Module: Elastic

Name

mod_mupro_elastic

Depends on

mod_mupro_size, mod_mupro_fft

Defined variables

None

Defined types

type_mupro_ElasticContext

Strain is NOT in voigt notation

The strain value in this module is NOT in voigt notation. The value of the strain are still as if it’s in tensor notation. The reason we have 6 component is to save memory space.

Defined Types

type_mupro_ElasticContext

Variables

Variable	Type	Dimension	Meaning
eigenstrain	real64, pointer	(6,Rn3,Rn2,Rn1)	Eigenstrain
strain	real64	(6,z,y,x)	Total strain
displacement	real64	(6,z,y,x)	Displacement
stress	real64	(6,z,y,x)	Stress
energy	real64	(6,z,y,x)	Elastic Energy
stiffness	real64	(6,6)	Elastic Stiffness
filmMisfitStrain11	real64	-	Epitaxial misfit strain \(\epsilon_{11}\) in thin film setup
filmMisfitStrain22	real64	-	Epitaxial misfit strain \(\epsilon_{22}\) in thin film setup
filmMisfitStrain12	real64	-	Epitaxial misfit strain \(\epsilon_{12}\) in thin film setup
filmTopAppliedStress33	real64	-	Applied stress \(\sigma_{33}\) on film surface in thin film setup
filmTopAppliedStress23	real64	-	Applied stress \(\sigma_{23}\) on film surface in thin film setup
filmTopAppliedStress13	real64	-	Applied stress \(\sigma_{13}\) on film surface in thin film setup
bulkAppliedStrain	real64	(6)	Bulk strain constraints
bulkAppliedStress	real64	(6)	Bulk stress constraints
BC	int32	-	choice of bulk constraint, 1 for strain, 2 for stress

Stiffness is in voigt notation

For convenience, the stiffness is expressed in voigt notation. The value of stiffness components in voigt notation are the same as their tensor counterparts, there is no multiplier between the conversion.

\[\begin{split} & \begin{pmatrix} C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16}\\ - & C_{22} & C_{23} & C_{24} & C_{25} & C_{26}\\ - & - & C_{33} & C_{34} & C_{35} & C_{36}\\ - & - & - & C_{44} & C_{45} & C_{46}\\ - & - & - & - & C_{55} & C_{56}\\ - & - & - & - & - & C_{66} \end{pmatrix} = \\ & \begin{pmatrix} C_{1111} & C_{1122} & C_{1133} & C_{1123} & C_{1113} & C_{1112}\\ - & C_{2222} & C_{2233} & C_{2223} & C_{2213} & C_{2212}\\ - & - & C_{3333} & C_{3323} & C_{3313} & C_{3312}\\ - & - & - & C_{2323} & C_{2313} & C_{2312}\\ - & - & - & - & C_{1313} & C_{1312}\\ - & - & - & - & - & C_{1212} \end{pmatrix} \end{split}\]

Procedures

setup

Link the user defined strain, stress, displacement, etc. arrays to the corresponding array used in the library. Then, perform some necessary setup before actually solve the equation.

call elasticContext%setup()

Important

setup must be called before the elastic solve subroutines.

solve

Solve the mechanical equilibrium equation, get the strain, stress, and displacement distribution from the eigenstrain distribution.

call elasticContext%solve()