 ## Structural & Thermal

#### What is the difference between secant and instantaneous coefficients of thermal expansion (CTE)?

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There are two ways of specifying CTE in Workbench Engineering Data: 1. Instantaneous (tangent) 2. Secant (average) If we plot thermal strain vs. temperature on a graph (origin represents zero thermal strain at the reference temperature), the secant CTE represents the linear slope from the reference temperature. The instantaneous CTE, however, is the slope of the curve at the temperature of interest. In practical terms, the secant CTE (“alpha”) is the measure of the thermal strain due to a change in temperature from the reference temperature to the current temperature. This value is typically used directly when we calculate thermal strains: thermal_strain = alpha * (current_temp – reference_temp) On the other hand, the instantaneous CTE represents the thermal strain generated due to an infinitesimal change in temperature around the current temperature. This quantity needs to be integrated with respect to temperature to calculate the thermal strains. The secant CTE is typically used as input for thermal expansion, but the instantaneous CTE is also available as input in Workbench Engineering Data, in case users may have material data in instantaneous CTE form. Please keep in mind that temperature-depedent secant CTE requires a reference temperature from which thermal strain is calculated. On the other hand, temperature-dependent instantaneous CTE does not require this additional information for the material definition (although a reference temperature is still needed in Mechanical to calculate thermal strains properly). Because of this reason, temperature-dependent CTE is sometimes published in instantaneous form. See Section 3.5 “Thermal Expansion” in the Material Reference of the Mechanical APDL Help for details. Also, refer to Section 2.1.3 “Temperature-Dependent Coefficient of Thermal Expansion” in the Theory Reference of the Mechanical APDL Help for information on temperature-dependent CTE. 