Hyperelastic Blatz - Ko Model
The Blatz-Ko strain energy density function is useful for modeling compressible
polyurethane foam type rubbers and can be expressed as:
where G is the shear modulus
under infinitesimal deformations = E/2(1+n), E
is Young's modulus of elasticity, n
is Poisson's ratio, Ik
is the invariants of C=Ik(C), C
is the Cauchy-Green deformation tensor = 2e+I,
e
is the Lagrangian strain tensor, and I
is the Identity matrix.
The above expression, contains only one material constant G.
Since n
= 0.25 for the Blatz-Ko model, the only material property which is considered
is the Young's modulus. Thus,
The Blatz-Ko model is currently supported by solid elements only (draft
and high quality) elements.
The selected Blatz-Ko model is a simplified form of the expression obtained
by Blatz and Ko (1962) to model the deformation of a highly compressible
polyurethane foam rubber. The strain energy was approximated by the following
expression:
where
A specific form of this three-parameter family of elastic potential
was later proposed in which the following values of the constants a, b, and
n
were assumed: b
= 0, n
= 0.25, and a
= 0.5.