where a,
b, and
c are constants. Thus, at the cross section
z = 0, one has
At the cross section z = 0, the deformation is in-plane and fully characterized by the in-plane displacement components
u(
x,
y) and
v(
x,
y).
In COMSOL Multiphysics, the coefficients a,
b, and
c in the expression for the
εz strain are modeled as extra degrees of freedom that are constant throughout the model (global variables).
Coefficients a,
b, and
c are assumed to be small. Then, using the above displacement field in the strain tensor expression and dropping quadratic and higher order terms in the coefficients, one obtains: