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)

where	= Young’s modulus
	= Poisson’s ratio
	= lineic dilatation coefficient (coefficient of thermal expansion)
	= temperature
	= reference temperature without stresses (reference temperature for dilatation)
	= the unit tensor

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.