diff --git a/docs/examples/example_neohooke.md b/docs/examples/example_neohooke.md index b951e87..a2a754a 100644 --- a/docs/examples/example_neohooke.md +++ b/docs/examples/example_neohooke.md @@ -6,7 +6,7 @@ parent: Examples --- # Neo-Hooke -This is a very basic example on how to implement a nearly-incompressible version of the Neo-Hookean material model in a commercial FEM package (HYPELA2 for Marc or UMAT for Abaqus). As no special two- or three-field variational principle is used in this example, it is not suitable for nearly-incompressible material behaviour. Otherwise the elements tend to show excessive volumetric locking during deformation and hence, wrong results are calculated. +This is a very basic example on how to implement a nearly-incompressible version of the Neo-Hookean material model in a commercial FEM package (HYPELA2 for Marc or UMAT for Abaqus). ## Hyperelasticity The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution, see Eq. $$\eqref{eq:psi}$$. The first one is assumed to be proportional to the first invariant of the isochoric part of the right Cauchy-Green deformation tensor whereas the volumetric part is only a function of the volumetric ratio (the determinant of the deformation gradient), see Eq. $$\eqref{eq:psi-nh}$$. @@ -54,6 +54,9 @@ $$ ## HYPELA2 User Subroutine for Marc Eq. $$\eqref{eq:pk2-nh}$$ and Eq. $$\eqref{eq:c4-nh}$$ are implemented in a Total Lagrange [user subroutine](Marc/hypela2_nh_ttb_simple.f) with the help of this Tensor module. +{: .warning } +> As no special two- or three-field variational principle is used in this example, it is not suitable for nearly-incompressible material behaviour. Otherwise the elements tend to show excessive volumetric locking during deformation and hence, wrong results are calculated. + ```fortran include 'ttb/ttb_library.f' @@ -203,4 +206,4 @@ Abaqus uses an Updated-Lagrange approach and hence, Eq. $$\eqref{eq:pk2-nh}$$ an end ``` - \ No newline at end of file +