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Viscoelastic Properties of Polymers
Cool Book
Chapter_1
The nature of viscoelastic behaviour
A. INTRODUCTION
Classical theory of elasticity
mechanical properties of elastic solids
Hokean body - body that hook law is walid for
Hook's law
ut tensio, sic vis [Robert Hook, 1678]
translate: "as the extension, so the force"
Hook low holds to some extend):
- wher elastic body is deformed
- wind blowing on a tall building
- musician plucking a string
- filling a party balloon
Hookean body or hookean material?
modulus [E]
Robert Hooke FRS (/hʊk/; 28 July [O.S. 18 July] 1635 – 3 March 1703) was an English natural philosopher, architect and polymath.
F = k x
stiffness
VALID - for small sxtentions
force [N]
extention [m]
It is a 1st order aprox. to real response of springs and other elastic bodies to applied forces
constant factor characteristic ~ stiffness[N/m]
Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached
classical
linear limits
F [N]
no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state
tan a = k
a
Linear or 1st order aprox.
Hook's Law
x [m]
linear limits
Generalization of Hook's law
The strain (deformation) of an elastic object or material is proportional to the stress applied to it.
general stresses and strains may have multiple independent components
k_xz
k_xy
k_xx
k_yx
k_yz
k_yy
k =
MODERN
k_zx
k_zy
k_zz
Hook's law in general form makes possible to deduce the relation between stress and stran for complex objects in therms of intristic material properties:
EX.
k~A
homogenious rod
k~fi^2
l
uniform cross section
k~1/l
A
fi