The parameter \(\varphi_{c}\) shows the maximum value of damage that is
allowed to heal during unloading. For a material point which goes
through the damage \(\varphi\geq\varphi_{c}\) the resulting
stress-strain curves will be nonlinear, with the amount of departure
from linearity dependent on the specific form of the degradation
function.
3. Numerical solution
This section is applied to the two-dimensional implementation, which is
performed under plane strain conditions in a finite element code within
the Abaqus by means of UEL and UMAT subroutines. The purpose of this
section is to introduce a straightforward implementation procedure. The
eight-node quadrilateral finite elements are used.
Finite element
approximation
In more compact form, the displacement field and phase-field are
visualized inside an eight-node quadrilateral element by the following
relations: