APL

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The finite-strain EoS do not accurately represent the volume variation of most solids under very high compression, under which conditions Thomas-Fermi theory predicts that K'T = 5/3. The APL EoS (e.g. Holzapfel, 2001) has this property.


The pressure is expressed as:


The parameters are:



Different orders of the APL EoS can be defined by using different numbers of  the ck parameters, defined by the value of the limit L in the summation. In EosFit three orders of the APL EoS are supported, as follows:


L

Name

Holzapfel refineable parameters

Traditional refineable parameters

EosFit order

1

AP1

2

2

AP2

3

3

AP3

4



The use of the constant aFG has important consequences - you must use the correct units for V0 and K0T :



For linear EoS the definitions are dubious, but if you have a0 in Angstroms, then Z corresponds to the number of electrons in the volume a03


And, if you fit data, the pressure units of the data must be GPa. If you get this wrong, you will calculate the wrong P-V values.


Important Warning about old .eos files:

The AP3 EoS was added to EosFit in v7.6, release of summer 2021. In order to accommodate the additional parameter for the AP3 EoS there has been some internal changes to the allocation of EoS parameters to variables inside the code. Consequently, there has been a change to the order in which the parameter values appear in the .eos files, and full backwards compatibility between program versions cannot be maintained. Thus: