The capability to do a thermoviscoelasic analysis exists in the following elements:

These elements support the thermoviscoelastic effect which manifests itself as an increase in temperature during viscoelastic deformation due to the conversion of some part of the viscoelastic loss into heat.

In a thermoviscoelastic analysis, the stress equation of motion (Equation 2–51) and heat flow conservation equation (Equation 6–1) are coupled by the viscoelastic heat density rate defined as:

(10–49)

where:

β = fraction of the energy dissipation density in a viscoelastic material converted to heat (input as QRATE on the MP command)

= energy dissipation density rate calculated from the incremental energy dissipation (output as SEND,VDAM); see Equation 4–51 in the Material Reference for the Prony series formulation (TB,PRONY) and Equation 4–232 in the Mechanical APDL Theory Reference for the Bergstrom-Boyce material model (TB,BB).

The coupled-field finite element matrix equation for the thermoviscoelastic analysis is:

(10–50)

where:

[M] = element mass matrix (defined by Equation 2–58)

[C] = element structural damping matrix (discussed in Damping Matrices)

[K] = element stiffness matrix (defined by Equation 2–58)

{u} = displacement vector

{F} = sum of the element nodal force (defined by Equation 2–56) and element pressure (defined by Equation 2–58) vectors

[Ct] = element specific heat matrix (defined by Equation 6–28)

[Kt] = element thermal conductivity matrix (defined by Equation Equation 6–28)

{T} = temperature vector

= sum of the element heat generation rate load and element convection surface heat flow vectors (defined by Equation 6–28)

= element viscoelastic heat generation rate load =

where:

= element viscoelastic heat density rate at substep n (output as NMISC,6)

{N} = element shape functions