[Music]
it's well known
that there are several types of
materials that are different from each
other
in terms of their mechanical behavior
we have seen how some materials such as
metals
undergo elastic deformation to a point
and loading them further will push them
into the regime of plasticity
before failing but
not all materials undergo plastic
deformation
also not all materials undergo elastic
deformation
that's linear in nature
in fact there's a whole class of
materials
that can deform even in the strain
ranges of 50
or more with zero to very little plastic
deformation
before failure and the stress strain
response for such materials
is usually highly non-linear
we see them pretty much every day in
both our domestic
and engineering lives these are called
as
the hyper elastic materials
in very simple terms hyper elastic
materials
can be defined as the class of materials
that can undergo
non-linear elastic deformation
typical examples of these materials that
showcase such behavior
are rubbers elastomers soft tissues
foams and many more
typically most soft materials behave
this way
and may be classified as hyperelastic
materials
but they still share some similarities
with the linear elastic materials
regarding the nature of deformation
in both the cases the work done on them
is stored as internal energy
and is fully recoverable if the
deformation is elastic
then why do we need a separate class of
material models
to mimic the behavior of hyperelastic
behavior
the key difference between the two is
seen in the stress strain response
from these materials in case of
hyperelastic materials
this response is usually highly
non-linear
to a point where a linear approximation
is inaccurate
take this response for example over here
we can see that the response is highly
non-linear with the material having
a stiff response to begin with that
slowly reduces
before stiffening again so
the stiffness is changing throughout the
deformation
and if one were to mimic this behavior
with a linear elastic material
how would they pick the value of elastic
modulus considering that it keeps
changing with the string
suppose we use the initial stiffness
which is
nothing but the slope of the tangent
drawn to the initial portion of the
curve in this case
let's compare the stress responses for
both the curves at a given string
we can see that the linear elastic
assumption
results in very large stress compared to
the actual hyperelastic response
this will result in a highly stiff
response for the structure
and can negatively affect the
engineering decisions
made based on this result
this is the reason why we need to have a
different way of modeling hyperelastic
materials
so we can capture the full complex
response of the soft materials
now let's look at the key
characteristics of hyperelastic
materials
the first thing that we notice in this
class of materials
is that they're generally soft in nature
especially compared to metals
next as we have discussed already their
stress strain response is non-linear
which means that the slope of the curve
which is the instantaneous stiffness of
the material
changes with the string
these materials are known to undergo
large deformation
with very little to no plastic
deformation
before they fail
this means that the stiffness or
the stress strain curve is monotonically
increasing
until its failure
since they mostly undergo elastic
deformation they follow the same path
during both loading and unloading
this also means that the energy is
conserved
meaning the work done and deforming it
is all stored
as internal energy and is fully
recoverable upon unloading
most of the hyper-elastic materials such
as rubbers and soft tissues
are nearly or fully incompressible
but other set of materials such as foams
and sponges
which are known to be compressible can
also be modeled
as hyperelastic materials using special
class of hyperelastic models
in this section we will learn what are
the different ways of modeling the
hyper-elastic materials
and see what kinds of experiments are to
be conducted to calibrate them
we'll also discuss a few applications
and see how the hyper elastic materials
are used in engineering analysis
in this course we will limit our
discussion to nearly
or fully incompressible hyper-elastic
materials
as these are the most commonly seen in
engineering applications
you