Finite Element Formulation of Internally Balanced Blatz Ko Material Model

Abstract

Material constitutive models often include internal variables in order to capture realistic mechanical effects such as viscosity. Recent work for compressible hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. The finite element formulation for this new treatment is developed, however, the implementation sheds light on a special form of constitutive model. In particular, the material model is a function of the first and third invariants of new quantities derived from the counterparts of the multiplicative decomposition. These new quantities are defined in analogy to the right Cauchy Green tensor. This work demonstrates the required treatment for a special material model that is formulated using the second and third principal invariants of these new derived quantities. Mainly, the treatment simplifies the internal balance equation that emerges from the variational treatment. This facilitates the linearization procedure of this new formulation for internally balanced compressible hyperelastic material. The present work permits the future use of more complicated internally balanced hyperelastic models.