For elasticity in a solid region, Ansys Polyflow solves the motion equation for displacement by:
(27–1) |
In Equation 27–1,
is the stress tensor and
is the body force, while
is the density of the solid and
is the acceleration undergone by the solid. In equipment involved in
polymer processing, the assumption of quasi-static behaviour is often accepted, either
because changes are usually slow enough for the inertia terms in the solid body to be
discarded, or because vibration of a structure is not the primary objective of a
simulation. However, there are transient situations where inertia of the solid can play
a role: this can be the case when the solid material involved is characterised by a
relatively low Young’s modulus, so that inertia and elastic stress may compete
until a steady response is achieved.
In Ansys Polyflow small deformation is assumed and the stress tensor is given by the following thermoelastic constitutive equation:
(27–2) |
The strain tensor is related to the displacement
by:
(27–3) |
,
, and
can be constant or temperature dependent using an Arrhenius law or an
approximated Arrhenius law. In 2D, Ansys Polyflow always assumes planar deformation. When
an elastic sub-task is defined, Ansys Polyflow can also compute the elastic stresses as a
postprocessor, using Equation 27–2.