The uniform temperature does not default to REFT (MP,REFT) but does default to the value specified on the TREF command.
The effects of thermal expansion can be accounted for in one of three different ways:
When you use ALPX to enter values for the secant coefficient of thermal expansion (α se), the program interprets those values as secant or mean values, taken with respect to some common datum or definition temperature.
For example, suppose you measured thermal strains in a test laboratory, starting at 23°C, and took readings at 200°, 400°, 600°, 800°, and 1000°. When you plot this strain-temperature data, you could input this directly via THSX. The slopes of the secants to the strain-temperature curve would be the mean (or secant) values of the coefficient of thermal expansion, defined with respect to the common temperature of 23° (To).
You can also input the instantaneous coefficient of thermal expansion (α in, using CTEX). The slopes of the tangents to this curve represent the instantaneous values. The following figure shows how alternate ways of inputting coefficients of thermal expansion relate to each other:
The program calculates structural thermal strain as follows:
εth = α se(T) * (T - Tref)
where:
| T = element evaluation temperature |
| Tref = temperature at which zero thermal strains exist (defined by TREF command or REFT) |
| α se(T) = secant coefficient of thermal expansion, with respect to a reference temperature defined by MP,REFT or TREF (ALPX ) |
If the material property data is in terms of instantaneous values of α, then the program will convert those instantaneous values into secant values as follows:
where:
| Tn = temperature at which an α se value is being evaluated |
| To = definition temperature at which the α se values are defined (in this case, same as TREF) |
| α in(T) = instantaneous coefficient of thermal expansion at temperature T (CTEX ) |
If the material property data is in terms of thermal strain, the program will convert those strains into secant values of coefficients of thermal expansion as follows:
where:
| εith(T) = thermal strain at temperature T (THSX) |
If necessary, the data is shifted so that the thermal strain is zero when Tn = Tref. If a data point at Tref exists, a discontinuity in α se may be generated at Tn = Tref. This can be avoided by ensuring that the slopes of εith on both sides of Tref match.
If the α se values are based upon a definition temperature other than TREF, it is necessary to convert those values to TREF (MPAMOD).
Thermal expansion is assumed to be isotropic when used with any hyperelasticity material model. The program uses the first secant coefficient (ALPX), instantaneous coefficient (CTEX), or thermal strain coefficient (THSX).
The secant thermal expansion is assumed to be isotropic if only the first secant coefficient (ALPX for MP, or CTEX for TB,CTE) is specified.