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.