Finite element implementation of slightly compressible and incompressible first invariant-based hyperelasticity: theory, coding, exemplary problems

The present study is concerned with the finite element (FE) implementation of slightly compressible
hyperelastic material models. A class of constitutive equations is considered where
the isochoric potential functions are based on the first invariant of the right Cauchy-Green
(C-G) deformation tensor. Special attention is paid to the most recently developed model
formulations. The incremental form of hyperelasticity and its numerical implementation into
both commercial and non-commercial FE software are discussed. A Fortran 77 UMAT code
is attached which allows for a simple implementation of arbitrary first invariant-based constitutive
models into Abaqus and Salome-Meca FE packages. Several exemplary problems
are considered.