element Procedure for the Human Civilization

Introduction (Cont.)
This has a negligible effect on the properties of the blast wave as it proceeds slower than the blast waves. The blast wave is a shock wave formed by a high - intensity
shock front that expands into the surrounding air from the surface of the explosive. As the wave expands the front impinges on the structure in its path and the whole
structure is swallowed up by shock pressure [1].
The material that is currently being used for blast protection is armored steel[2]. All the other materials are either in the prototype stage or concept stage. Although steel
has high strength and toughness, its strength to weight ratio is low, For example, the weight of armored steel is about 2.4 tonnes for 2.73 × 1.1 × 0.0315 m plate and
literature survey [2] verified that the performance of steel degrades with temperature. Hence we need an alternative for steel which has better strength to weight ratio.
A study by Xiaochao Jin et al[3] describes the performance and advantages of using a sandwich composite for blast protection. A sandwich structure comprises of two
high strength plates and a low-density core layer. The main objective of this type of structure is to combine the stiffness and strength of the thin face-sheet and the
lighter weight of thicker flexible core to achieve superior material and structural properties. Hence, a sandwich construction was chosen for the composite material.
The top layer of the sandwich composite is a ceramic matrix composite whose matrix is Zirconium diboride and reinforcement is Silicon Carbide fibers. The core is a
honeycomb core made of armored steel. The bottom layer is polymer matrix composite whose matrix is Poly Ether Ether Keytone (PEEK) and reinforcement is poly (p-
phenylene-2,5-benzobisoxazole) (PBO) fibers.
Temperatures resulting from a blast can reach upto 4000 °C and hence Zirconium diboride (ZrB2), a ultrahigh temperature ceramic (UHTC)was considered for the top
layer of the composite [4]. Properties such as a melting point of 3246 °C, density of∼6.09 g cm−3 and high strength made it an ideal candidate to withstand blast
loading. Silicon Carbide(SiC) [5] is capable of withstanding thermal shocks primarily due to its superior properties such as higher thermal conductivity, high elastic
modulus and moderate coefficient of thermal expansion. PEEK[6, 7] has high plastic toughness and rigidity. It also has excellent corrosion, abrasion resistance,
tenacity and tensile strength. It performs well in high temperatures up to 260 °C where heat is a major concern. Advantages of PEEK over metals include tolerance to
mechanical and physical stress along with excellent chemical and thermal resistance. PBO [8] is the strongest fiber with a high tensile strength of 5.8 Gpa which is 1.6
times that of Kevlar, a tensile modulus of 180 to 270 GPa, Heat resistance up to 650 °C and thermal stability high-performance fibers such as p-aramid, m-aramid,
steel fibers, PBI, polyester, etc. These qualities make PBO fiber a good candidate for blast resistant composite material. Sandwich panels composed of conventional
steel honeycomb cores are chosen for their performance to impulse loads.
Once the material was chosen, the analysis began by modeling the composites Abaqus/Explicit. Micromodeling [9]was utilized to model the top and bottom layer and a
solid model was utilized to model the honeycomb core. With the help of literature [1], the load was modeled as a triangular pulse and the properties of different
materials and their failure criteria were obtained. The composite was analyzed for its behavior under load from different amounts of explosives and its performance was
characterized by the amount of energy absorbed upon impact. The composite’s performance was compared with steel to find which offers better protection under a
given blast.

Analytical Study
Determination of blast load
Blast loads are not characterized by any international organization. Hence this topic needs to be explored further as there are no standard procedures to design or
evaluate structures which is under a blast load. To do this a fundamental understanding of the blast phenomena as well as the dynamic response of various materials
are required. On the other hand, this topic is of interest in military perspective as the important experimental data are restricted to military use. Nevertheless, a
number of literatures are available which investigates various methods to characterize a blast load and to analyze a material under a blast load [10]. The TM 5 1300
(1990) manual[1] from the US army was utilized to calculate the pressure forces that impinges on a structure under a blast load with the following configuration.
Figure 2 shows the parameters required to calculate the pressure acting on material due to an explosion. The empirical formulae and experimental data available in
the TM 5 1300 (1990) manual was utilized to calculate the pressure behind a blast for a given standoff distance.
Figure 2.Illustration of explosive setup.
The utilization of cubicle structures or other comparable boundaries with at least one surfaces either adequately frangible or open to the environment will give some
level of venting relying upon the opening size. This type of structure will allow the blast wave from an internal explosion to leak out to the surrounding area, thus
significantly reducing internal pressure magnitude and duration.

Therefore the pressure impinging on a surface can be categorized into
• Shock pressure—The pressure within the containment which is reflected and strengthened.
• Gas Pressure—The pressure associated with gas particle accumulation and increased temperature.
• Leakage pressure—The pressure from the gases that fled through the vents[1].
Since the explosion happens near the ground the effect of temperature is negligible when compared with the effects of pressure. Therefore, only shock pressure
was considered and its effect on the structure was analysed.
Figure 3 shows the pressure versus time graph obtained from following the steps in TM 5 1300 (1990) manual. Since the experimental data was limited in the book
interpolations and extrapolations was utilized to extend the experimental data for our design conditions.
Determination of blast load (Cont.)
Figure 3. Pressure versus Time plot.

Finite element analysis
Finite Element Method was utilized to analyze the response of the sandwich composite under a blast load. The analysis was conducted in ABAQUS explicit. A quarter
model was utilized for analysis because of its ease in modeling and assign finer meshes. The behavior of the quarter model was extended to the whole model with the
help of the symmetry condition.
Micro-modeling [8]was utilized to model the top and bottom layer. In this approach, matrix and reinforcements are modeled as a separate deformable continuum. This
approach could be used when microscopic behavior of individual fibers and their interaction with the matrix are of importance. The solid model was utilized to model
the honeycomb core to understand the response of the material in 3D. Shell elements were not utilized for modeling the top and bottom layer because it ignores out of
plane stresses which is an important criterion to analyze a material’s behavior under impact load.
Figure 4 shows the boundary conditions assigned to the model. Under symmetric boundary condition, symmetry is maintained about a plane of a constant coordinate.
Abaqus[11] offers symmetry in x,y,z coordinates. Due to the nature of the simulation, the structure subjected to blast loading was fixed on two sides while symmetry
condition was applied across other ends as quarter model was only designed to reduce computational time. Under symmetric boundary condition, symmetry is
maintained about a plane of constant coordinate. Abaqus offers symmetry in x,yx,z coordinates. Since the force is acting in a x-y plane the X-Symmetry and Y-
Symmetry boundary conditions are used. Encastre condition constraints all displacement and rotation at a node. It is similar to fixed boundary condition in solid
mechanics where the slope and displacement at the point is zero.
Figure 4. Boundary conditions.

Finite element analysis (Cont.)
The properties of different material of fiber reinforced composites and honeycomb core were utilized separately because the micro model and solid model was utilized
and is shown in figures 5 and 6. A paper by Khan et al[12] suggests that brittle cracking model can be used to predict crack initiation in Plexiglas plate when subjected
to sharp indentation loading without experiments. Hence The Failure is initiated through brittle cracking criteria for the top and bottom layer. The failure is initiated in
the honeycomb core through Johnson Cook’s damage criteria.
The damage initiation criteria for fibre reinforced composites are based on Hashin’s theory. These criteria consider four different damage initiation mechanisms: fibre
tension, fibre compression, matrix tension and matrix compression.
Figure 5. Final Assembly. Figure 6. Final assembly exploded view.

Table 2. (a) Mechanical properties of Steel [13].
(b) Failure properties of steel [13].
Table 3. Properties of Top layer[14]. Table 4. Properties of bottom layer[15, 16].
Prior to any damage initiation and evolution the damage operator, M, is equal to the identity matrix so σˆ = σ. Once the damage initiation and evolution has occurred
for at least one mode, the damage operator becomes significant in the criteria for damage initiation of the modes. The effective stress, σˆ , is intended to represent the
stress acting over the damaged area that effectively resists the internal forces.
The initiation criteria can be specialized to obtain the model proposed by Hashin and Rotem (1973) by setting α = 0.0 and ST=YC/2 or the model proposed in Hashin
(1980) by setting α = 1.0.
An output variable is associated with each initiation criterion (fibre tension, fibre compression, matrix tension and matrix compression)to indicate whether criterion has
been met. A value of 1.0 or higher indicates that the initiation criterion has been met. If you define a damage initiation model without defining an associated evolution
law, the initiation criteria will affect only output. Thus, these criteria can be used to evaluate the propensity of the material to undergo damage without modeling the
damage process.

The Johnson-Cook failure model has been used to model ductile failure of materials experiencing large pressures, strain rates and temperatures. The model is
constructed in a similar way to the Johnson-Cook Plasticity model where it consists of three independent terms that define the dynamic fracture strain as a function of
pressure, strain rate and temperature.
The ratio of the incremental effective plastic strain and effective fracture strain for the element conditions is incremented and stored in custom results variable, DAMAGE.
The material is assumed to be intact until DAMAGE = 1.0. At this point failure is initiated in the element. An instantaneous post failure response is used.
Abaqus/Explicit uses a smeared crack model to represent the discontinuous brittle behavior. It does not track individual macro cracks; instead, constitutive calculations
are performed independently at each material point of the finite element model. The presence of cracks enters into these calculations by the way in which the cracks
affect the stress and material stiffness associated with the material point. The term ‘crack’ is used to mean a direction in which cracking has been detected at the single
material calculation point in question: the closest physical concept is that there exists a continuum of micro-cracks in the neighbourhood of the point, oriented as
determined by the model. The anisotropy introduced by cracking is assumed to be important in the simulations for which the model is intended.
The Abaqus/Explicit cracking model assumes fixed, orthogonal cracks, with the maximum number of cracks at a material point limited by the number of direct stress
components present at that material point of finite element method (a maximum of three cracks in three dimensional, plane strain, and axisymmetric problems; two
cracks in plane stress and shell problems; and one crack in beam or truss problems). Internally, once cracks exist at a point, the component forms of all vector and
tensor-valued quantines are rotated so that they lie in the local system defined by the crack orientation vectors(the normals to the crack faces). The model ensures that
the se crack face normal vectors will be orthogonal, so that this local crack system is rectangular Cartesian. For output purposes you are offered results of stresses and
strains in the global and/or local crack systems.
A simple Rankine criterion is used to detect crack initiation. This criterion states that a crack forms when the maximum principal tensile stress exceeds the tensile
strength of the brittle material. Although crack detection is based purely on Mode I fracture considerations, ensuing cracked behaviour includes both Mode I(tension
softening/stiffening) and Mode II(shear softening/retention) behaviour. As soon as the Rankine criterion for crack formation has been met, we assume that a first crack
has formed. The crack surface is taken to be normal to the direction of the maximum tensile principal stress. Subsequent cracks may form with crack surface normals in
the direction of maximum principal tensile stress that is orthogonal to the directions of any existing crack surface normals at the same point. Cracking is irrecoverable in
the sense that, once a crack has occurred at a point, it remains throughout the rest of the calculation. However, crack closing and reopening may take place along the
directions of the crack surface normals. The model neglects any permanent strain associated with cracking; that is, it is assumed that cracks can close completely when
the stress across them becomes compressive.

An important feature of the cracking model is that, Crack initiation is based on Mode I fracture only, post cracked behaviour includes Mode II as well as Mode I. The
Mode II shear behaviour is based on the common observation that the shear behaviour depends on the amount of crack opening. More specifically, the cracked shear
modulus is reduced as the crack opens. A shear retention model in which the post cracked shear stiffness is defined as a function of the opening strain across the
crack; the shear retention model must be defined in the cracking model, and zero shear retention should not be used.
In these models the dependence is defined by expressing the post cracking shear modulus, GC, as a fraction of the uncracked shear modulus:
where G is the shear modulus of the uncracked material and the shear retention factor, 𝜌(𝑒𝑛𝑛
𝑐𝑘
) depends on the crack opening strain, 𝑒𝑛𝑛
𝑐𝑘
.
As different layer of the sandwich composite was modelled separately, they were joined together in assembly module in Abaqus and tied together using a tie constraint
[17]. From the previous section, we know that the load is approximated as a triangular pulse and from TM 5 1300 (1990) manual[1]we found that for initial analysis the
load can be assumed as a uniform load to reduce the complexity involved in the analysis. Hence the load was given as a triangular pulse which is uniformly distributed
over the top surface of the sandwich composite. For this analysis swept meshing was utilized to mesh the geometry. The swept meshing technique involves two
phases: Intially the software creates a mesh on one side of the region, known as source side and then the software copies the nodes of the mesh, one element layer at
a time, until the final side known as the target side is reached. Abaqus/CAE copies the nodes along an edge, and this edge is called the sweep path. The sweep path
can be any type of edge- a straight edge, a circular edge or a spline. If the sweep is a straight edge or a spline, the resulting mesh is called an extruded swept mesh. If
the sweep path is a circular edge, the resulting mesh is called a revolved swept mesh.
In addition, the sweep path controls the default orientation of hexahedral and wedge elements that are used to model gaskets, continuum shells, cylindrical region
using cylindrical elements and adhesive joints using cohesive elements.
Four—node doubly curved thin or thick shell, reduced intergration, hourglass control, finite membrane strains were used for the finite element modeling of the structure.
The settings are required to obtain a result that can be used to make predictions. Excessive distorted elements will lead to errors aborting the analysis. Hence element
deletion option is used which deletes based on the failure criteria. Second order accuracy and hourglass controls are used to obtain more accurate results. The total
number of elements was about 110,326.

Results
According to an investigation by Tiju Thomas and Gaurav Tiwari [18], the response of honeycomb structure to quasi static and dynamic loading was dependent on
design parameters of the honeycomb structure like relative density of the core, cell configuration, cell wall thickness, node length and cell size. Relative Density was
one of the most influential parameters in determining the performance of the Honeycomb in static and dynamic conditions.
This analysis explores the effect of modifying the face dimension of the honeycomb core on the sandwich composite. Figures 7 and 8 show honeycombs with different
cell densities where cell density of figure 7 is higher than the cell density of figure 8. Two models with same dimensions of the top and bottom layer but one having
HC-coarse and the other having HC-fine as its core were considered for analysis.
Figure 9 shows that higher the cell density of the honeycomb core higher the amount of internal energy the sandwich composite. This shows that the core with higher
cell density can absorb more energy through deformation before failure. Therefore, increasing the cell density of the honeycomb core increases the strength and
toughness of the sandwich composite.
Figure 7. Dimensions of HC-fine. Figure 8. Dimensions of HC-coarse
Figure 9. Effect of changing face dimension
of the core on the sandwich composite.

The effects of changing the thickness of the top layer ceramic matrix composite were also studied. Three models whose dimensions are given in table 5 were
considered for analysis.
Figure 10 shows that increasing the thickness of the top layer increases the amount of energy the sandwich composite can absorb before failure. This might be due
to the fact that with an increase in thickness of the top layer the amount of molecules available for interaction also increases which effectively disperses the load to
the fibers and the other layers of the sandwich composite. Therefore, Increasing the thickness of the top layer increases the strength and toughness of the sandwich
composite.
Figure 10.Changing the thickness of
ceramic matrix composite.
Table 5. Models chosen to study the effects of variation
of thickness of top layer on the sandwich composite.
Results (Cont.)

The dimensions given in table 6 was used to model the sandwich composite and figure 7 was chosen for the face dimension of the honeycomb core. After finalizing
the dimensions, the model was subjected to various blast loads and its performance was compared with the performance of armored steel to find out which material
offers better protection.
Figure 11 shows that the amount of energy absorbed by the sandwich composite is higher than the amount of energy absorbed by steel. Therefore, the energy of the
shock wave after passing through the material is lower for the sandwich composite than for steel. This results in sandwich structure offering better protection than steel
when exposed to an explosion of 1 kg TNT.
Table 6. Final thickness for the
sandwich composite.
Figure 11. Performance of sandwich composite
and steel under explosive load of 1 kg TNT.
Figure 12 shows that the amount of energy absorbed by steel and sandwich composite is approximately equal. This might be due to the failure of the top layer exposing
the core to the blast environment. Hence, the amount of material available to withstand the blast load is reduced in the case of sandwich composite whereas it is still the
same for steel.
Results (Cont.)

Figure 13 shows the amount of energy absorbed by steel is higher than that of sandwich composite when exposed to an explosion of 10 kg TNT. The difference in
performance is because the load exerted on the Sandwich structure due to the detonation of 10 Kg TNT results in completefailure of top layer—ceramic matrix
composite and bottom layer—polymer matrix composite. This results in maximum deformation of the honeycomb core. Due to the above event, the performance of
sandwich composite is very less when compared to that of steel.
Results (Cont.)

Discussions
The main objective of this analysis was to study the performance of the sandwich composite and compare it with the performance of armored steel to find whether the
sandwich composite is a better material than steel for blast protection. To achieve the above objective various models were made varying the dimensions of the
different layers of the sandwich composite and their effects on the performance of the sandwich composite were studied. Finally, the dimensions of different layers of
the sandwich composite were finalized, modeled and analyzed for blast load by varying the amount of TNT.
Figure 8 shows that decreasing the honeycomb’s cell size increases the energy absorption character of the honeycomb panel. A similar result was obtained in a study
by Mete Onur Kaman and Murat Yavuz Solmaz [19], where it was seen that the buckling strength of the specimens increases by the increase of core density. This
might be because as the core density increases more surface is in contact with the force. Hence, the load gets distributed uniformly throughout the honeycomb
structure resulting an increase in buckling strength.
Figure 12 shows the demarcating point. Till this point, the sandwich composite performs better than steel and beyond this point armored steel performs better than the
sandwich composite. The trend shown by the composite material in the figures 11–13 is due to the fact that composites are brittle in nature. They absorb energy until
their maximum strength is reached and breakdown or result in the formation of cracks when the load exceeds its maximum strength. The plot of energy versus time
from Uddin et al[20]study is similar to figures 11–13. The initiation of internal damage is characterized by the first fluctuations in the energy versus time plot. After the
initial damage, the maximum load is observed at the point where the material fails. This point marks the onset of the propagation phase and the cracks propagate
through the material rapidly. Following the failure of the material due to shear, the load drops linearly to zero and the impact event ends.
The trend shown by armored steel in figures 11–13 is due to the fact that armored steel is ductile in nature and it absorbs energy through deformation. Hence, as the
load increases the deformation of steel increases and hence the amount of energy absorbed increases. This similar trend is found in a study by Dariusz Szwedowicz
et al [21]where the amount of energy absorbed increased with displacement and was verified experimentally.
The use of armor in a vehicle increases the weight of the vehicle by tenfold. This increase in weight not only increases fuel consumption but also limits the use of
these vehicles within a geographical boundary. Steel is the currently utilized material for blast protection. Due to its low strength to weight ratio, it adds more than 2
tonnes to the weight of a vehicle. From the literature survey, all the materials proposed for blast protection do not try to solve this problem.
The studies performed until now did not consider weight as a constraint. Hence, in this study, a lightweight sandwich composite was designed. The dynamic behavior
of the chosen composite was analyzed using FEM for different blast loads. Its performance was characterized by the amount of energy absorbed by the material upon
impact and was compared with that of steel to find whether it’s a better alternative to steel so that steel can be replaced by a light weight material which offers better
protection than steel.

Conclusion
Explosive devices are improving day by day increasing the damage caused by an explosive. But the improvements made to the material used for blast protection is
very less. Therefore, a new material with light weight and high strength to weight ratio is required to improve the currently available blast protection. A lightweight
sandwich composite was proposed in this paper as a candidate for blast protection. It was analyzed using FEM and its performance was compared with that of steel.
This investigation has led to the following conclusions.
 The top layer- Ceramic matrix composite is a very important part of the sandwich structure as it faces the impact load from the explosion. The composite
performs better than steel until the strength of the top layer is reached.
 Once the top layer fails it results in excessive deformation of the honeycomb core and the failure of the bottom layer.
 Therefore, the sandwich composite with the given thickness of the top and bottom layer and the configuration of honeycomb core taken for this study will
perform better than steel only under a given working condition.
 Its usage reduces the weight of the material used by one-third, in numbers weight of the composite is approximately 920 Kg, whereas that of steel is
approximately 2.7 Tonnes (for the given dimensions).
 Beyond the working conditions, the performance of the sandwich composite degrades and it becomes lower than that of armored steel.

Scope for Future Work
This investigation has proved that the proposed composite is a better performer than steel under a given working condition and reduces the weight of the material
required by almost one third when compared with steel. To extend the working condition of the material.
 Different shapes of honeycomb cores and different orientation of honeycomb cores can be researched.
 The thickness of the top layer and the bottom layer of the sandwich composite can be varied and the performance of the sandwich composite can be
studied, thus effectively extending the working condition of the sandwich composite.
 The best method to manufacture the sandwich composite should be found. Compression molding preferred for high volume production. Hand layup or
vacuum bagging is preferred for low volume production.
 The best adhesive that can ensure perfect contact between the composite layers and the steel honeycomb core should be found [22].
 The best cementary for the reinforcement used in the top and bottom layer can be found experimentally
 The best volume fraction of the matrix and reinforcement of the top and bottom layer can be found experimentally.
 The performance of the sandwich composite and steel can be compared experimentally.

New Techniques in Solving Real Life Scenarios in Finite Element Procedures
The present state of development of a new finite element approximation procedure has been reviewed. In this procedure the finite element mesh is fixed and the
number or type of basis functions is varied over the mesh, either uniformly or selectively, until some desired level of precision is reached. The basis functions are
complete polynomials, optionally supplemented by rational or other non-polynomial basis functions. They are hierarchic, i.e. the set of basis functions associated with
an element is a subset of the basis functions associated with each higher order element of the same kind. Consequently, the stiffness matrix of each element is
embedded in the stiffness matrices of all higher order elements of the same kind. There are several computational advantages, the most important of which are that
the rate of convergence is much faster than the rate of convergence achieved through mesh refinement and the number and distribution of degrees of freedom can
be modified without sacrificing the effort spent on triangular zing the initial stiffness matrix. Thus the approximation error can be efficiently controlled. It is concluded
that development of adaptive finite element software systems, in which redistribution of the degrees of freedom is achieved through controlling the number and type
of basis functions, is feasible. Such systems are likely to be more efficient, by an order of magnitude or more, than conventional finite element software systems.
Any real life problem can be modelled on paper or virtually using differential equation which obeys laws of physics and boundary condition. And solution of unknown
can be obtained by solving this equation. When problem is complex then direct or straight forward approach ( which is also called analytical approach ) is not
sufficient to solve the problem. Hence Numerical methods are adopted which though do not give exact result but sufficient enough to predict output of the problem.
There are many techniques to solve these real life problem which are FEM, FVM, FDM, BEM, DEM and many more. All these techniques are based on numerical
methods and linear algebra. As we are gradually relying on the virtual simulation to capture natural phenomena, hence these techniques are rapidly being picked up
the popularity by various domain ( engineering, medical, biology, natural science , and many more ).
Now coming to FEM. In this technique an unknown equation( which is also called shape function) is assumed for solution then that equation is put to the differential
equation with a weight value. Then this differential equation will become set of algebraic equation. Then this set of algebraic equation is solved by solving [F]=[K][X].
Due to its shape function the result can not be exact. Till now this technique is very popular for structural analysis. Fluid simulation can be also done using it. ANSYS
Solves fluid problem using this technique.
So bottom line is that to solve complex problem convert any differential equation into set of algebraic equation and form a matrix. And solve it. This basic philosophy
is same for FEM, FDM, FVM. Only initial approach is different to each other. In future new numerical techniques may come which reduced approximation error hence
result will be more realistic. But whatever new techniques come all could be based on numerical techniques and linear algebra. Only initial assumption will be
different but derivation afterward will be all based on linear algebra.

References
[1] Army TM. TM 5-1300 1990 Structures to Resist the Effects of Accidental Explosions
[2] Cimpoeru S J 2016 The Mechanical Metallurgy of Armour Steels. (Australia: Defence Science and Technology Group Fishermans Bend VIC)
[3] Jin X, Wang Z, Ning J, Xiao G, Liu E and Shu X 2016 Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading
Composites Part B: Engineering. 106 206–17
[4] Zirconium DiBoride/ Zirconium Boride Powder (ZrB2)(https://reade.com/products/zirconium-diboride-zirconium-boridepowder-zrb2) (accessed October 5, 2018)
[5] Silicon Carbide (SiC): Properties and applications. CarboSystem (http://carbosystem.com/en/silicon-carbide-propertiesapplications/) (2018, accessed November 2,
2018)
[6] Products Sby ZI. A Comparison Between PEEK and Metal. Why is Plastic Better? AZoM.com (https://azom.com/article.aspx? ArticleID=13532) (2018, accessed
October 2, 2018)
[7] Bhatnagar N, Jha S and Bhowmik S 2010 Application of high performance polymer-polyetheretherketones(peek) in aerospace industry Inventi Impact: Tech
Research & Reviews (Inventi Journals(P) Ltd) 1
[8] Zylon. EuroFibers (https://eurofibers.com/fibers/zylon/) (accessed October 2, 2018)
[9] Kouznetsova V, Wilson W and Geers M Multi–scale modeling of textile composites Thiam Wai Chua MT 10.19
[10] Draganić H and Sigmund V 2012 Blast loading on structures Technical Gazette. 19 643–52
[11] Boundary Conditions 2013 Manual AU. Version 6.13-2. Dassault Systémes Simulia Corp., Providence, Rhode Island, USA
[12] Khan A J, Iqbal N, Saeed H A and Tarar W A 2016 Development of material model for assessment of brittle cracking behavior of plexiglasInIOP Conf. Series:
Materials Science and Engineering (Bristol)(IOP Publishing) 146p012008

References (Cont.)
[13] Wang K 2016 Calibration of the Johnson-Cook failure parameters as the chip separation criterion in the modelling of the orthogonal metal cutting process Doctoral
Dissertation
[14] Teague M P, Hilmas G and Fahrenholtz W Finite element modeling of internal stress factors for ZrB2-SiC ceramics
[15] Wang K 2016 Doctoral Thesis, McMaster University (accessed October 2, 2018) (https://azom.com/properties.aspx?ArticleID= 1882)
[16] Govarthanam K K, Anand S C and Rajendran S 2016 Technical textiles for knife and slash resistance InHandbook of Technical Textiles. (Woodhead Publishing) pp
193–236
[17] Tie Constraint 2013 Manual AU. Version 6.13-2. Dassault Systémes Simulia Corp. (Rhode Island, United States of America: Providence)
[18] Thomas T and Tiwari G 2019 Crushing behavior of honeycomb structure: a reviewInt. J. Crashworthiness 24 1–25
[19] Kaman M O, Solmaz M Y and Turan K 2010 Experimental and numerical analysis of critical buckling load of honeycomb sandwich panelsJ. Compos. Mater. 44
2819–31
[20] Uddin N, Mousa M A and Fouad F H 2013 Impact behavior of hybrid fiber-reinforced polymer(FRP)/autoclave aerated concrete (AAC) panels for structural
applicationsInDevelopments in Fiber-Reinforced Polymer (FRP) Composites for Civil Engineering (Woodhead Publishing) pp 247–71
[21] Szwedowicz D, Estrada Q, Cortes C, Bedolla J, Alvarez G and Castro F 2014 Evaluation of energy absorption performance of steel square profiles with circular
discontinuities Latin American Journal of Solids and Structures. 11 1744–60
[22] 8 Iqbal H M, Bhowmik S and Benedictus R 2019 Durability of PBI adhesive bonded joints under various environmental conditionsInt. J. Adhes. Adhes 89 154–160

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