10.3. Thermoplasticity

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

PLANE222 - 2-D 4-Node Coupled-Field Solid
PLANE223 - 2-D 8-Node Coupled-Field Solid
SOLID226 - 3-D 20-Node Coupled-Field Solid
SOLID227 - 3-D 10-Node Coupled-Field Solid

These elements support the thermoplastic effect which manifests itself as an increase in temperature during plastic deformation due to the conversion of some of the plastic work into heat.

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

(10–40)

where:

β = fraction of plastic work coefficient (input as QRATE on MP command)
= plastic work rate =

where:

= stress vector =
= plastic strain vector =

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

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 6–22)
[Kt] = element diffusion conductivity matrix (defined by Equation 6–22)
{T} = temperature vector
{Q} = sum of the element heat generation rate load and element convection surface heat flow vectors (defined by Equation 6–22)
= element plastic heat generation rate load =

where:

= element plastic heat density rate at substep n (output as NMISC,5)
{N} = element shape functions


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